Modules

441 results

Elective Modules441

3D Scanning & Motion CaptureNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn methods for 3D capture and motion capture with a focus on RGB-D sensors and algorithmic fundamentals. In the end you can capture data with consumer RGB-D scanners, understand rigid and non-rigid 3D reconstructions, pose and face tracking, as well as suitable optimization methods, and you can practically implement selected approaches.6 ECTSruns this semesterIN2354Actuarial Risk TheoryNo ratings for this module yet.Mathematical ModulesYou will learn fundamental models and methods of actuarial risk analysis. The focus is on Poisson and compound-Poisson processes, collective claims model, Renewal theory, and Ruin theory for light and heavy claim distributions; in the end you will be able to apply these concepts and make basic statements about ruin probabilities.5 ECTSruns this semesterMA3442Advanced Deep Learning for Computer Vision: Visual ComputingNo ratings for this module yet.C Mathematical Theories in other DisciplinesThe module conveys current deep-learning methods for computer vision. You will learn both theoretical foundations of modern neural architectures and practical methods such as generative models (GANs, diffusion models, Large Reconstruction Models) and modern 3D representations (e.g., Neural Radiance Fields, 3D Gaussian Splatting). In the end you will be able to apply, evaluate, and implement state-of-the-art methods in project work.8 ECTSruns this semesterIN2390Advanced Deep Learning for RoboticsNo ratings for this module yet.C Mathematical Theories in other DisciplinesIn this module you deepen advanced deep learning methods with a focus on robotic applications and deep reinforcement learning. You learn both theoretical foundations of modern network architectures and probabilistic methods as well as their practical implementation in simulations and projects for robotics tasks.8 ECTSruns this semesterCIT433027Aircraft PerformanceNo ratings for this module yet.C Mathematical Theories in other DisciplinesIn this module you will learn the fundamentals of flight performance calculations and the underlying flight dynamics. Starting from a unified nomenclature, nonlinear equations of motion are derived and from them stationary flight states as well as performance quantities (e.g., minimum glide angle, maximum range) are computed. At the end you can apply typical flight performance calculations as used in the preliminary aircraft design.5 ECTSruns this semesterMW0832
436 more in Elective ModulesAlgebra 2No ratings for this module yet.Mathematical ModulesYou will learn fundamental concepts of commutative algebra (rings, ideals, prime ideals, modules) as well as important tools such as localization, embeddings, and tensor products. You will also gain insight into affine algebraic varieties and questions on finiteness conditions and dimension theory. In the end you will be able to apply the learned theorems to rings, in particular finitely generated algebras over a field, and transfer the results to the corresponding affine varieties.9 ECTSruns this semesterMA5120Algebraic TopologyNo ratings for this module yet.Mathematical ModulesYou will learn fundamental algebraic invariants of topological spaces and how to apply them. The focus is on singular homology and cohomology as well as their computational methods and applications (e.g. Poincaré duality for manifolds). In the end you can compute these theories on concrete examples and solve typical problems with them.9 ECTSruns this semesterCIT413039Allgemeine Relativitätstheorie und KosmologieNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn the fundamentals of general relativity and its application in astrophysics and cosmology. You understand how spacetime curvature generates gravity, you will become familiar with the Schwarzschild solution and black holes, you will engage with gravitational waves and the basics of modern cosmology.10 ECTSruns this semesterPH2043Angewandte CFDNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou receive a practice-oriented introduction to numerical fluid dynamics (CFD). You will learn modeling of turbulent flows, numerical methods for solving the Navier–Stokes equations, boundary conditions, grid generation, as well as visualization and evaluation of simulation results and you will apply this practically with ANSYS CFX/ICEM.5 ECTSruns this semesterMW1628Angewandte Multi-Messenger-Astronomie 1No ratings for this module yet.C Mathematical Theories in other DisciplinesIn this module you will learn fundamentals and current topics of multi-messenger astronomy, focusing on high-energy processes and measurements of neutrinos, gamma rays and cosmic rays (MeV–EeV). By the end you will be able to contextualize relevant scientific results and apply basic statistical and programming techniques for data analysis in Python.5 ECTSruns this semesterPH2281Applied Statistics and EconometricsNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn fundamental methods of applied econometrics and statistics and how to apply them to real economic data sets. In the end you can describe data, select appropriate models, apply estimation methods, and test and economically interpret results (cross-section, time series, panel).5 ECTSruns this semesterWZ1705Approximate Dynamic Programming and Reinforcement LearningNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn methods of Approximate Dynamic Programming (ADP) and Reinforcement Learning (RL) to solve sequential decision problems. In the end you will be able to describe fundamental models and algorithms, follow derivations, and implement simple ADP/RL methods and apply them to simple tasks (e.g., robotic).6 ECTSruns this semesterEI7649Asset ManagementNo ratings for this module yet.C Mathematical Theories in other DisciplinesIn this module you will learn the theoretical foundations of asset management as well as practical applications to solve typical tasks (e.g., portfolio optimization). By the end you will be able to apply risk and utility concepts, optimize portfolios under different constraints, use basic asset-pricing models, and measure portfolio performance.6 ECTSruns this semesterWI000231Astroteilchenphysik 1No ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn the connections between cosmology and particle physics: fundamentals of the Standard Model and cosmology, important cosmological observations, and how elementary particles influence the evolution and geometry of the universe. In the end you will be able to explain observations such as the cosmic microwave background and primordial nucleosynthesis, and discuss the role of dark matter as well as possible detection methods.5 ECTSruns this semesterPH2073Ausgewählte Themen aus dem Bereich Formale Methoden und ihre AnwendungenNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou engage with current topics from the area of Formal Methods and their application. In the end you know the research and development state in selected subfields and you can deal with current research projects and results.5 ECTSruns this semesterIN3350Automata and Formal LanguagesNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn how different classes of automata (finite, deterministic, nondeterministic, Büchi automata) are used as data structures for the representation and manipulation of (also infinite) sets and relations. You practice building and composing automata, automatic operations (e.g., boolean operations, joins) and the connection between automata and logic as well as their application in pattern matching, program verification and in problems such as Diophantine equations.8 ECTSruns this semesterIN2041AV Artificial IntelligenceNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will gain a broad overview of methods in Artificial Intelligence and Machine Learning with a view to applications in vehicle engineering. In the end you will be able to classify appropriate ML and AI methods, implement them in code, evaluate and judge them, and apply fundamental neural networks and their variants to concrete tasks.5 ECTSruns this semesterED150049AV Development and SimulationNo ratings for this module yet.C Mathematical Theories in other DisciplinesThis module covers the development and simulation of systems for automated driving. You will learn methods and tools used in the development and simulation of autonomous driving functions, and you will be able to apply simulation approaches for validating such systems.5 ECTSruns this semesterED150048Banking and Risk ManagementNo ratings for this module yet.C Mathematical Theories in other DisciplinesThe module conveys the fundamentals of banking business, regulation and risk measurement, as well as basic knowledge on financial derivatives. You will learn how banks operate, why bank regulation and central banks are important, how futures and options are valued, and how different risk measures work and can be categorized.3 ECTSruns this semesterWI000092Bildverarbeitung in der PhysikNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn basic and advanced techniques of image processing and image reconstruction with a focus on applications in physics. In the end you will be able to apply filter- and Fourier-based methods, interpolation, segmentation, noise and resolution analysis, tomographic reconstruction as well as fundamental concepts of wave propagation and phase-contrast imaging, and assess their respective strengths and limitations.5 ECTSruns this semesterPH2181Biomedizinische Physik 1No ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn the physical foundations of the most important imaging procedures in clinics and research. After the module you will be able to explain the generation of images in CT, MRI, PET/SPECT, X-ray and ultrasound, assess their advantages and disadvantages, and name the basic principles of detection and measurement.5 ECTSruns this semesterPH2001Biomedizinische Physik 2No ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn the physical foundations of important biomedical applications in clinics and research, including radiation therapy, laser applications, and various microscopy techniques. In the end you will be able to describe the operating principles, advantages and disadvantages of these procedures and explain basic aspects of radiation planning and radiation sources.5 ECTSruns this semesterPH2002BioMEMS and MicrofluidicsNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn fundamental concepts and applications of microfluidic and microelectromechanical systems (BioMEMS) for biological questions. The module combines electrodynamics, surface science and fluid mechanics, shows principles of lab-on-a-chip systems and covers cell-based microfluidic systems as well as chip-based neuroscience applications. In the end you will be able to explain physical mechanisms and assess their application in BioMEMS and microfluidics.5 ECTSruns this semesterEI7473Biophysik der Zelle 1No ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn physical principles that determine the behavior of cells and their building blocks, e.g. fluid mechanics at low Reynolds numbers, diffusion, gene regulation, reaction kinetics, conformational dynamics, enzymatic catalysis, polymer elasticity and membrane physics. By the end you can explain dynamic and steady-state properties of macromolecular state changes and bimolecular reactions and classify terms such as entropy elasticity, dissociation constant, transition state and transition rate, as well as describe enzymatic catalysis.5 ECTSruns this semesterPH2013Business Analytics and Machine LearningNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn methods of statistical analysis and machine learning for classification, numerical prediction and clustering. After the module you can explain the assumptions and workings of common procedures and analyze datasets with R as well as interpret results.5 ECTSruns this semesterIN2028Channel CodingNo ratings for this module yet.C Mathematical Theories in other DisciplinesIn this module you will learn modern principles of channel coding. You will understand mathematical foundations (e.g., finite fields) and various code classes (linear block codes, Reed–Solomon, BCH, convolutional codes, Reed–Muller, concatenated codes) as well as decoding algorithms, so that you can select, adapt and assess the error-correcting capability of coding schemes.5 ECTSruns this semesterEI70320Cluster und Nanopartikel: Grundlagen und Anwendungen in der Katalyse, KlausurNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn the physical and chemical foundations of nanoscale matter at the transition from atom to solid as well as their applications in catalysis. In the end you will be able to explain manufacturing routes, size-dependent properties and experimental characterization of clusters and nanoparticles and apply this knowledge to catalytic questions.5 ECTSruns this semesterCH3067Computational AcousticsNo ratings for this module yet.C Mathematical Theories in other DisciplinesIn this module you will learn numerical methods for solving acoustic problems, in particular the Finite Element Method (FEM) and the Boundary Element Method (BEM). In the end you will be able to explain the fundamental methodology, assess typical problems in outdoor space and fluid-structure interactions, and implement a simple FEM- or BEM-program in MATLAB.5 ECTSruns this semesterMW2323Computational Design and Fabrication 1No ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn the fundamentals of geometric modeling, algorithmic design and their application to 3D form generation, simulation, structural design and digital fabrication. In the end you will be able to develop simple algorithm-based design solutions, couple with common CAD tools, and apply knowledge on form-finding, geometry processing as well as fabrication-aware design.6 ECTSruns this semesterED120115Computational Methods for Nanoelectronics: Semiclassical ModelsNo ratings for this module yet.C Mathematical Theories in other DisciplinesIn this module you will gain an overview of the most important semi-classical numerical methods in nanoelectronics and their application to modern semiconductor devices. You will learn both basic concepts of organic and inorganic semiconductor materials and practical simulation approaches (drift-diffusion, Boltzmann transport, various Monte-Carlo methods) and apply them. In the end you will be able to select appropriate semi-classical methods and numerically solve simple charge-transport problems.5 ECTSruns this semesterEI71094Computational Methods for Single-cell BiologyNo ratings for this module yet.Mathematical ModulesIn this module you will learn modern computational methods for the analysis of single-cell data and apply them practically. After lectures on important topics in single-cell biology and data analysis, you will work eight weeks in an ICB laboratory on a concrete project to gain practical experience.6 ECTSruns this semesterMA5617Computational NeuroscienceNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn concepts and implementations of central models and methods of Computational Neuroscience in Python. At the end you will be able to implement single-neuron and network models, analyze their properties, and transfer models to new questions, as well as apply fundamental methods of Machine Learning and information analysis.5 ECTSruns this semesterLS20056Computational Neuroscience: Eine Ringvorlesung von Modellen bis zu AnwendungenNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will obtain an interdisciplinary overview of fundamentals and models of Computational Neuroscience as well as their applications, for example in neuroprostheses. In the end you will know anatomical and physiological basics, methods for modeling neuronal activity, and how such models can be used for technical applications.3 ECTSruns this semesterEI7646Computational Plasma PhysicsNo ratings for this module yet.Mathematical ModulesYou will learn numerical methods for solving and applying models from plasma physics. The focus is on the discretization of partial differential equations (e.g., Poisson, conservation and kinetic equations) and the implementation of these procedures in Python. In the end you will be able to derive an appropriate numerical method for a concrete model, implement it, and test and verify the code.5 ECTSruns this semesterMA4304Computer Vision III: Detektion, Segmentierung und TrackingNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn modern methods for object recognition, segmentation and tracking in images and videos. In the end you will understand the underlying deep-learning concepts and be able to work on real computer-vision problems with state-of-the-art models in PyTorch.6 ECTSruns this semesterIN2375Computer Vision und Maschinelles Lernen 1No ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn the fundamentals of image acquisition, projective geometry and image processing as well as basic methods of machine learning. In the end you will be able to geometrically and in the frequency/spatial domain analyze images, implement simple CV operations and design and evaluate classical methods for classification and regression.5 ECTSruns this semesterED110001Data Analytics in ApplicationsNo ratings for this module yet.C Mathematical Theories in other DisciplinesIn this module you work on Data-Analytics use cases from problem formulation to implementation. You will learn methodology (CRISP-DM), data preparation, modeling (e.g., classification, clustering, regression), evaluation and deployment, and you will practically apply what you have learned in a real team project with Python.6 ECTSruns this semesterMGT001307Data Mining und Knowledge DiscoveryNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn methods of Data Mining and Knowledge Discovery: from data sources and quality through preprocessing, visualization and feature selection to correlation, regression, forecasting, classification and clustering. In the end you will be able to select appropriate methods, apply them and critically evaluate them, as well as deepen the foundations independently.3 ECTSruns this semesterIN2030Differential GeometryNo ratings for this module yet.Mathematical ModulesYou learn the basics of smooth manifolds, bundles (tangent, vector, and principal bundles) as well as Riemannian metrics, curvature tensors and geodesics. In addition, symmetric spaces and Lie groups are treated. In the end you can transfer metric properties of Euclidean space to 'curved' spaces and derive properties of such spaces using analytical methods.9 ECTSruns this semesterMA3205Digital Signal ProcessingNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn advanced concepts of digital signal processing for single- and multidimensional signals and how to apply them. Topics include 2D/multidimensional signals and systems, filter design, linear block transforms, wavelets/filter banks, as well as inverse problems and applications in media processing. In the end you can switch between time/space and frequency representations, select suitable representations, and solve problems both analytically and with Matlab.5 ECTSruns this semesterEI70220Discrete Differential GeometryNo ratings for this module yet.Mathematical ModulesYou learn the fundamentals of the differential geometry of curves and surfaces in a discrete framework. The focus is on structurally analogous concepts (e.g. discrete tangents, normals, curvature) and not on numerical approximation. In the end you will be able to treat discrete analogues of smooth curves and surfaces as well as their invariants in a structural and analytical way.6 ECTSruns this semesterMA5205Discrete OptimizationNo ratings for this module yet.Mathematical ModulesYou will learn central concepts and algorithms of linear integer optimization and combinatorial optimization. In the module you will analyze mathematical structures that allow efficient solution methods, and you will be able to model real problems as discrete optimization problems and identify special cases that are efficiently solvable.9 ECTSruns this semesterCIT413041Efficient Algorithms and Data StructuresNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn the fundamentals of analyzing algorithms as well as central data structures and fundamental algorithmic problems. The focus is on runtime and space analysis, various search trees, hashing methods, priority queues, union-find structures, as well as maxflow/mincut and matching algorithms. In the end you will be able to analyze algorithms, assess the efficiency of data structures, and design new solutions for problems.8 ECTSruns this semesterIN2003Einführung in die DatenanalyseNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn fundamental methods for analyzing experimental data: concepts of probability, distributions, error propagation, parameter estimation (Least Squares and Maximum Likelihood) and significance estimation. In the end you will be able to apply these methods to suitable data and estimate uncertainties as well as the significance of signals.5 ECTSruns this semesterPH2099Einführung in Quantum ComputingNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn the mathematical foundations of Quantum Computing as well as the basic concepts of quantum mechanics and quantum circuits. In the end you will be able to analyze simple quantum algorithms, design and assess quantum circuits for fundamental tasks, and understand how quantum computers may be used in the future.5 ECTSruns this semesterIN2381Eisenbahnverkehrsplanung und -betriebNo ratings for this module yet.C Mathematical Theories in other DisciplinesThe module covers planning and operation of railway systems: from stakeholders and planning processes to infrastructure, vehicle, and timetable aspects, up to capacity, delay modeling, and train service management. By the end you will be able to recognize planning problems, assess them methodically, and apply the discussed procedures to small, practical tasks.6 ECTSruns this semesterED150037Energy Markets INo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will gain a comprehensive overview of energy markets and industries across all commodities. You will learn value chains from primary energy supply to energy demand, central economic concepts, price formation, merit orders and organized energy trading. In the end you will be able to economically analyze energy-related problems and develop solution approaches using learned mathematical techniques.6 ECTSruns this semesterWI000946Environmental Sensing and ModelingNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn measurement methods and instrumentation to capture atmospheric and solar parameters as well as to apply statistical evaluation and modeling procedures. In the end you will be able to evaluate different sensor principles, analyze datasets from real atmospheric measurements, and use modeling approaches for interpretation and inversion of measurement data.6 ECTSruns this semesterEI7465Financial Mathematics 1No ratings for this module yet.Mathematical ModulesYou will learn the fundamentals of mathematical finance in discrete time: pricing and valuation of derivatives in one- and multi-period models, concepts of arbitrage and completeness, as well as basics of portfolio optimization. By the end you will be able to understand price models and implement them numerically, and analyze and optimize portfolios according to risk-return criteria.9 ECTSruns this semesterMA3407Finite Elemente Methode für Fluid-Struktur Interaktion mittels Open-Source SoftwareNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn how finite element methods are used for the simulation of fluid–structure interaction (FSI). The module covers the fundamentals of coupling fluid and structural mechanics, numerical discretization and solution strategies, and practical implementation with open-source software (Kratos Multiphysics). In the end you will be able to model FSI problems, solve them numerically, and evaluate various algorithmic or software-based approaches.3 ECTSruns this semesterBGU32022Flight GuidanceNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn the technical fundamentals of flight guidance in civil aviation: structure of the cockpit, the functioning of onboard instruments as well as ground facilities and air traffic control technology. In the end you will be able to describe the measurement and navigation systems in use, assess their reliability and accuracy, and evaluate the operational aspects of these facilities.5 ECTSruns this semesterMW2237Food EconomicsNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn economic questions around food markets and value chains. The module covers market trends, characteristics of supply and demand, food safety, labeling, consumption, nutrition and policy measures and makes you familiar with the economic models used to analyze these topics.6 ECTSruns this semesterWI000948Formale Methoden für Cyber-Physical SystemsNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn formal methods for verification, control, observation and identification of cyber-physical systems (e.g., autonomous vehicles, robots, smart grids). In the end you can verify and practically apply systems using set representations, reachability analysis and correct-by-construction methods.5 ECTSruns this semesterIN2383Fortgeschrittene elektronische Struktur, KlausurNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn concepts and technologies of electronic structure theory, starting with potential energy surfaces up to methods such as Hartree–Fock, correlated wave functions and density functional theory. In the end you will be able to qualitatively explain the methods, assess their applications and limitations, and solve simple electronic structure problems independently.5 ECTSruns this semesterCH3333Fortgeschrittene HalbleiterphysikNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn advanced concepts of semiconductor physics and can, at the end, computationally and conceptually address central electronic properties of semiconductors as well as transport and interface phenomena. The module provides an understanding of band structure, effective masses, Fermi level calculation, and currents at metal-semiconductor interfaces.10 ECTSruns this semesterPH2155Fortgeschrittene statistische PhysikNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou deal with phase transitions, critical phenomena and their theoretical descriptions (Landau-Ginzburg, renormalization group). You also learn the basics of irreversible and non-equilibrium processes as well as percolation theory. In the end you will be able to interpret critical exponents and apply renormalization group methods to concrete models.10 ECTSruns this semesterNAT3002Foundations and Application of Generative AINo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn the fundamentals and practical applications of generative AI, including modern models such as transformer architectures, Large Language Models, and Stable Diffusion. In the end you will be able to apply prompt engineering, load open-source models and fine-tune them, as well as assess opportunities, risks, and security aspects of generative AI.6 ECTSruns this semesterCITHN2014Foundations of Modern RoboticsNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn how to mathematically model robotic systems, simulate their motion, and apply modern planning and control algorithms. In the end you will be able to compute forward/inverse kinematics and dynamics, use advanced planning and control methods, and apply common robotics software.5 ECTSruns this semesterCIT433028Fundamentals of Artificial IntelligenceNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn the foundations of artificial intelligence: from search procedures and constraint-satisfaction to logic and probabilistic models to decision making, learning and an introduction to robotics. In the end you will be able to design simple AI systems and apply basic methods from search, logic, probability and decision theory.6 ECTSruns this semesterIN2406Fundamentals of Energy ModellingNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn how expansion and modernization planning of power plants as well as load-flow problems in modern energy systems are formulated and solved as mathematical optimization problems. In the end you can formulate (non-)linear and mixed-integer models and apply and assess suitable solution approaches for applications such as optimal load flow or power plant deployment planning.5 ECTSruns this semesterED180003Fundamentals of Mathematical StatisticsNo ratings for this module yet.Mathematical ModulesYou will learn the fundamental principles and methods of statistical inference, including likelihood approaches, Bayesian methods and minimax estimation. You will deal with asymptotic theory for large samples and apply it in particular to the study and application of maximum-likelihood techniques.9 ECTSruns this semesterMA5441FunktionalanalysisNo ratings for this module yet.Mathematical ModulesYou will learn the basics of functional analysis in Banach and Hilbert spaces. In the end you will be able to analyze linear functionals and bounded as well as compact self-adjoint operators, understand duality, and apply concepts such as weak and weak* convergence.9 ECTSruns this semesterMA3001Games on GraphsNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn the theory of games on finite graphs. Building on reachability games, both qualitative and quantitative variants are treated, and in the end you will be able to apply the fundamental solution methods and solve smaller game instances on your own.5 ECTSruns this semesterIN2296Grundlegende Algorithmen (CSE)No ratings for this module yet.C Mathematical Theories in other DisciplinesYou receive an introduction to fundamental sequential and simple parallel algorithms as well as the methods for their analysis. By the end you will be able to apply typical algorithms (sorting, searching, graph algorithms, some parallel arithmetic procedures), analyze their complexity and parallelism, and formally justify correctness and performance statements.5 ECTSruns this semesterIN2157Höhere AlgorithmikNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn fundamental techniques for the development and analysis of efficient algorithms (e.g., Divide-and-Conquer, dynamic programming, randomization, Greedy methods, amortized analysis) and apply them to central problems such as sorting, graph problems, string and sequence algorithms, as well as data structures. In the end you will be able to understand, analyze, and use classical algorithmic procedures to solve fundamental tasks.8 ECTSruns this semesterCIT323004Information TheoryNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn the fundamental concepts of information theory (e.g., entropy, mutual information, divergence) and how to apply them to the analysis of data compression and channel transmission. In the end you can explain the central quantities and their properties as well as use information measures to evaluate coding and transmission systems.5 ECTSruns this semesterEI70350Insurance Mathematics 1No ratings for this module yet.Mathematical ModulesYou learn the fundamental stochastic methods of damage/non-life insurance. The focus areas are tariff calculation, capital allocation, individual and collective model, claims provisions, as well as reinsurance. In the end you will be able to understand and apply the most important models for premium calculation, reserving and risk sharing.9 ECTSruns this semesterMA3405Introduction to Deep LearningNo ratings for this module yet.C Mathematical Theories in other DisciplinesIn this module you will learn the fundamentals and current methods of Deep Learning, with a special focus on neural networks and Convolutional Neural Networks. You understand theory (e.g. backpropagation, SGD, regularization) and acquire practical experience in training and optimizing network architectures, so you can solve simple applications such as digit recognition or image classification.6 ECTSruns this semesterIN2346Introduction to Deep Reinforcement LearningNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn the theory and fundamentals of Deep Reinforcement Learning (DRL) as well as relevant deep-learning and reinforcement-learning concepts. By the end you will be able to model problems as Markov Decision Processes, understand and apply DRL algorithms, and assess their advantages and disadvantages.6 ECTSruns this semesterMGT001299Kausale Inferenz im Klima- und ErdsystemNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn how to derive causal relationships from data in the climate and earth system, which methods exist for this purpose and what their limits are. In the end you will be able to compare different correlation- and causality-based approaches, assess their assumptions and apply methods to questions of the earth system.3 ECTSruns this semesterED110089Kipppunkte in der Dynamik des ErdsystemsNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn how nonlinear and abrupt behavior in the Earth system is described and analyzed. You will receive methodological foundations for mathematical modeling of nonlinear dynamics and will become familiar with typical multistable components of the Earth system as well as their interactions.3 ECTSruns this semesterED110066Künstliche Intelligenz in der MedizinNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn the fundamentals and current methods of Artificial Intelligence in the medical context, from ML for medical imaging through NLP for clinical data to data protection, interpretability and ethical aspects. In the end you can classify the most important topics, apply them to your own deep-learning projects and develop strategies for evaluation and implementation in clinical practice.5 ECTSruns this semesterIN2403Large DeviationsNo ratings for this module yet.Mathematical ModulesYou will learn the theory of large deviations, which describes how unlikely events occur in probability models and how quickly their probabilities decay. In the end you will be able to apply fundamental techniques of large-deviation theory and understand applications such as for sums of random variables and empirical distributions.5 ECTSruns this semesterMA5417Logistics and Operations StrategyNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn how logistics and operational decisions are strategically anchored in the corporate and competitive environment. You will use models and optimization methods to analyze procurement, location, capacity, and network decisions, and you will derive robust strategies for different industries.6 ECTSruns this semesterWI000976Machine LearningNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn the probabilistic foundations of machine learning and central learning algorithms — from simple neighborhood and clustering methods to linear models and support vector machines up to neural networks and the EM method. By the end you will be able to select, describe and derive suitable algorithms for given problems.8 ECTSruns this semesterIN2064Machine Learning for 3D GeometryNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn theoretical foundations and modern machine‑learning methods for 3D geometric data. The module covers representations of shapes and scenes as well as deep‑learning architectures for discriminative and generative tasks such as classification, segmentation, reconstruction and synthesis. In the end you will be able to understand and practically apply common approaches to point clouds, volumetric data, multi‑view inputs and graphs.6 ECTSruns this semesterIN2392Maschinelles Lernen im EnergiemanagementNo ratings for this module yet.C Mathematical Theories in other DisciplinesThe module conveys data-driven prediction and control methods for next-generation energy management systems. You will learn how machine learning techniques are used for load and generation forecasting, system identification, and data-driven control (e.g., model predictive control, Deep Reinforcement Learning) to improve efficiency and the use of renewable energies.5 ECTSruns this semesterED180026Maschinelles Lernen in der ErdsystemmodellierungNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn data-driven and process-based approaches to modeling the Earth system and its components. In the end you will be able to name classical process-based models and various machine-learning methods for describing Earth system dynamics, apply interpretable AI methods, and critically evaluate approaches that combine process- and data-driven models.3 ECTSruns this semesterED110065Mathematical EcologyNo ratings for this module yet.Mathematical ModulesYou will learn to apply mathematical methods and models to ecological questions. In the end you can describe, analyze, and ecologically interpret populations, their interactions, spatial spread, and structure with suitable mathematical models.9 ECTSruns this semesterMA5602Mathematical Models in BiologyNo ratings for this module yet.Mathematical ModulesYou learn how dynamic and stochastic models are constructed and applied in biology. The module covers, among other things, linear compartment models, Markov chains, birth–death and branching processes, as well as age- and space-structured populations. In the end you will be able to compare different modeling approaches and choose the appropriate model level for a biological system.9 ECTSruns this semesterMA3601Mathematik der Klima- und ErdsystemwissenschaftenNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn mathematical methods for the analysis and modeling of nonlinear processes in the climate and Earth system. In the end you will be able to explain the basics of energy balance modeling, nonlinear and stochastic dynamics as well as fundamental equations of fluid mechanics, and mathematically analyze time series from climate and Earth system processes.9 ECTSruns this semesterED110088Mathematische KontinuumsmechanikNo ratings for this module yet.Mathematical ModulesYou learn the fundamental conservation laws of continuum mechanics (mass, momentum, energy) as well as the mathematical methods with which these laws are formulated and applied. After the module you can apply these methods to specific models such as fluid dynamics, chemical/biological reactions, self-gravitation, or liquid crystals, and understand elasticity theory as well as distributions.9 ECTSruns this semesterMA5019Mathematische Methoden zur Unsicherheitsquantifizierung in der HydrologieNo ratings for this module yet.Mathematical ModulesYou will learn methods for quantifying uncertainties in hydrological questions and apply them. In the end you will be able to select suitable UQ methods and apply them to simple to complex hydrological models as well as present the results interdisciplinary.9 ECTSruns this semesterBGU54027Medizintechnik 1 - ein organsystembasierter AnsatzNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn the fundamentals of therapeutic and diagnostic medical technology based on selected organ systems (skin, sense organs especially the eye, cardiovascular system, musculoskeletal and movement system). You will understand the relevant anatomical-physiological fundamentals, typical disease patterns and common medical-technical diagnostic and therapeutic approaches and you will be able to apply this knowledge to medical-technical questions.5 ECTSruns this semesterMW0056Moderne RöntgenphysikNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will get to know the fundamentals of modern X-ray physics with a focus on imaging methods, both for synchrotron radiation and for modern laboratory sources (e.g. compact synchrotron MuCLS). In the end you can assess sources, interactions with matter, detectors and imaging methods and name suitable parameters for experiments (source size, coherence, energy resolution, detector choice).5 ECTSruns this semesterPH2182Multi-criteria Optimization and Decision Analysis for Embedded Systems DesignNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn how to consider multiple criteria simultaneously in the design of embedded systems — from modeling over multi-dimensional optimization to multi-criteria decision procedures. In the end you will be able to analyze problems, select appropriate optimization and decision methods, and apply the results in practice.5 ECTSruns this semesterEI71095Multilinear AlgebraNo ratings for this module yet.Mathematical ModulesYou will learn concepts and tools of multilinear algebra and apply them, in particular in connection with matrix analysis and matrix algebra. In the end you will be able to understand tensor products, Kronecker operations and related structures and use them in mathematical contexts.5 ECTSruns this semesterCIT413063Natural Language ProcessingNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will receive a solid introduction to modern Natural Language Processing (NLP) methods. In the end you will know central concepts, algorithms and models from tokenizing, through parsing, embeddings and NER, to modern neural approaches and you will be able to read, analyze and contextualize scientific publications in the discipline for your own projects or theses.6 ECTSruns this semesterIN2361Network SecurityNo ratings for this module yet.C Mathematical Theories in other DisciplinesIn this module you will receive an introduction to network security: threat scenarios, protection requirements and the integration of security measures into network architectures and protocols. You will learn cryptographic fundamentals as well as security protocols and will be able to classify and apply techniques such as PKI, Kerberos, IPsec, TLS as well as firewall and intrusion detection concepts.5 ECTSruns this semesterIN2101NeuroprostheticsNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will obtain the theoretical foundations of neuroprosthetics and implement them numerically in a accompanying computer exercise. The focus is on electrical stimulation of neurons using the example of cochlear implants; the goal is to develop and simulate a virtual middle ear implant model including the response of the auditory nerve.5 ECTSruns this semesterEI70270Nichtlineare Dynamik und komplexe Systeme 1No ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn the fundamental concepts of nonlinear dynamical systems: how cooperative phenomena such as bistability, self-sustained oscillations, and deterministic chaos arise from nonlinearities. In the end you will be able to perform phase-space analyses, describe stability and bifurcations, and characterize simple chaotic attractors with suitable measures.5 ECTSruns this semesterPH2027Nichtlineare OptimierungNo ratings for this module yet.Mathematical ModulesYou engage with theory and numerical methods of nonlinear optimization. You will learn advanced methods for unconstrained and, in particular, constrained optimization problems (e.g., SQP, barrier and interior-point methods) and you will be able to assess and apply convergence properties of such methods in the end.5 ECTSruns this semesterMA3503Nonconvex Global OptimizationNo ratings for this module yet.Mathematical ModulesYou will learn methods of global optimization for nonconvex and possibly nonsmooth objective functions and how to apply them. Beginning with (stochastic) gradient methods and simulated annealing, you walk toward multi‑particle methods such as Particle Swarm Optimization (PSO) and Consensus‑Based Optimization (CBO) and understand their global convergence properties.6 ECTSruns this semesterCIT4130019Numerik der DifferentialgleichungenNo ratings for this module yet.Mathematical ModulesYou will learn numerical methods for solving ordinary and simple partial differential equations. Topics include stiff and non-stiff initial value problems, fundamentals of boundary value problems, and methods such as finite differences, finite elements, and spectral methods (focus on 1D, elliptic problems partly in 2D). By the end you will be able to understand, assess and apply basic algorithms on the computer as well as estimate discretization errors.9 ECTSruns this semesterMA3301Numerische Algorithmen im HochleistungsrechnenNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn selected numerical algorithms for high-performance computing (HPC), e.g. solvers for partial differential equations, methods of numerical linear algebra, particle-based simulations and spectral methods. You can assess their range of applications, analyze fundamental performance characteristics and evaluate and use the parallelizability and scalability of the algorithms.8 ECTSruns this semesterIN2398Optimal Control and Decision MakingNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn methods of optimal control, optimization, model predictive control and learning-based controller design (including reinforcement learning). In the end you can formulate problems of optimal control, select numerical solution procedures and implement controllers as well as evaluate modern learning-based approaches.5 ECTSruns this semesterEI70140Optimierung und ModellanalyseNo ratings for this module yet.C Mathematical Theories in other DisciplinesIn this module you will learn fundamental concepts and methods of optimization, model analysis and numerical solution techniques. In the end you will be able to translate technical questions into mathematical optimization tasks and select appropriate solution approaches as well as assess the advantages and disadvantages of the procedures.5 ECTSruns this semesterMW2249Parallel ComputingNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn the basics and practices of parallel computing on multi-core CPUs, GPUs, and in distributed systems. In the end you will be able to assess performance bottlenecks, design and implement parallel algorithms (OpenMP, CUDA/HIP/SYCL, MPI/PGAS) and analyse performance using models such as Roofline.5 ECTSruns this semesterCITHN2003Particle-Simulation Methods for Fluid DynamicsNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn particle-based simulation methods for flow problems – from atomistic methods through kinetic models to macroscopic particle solvers. In the end you will understand the fundamentals of the respective models, their algorithms, and know when which method is applicable.3 ECTSruns this semesterMW0696Plasmaphysik 1No ratings for this module yet.C Mathematical Theories in other DisciplinesYou receive an introduction to plasma physics: fundamentals, typical models and applications in nature and technology. At the end you will be able to describe basic plasma phenomena, explain the behavior of charged particles and plasmas in magnetic fields, as well as analyze stability, instabilities and Alfvén waves and explain simple plasma diagnostics and applications.5 ECTSruns this semesterPH2035Praktikum Energy InformaticsNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou work on practical tasks related to data-driven forecasting and optimization methods for energy management systems. In the end you will be able to use Python and Jupyter Notebooks for the analysis of energy-relevant datasets as well as apply ML and optimization algorithms in selected use cases.5 ECTSruns this semesterED180015Principles of EconomicsNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will receive an introduction to the fundamentals of economics, divided into microeconomics and macroeconomics. You will learn how individual behavior of households and firms leads to market supply and demand, which causes and consequences of market failures exist, and what role government interventions play. At the macro level you will learn how to measure economic growth, inflation and unemployment and which instruments of monetary and fiscal policy can influence fluctuations.6 ECTSruns this semesterWI001056_1Probabilistische Techniken und Algorithmen in der DatenanalyseNo ratings for this module yet.Mathematical ModulesYou will learn probabilistic techniques and algorithms used in data analysis for dimensionality reduction and data recovery from incomplete information. In the end, you will understand the basics of random matrices, assess randomized algorithms, and apply and analyze methods such as JL embeddings, compressed sensing, and randomness-based matrix/tensor reconstruction.6 ECTSruns this semesterMA4803Probability TheoryNo ratings for this module yet.Mathematical ModulesYou will learn the measure-theoretic probability theory for sequences of random variables and martingales. By the end you will be able to understand and apply central results such as the law of large numbers, central limit theorems, and fundamental martingale results.9 ECTSruns this semesterMA2409Project ManagementNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn quantitative techniques for planning, controlling and evaluating projects. In the end you can model projects (e.g. WBS, AON/AOA, MPM/CPM), create time and resource plans, assess risks with PERT/Monte-Carlo, and financially and multi-criteria analyze and control projects (e.g. EVA, DTA, AHP).6 ECTSruns this semesterWI000264Projektive Geometrie 1No ratings for this module yet.Mathematical ModulesYou will learn the fundamentals of projective geometry: projective spaces, their transformation groups and algebraic representations of geometric structures. In the end you will be able to apply projective viewpoints to different geometries and understand the role of transformations and algebraic methods in this context.9 ECTSruns this semesterMA3203Quanten-VielteilchenphysikNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn the theoretical foundations of quantum many-body physics, common methods and typical phenomena. In the end, you can apply these methods computationally and explain the phenomena discussed at the level of the presented models.10 ECTSruns this semesterPH2256QuantenfeldtheorieNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn the fundamental concepts and calculation methods of quantum field theory: path integrals, perturbation theory and Feynman diagrams, Green's functions and their connection to scattering cross sections, as well as renormalization and effective field theories. In the end you will be able to perform perturbative calculations including loop corrections, quantize gauge theories and use the renormalization group to improve perturbative computations.10 ECTSruns this semesterPH2041Quantenmechanik 2No ratings for this module yet.C Mathematical Theories in other DisciplinesYou deepen concepts of quantum mechanics beyond the nonrelativistic single-particle description: path integrals, open quantum systems, second quantization, identical particles as well as relativistic single-particle equations (Klein–Gordon, Dirac) and their applications (e.g. hydrogen spectrum). In the end you will be able to apply these formalisms, describe quantized fields and solve simple problems such as the open two-state system or the Dirac equation in a central potential.5 ECTSruns this semesterNAT3001Quantitative Genetics and SelectionNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn the fundamentals of quantitative genetics and their importance for plant breeding. You understand basic concepts of population genetics and learn how variance components, relatedness, heritability, and genotype‑×‑environment interaction can be determined and used to optimize breeding programs.5 ECTSruns this semesterWZ1584Quantum Information TheoryNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn how to mathematically model information transmission and storage with quantum mechanical systems. In the end you will understand the fundamental concepts and proof methods of the Shannon-theoretic description of discrete, memoryless semi-classical and quantum communication scenarios and know the corresponding coding theorems.5 ECTSruns this semesterEI76471Random Graphs and NetworksNo ratings for this module yet.Mathematical ModulesYou will learn models of random graphs and how they describe real networks. The focuses are Erdős–Rényi models, generalized random graphs, the configuration model and preferential-attachment models as well as proof techniques for the number of components, degree distribution and distances.5 ECTSruns this semesterMA5436Robot and Swarm NavigationNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn how cooperative navigation and positioning for swarms of robots work. The module conveys Bayesian estimation methods (including Kalman filters and sequential Monte Carlo/particle filters), radio localization concepts, and methods of estimation theory for the analysis and optimization of swarm navigation. At the end you will be able to design a radio-based swarm navigation system and evaluate its performance.5 ECTSruns this semesterEI71026RoboticsNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn how mechanical systems — in particular robotic manipulators — are translated into mathematical models to describe motion and dynamics. On this basis you derive control parameters (for example for PID controllers) to compensate deviations along predefined trajectories and to regulate position or force.6 ECTSruns this semesterIN2067Rotorcraft Engineering - VorentwurfNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn the preliminary design process for helicopters: from requirements through dimensioning to flight performance and estimation of costs and weight. In the end you can analyze and evaluate a helicopter concept in terms of feasibility, power requirements, and mission suitability.5 ECTSruns this semesterMW1397Scientific Computing INo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn the steps of the scientific computing pipeline in scientific data processing, with a focus on model development and discretization. In the end you will be able to derive and classify simple mathematical models and apply suitable discretization and time integration methods, and assess their accuracy and suitability.5 ECTSruns this semesterIN2005Security in Communications and StorageNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn methods and concepts to achieve security in communication and storage systems. The module covers classical and post-quantum cryptography, error-correcting codes and their application in distributed data storage, as well as Private Information Retrieval; in the end you will be able to understand, evaluate and practically apply these schemes.5 ECTSruns this semesterEI71060Simulation of Quantum DevicesNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn how quantum effects in nanoscale devices are described and how to apply suitable numerical methods to simulate such systems. Topics range from the Schrödinger equation and its numerical treatment to quantum transport simulations. In the end you can formulate physical models and solve them numerically as well as develop simple own simulation codes.5 ECTSruns this semesterEI70760Starke Wechselwirkung in BeschleunigerexperimentenNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn the experimental and theoretical foundations of the strong interaction (QCD) in the context of accelerator experiments. In the end you will understand how hadron production and jets arise in e+e-, ep- and pp/p anti-p scattering, how to apply event shapes and jet algorithms, and how QCD coupling constants and fragmentation models are determined experimentally.5 ECTSruns this semesterPH2254Statistical Foundations of LearningNo ratings for this module yet.Mathematical ModulesYou learn statistical foundations of machine learning theory and mathematical tools for the analysis of learning algorithms. In the end you will be able to evaluate generalization and consistency questions, theoretically analyze algorithms such as k‑NN, SVM and simple neural networks, and contextualize newer developments such as overparameterization and training dynamics.8 ECTSruns this semesterCIT4230004Statistical LearningNo ratings for this module yet.Mathematical ModulesYou learn the basics and advanced methods of supervised and unsupervised statistical learning. In the end you will be able to understand and apply models for regression and classification, use techniques for dimensionality reduction and cluster analysis, and follow probabilistic formulations of learning problems while designing new algorithms.6 ECTSruns this semesterMA4802Stochastic Modeling and OptimizationNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn methods for decision support in stochastic multi-period environments. The module covers both the mathematical theory (e.g. stochastic processes, Markov decision processes, stochastic programming) and their application to practical problems such as inventory management or personnel planning. In the end, you can select suitable procedures, apply them, and assess their advantages and disadvantages.6 ECTSruns this semesterWI000977Symmetrie und Gruppentheorie, KlausurNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn the fundamentals of group theory and its application to symmetry questions in molecules and solids. In the end you will be able to apply group-theoretical tools to simplify and solve problems in chemistry and quantum mechanics and you will know the most important examples from inorganic, organic and solid-state chemistry.5 ECTSruns this semesterCH3337Systems Theory and ModelingNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn how to model, analyze and prepare finite-dimensional dynamic systems for numerical treatment. The focus is on linear time-invariant state-space models, their properties (stability, controllability, observability), discretization for sampling control loops, and projection methods for model order reduction.5 ECTSruns this semesterLRG0113Theoretische FestkörperphysikNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou receive a compact introduction to theoretical solid-state physics: from symmetries and crystal structures through lattice vibrations and electronic conduction to interacting electron systems. In the end you will be able to mathematically describe and calculate simple models for the structure, dynamics, and phase transitions of condensed matter.10 ECTSruns this semesterPH1001Theorie und Anwendung einfacher Lie-AlgebrenNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will receive an introduction to the fundamentals and examples of Lie algebras of small and medium size and their representations. By the end you will know the classification by root systems and Dynkin diagrams, understand highest weights for representations, and the complete classification of real and complex Clifford algebras.5 ECTSruns this semesterPH2136Trustworthy Distributed LearningNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn the fundamentals and current research on distributed learning (centralized, federated, decentralized) with a focus on data privacy, robustness against malicious clients, and reduction of communication costs. In the end you will be able to analyze, implement yourself, and critically evaluate algorithms for privacy, robustness, and communication efficiency.6 ECTSruns this semesterCIT433044VerkehrsmanagementNo ratings for this module yet.C Mathematical Theories in other DisciplinesIn the module you will learn to model traffic flows on highways and in cities and to plan and evaluate traffic control and management measures based on these models. In the end you will be able to apply traffic flow models and control procedures as well as assess the quality and effects of dynamic traffic information.6 ECTSruns this semesterBV560024Virtuelle Physik: Moderne Modellierungstechnik und ihr Einsatz in der ComputersimulationNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn how physical systems are modeled equation-based with modern, object-oriented languages such as Modelica, and how these models are used in computer simulations. In the end you will be able to model electrical and mechanical systems, build model libraries, and select suitable time integration methods for simulations.4 ECTSruns this semesterIN2236Wissenschaftliche VisualisierungNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn the entire visualization pipeline — from data acquisition and preprocessing over interpolation and filtering to presentation. You understand methods of information and scientific visualization for 2D/3D scalar and vector fields as well as terrain rendering and can evaluate and apply suitable techniques.5 ECTSruns this semesterIN2026ZinsmärkteNo ratings for this module yet.Mathematical ModulesYou will gain a solid introduction to interest rate markets and models for describing term structures. At the end you will be able to value interest-rate instruments and interest rate derivatives as well as measure and manage interest rate risks.5 ECTSruns this semesterMA3703Abelian VarietiesNo ratings for this module yet.Mathematical ModulesYou learn the fundamental concepts and constructions of abelian varieties within algebraic geometry. In the end you will be able to derive their most important properties and apply the learned concepts to abelian varieties in a broader geometric context.5 ECTSno date this semesterMA5125Advanced Deep Learning for PhysicsNo ratings for this module yet.C Mathematical Theories in other DisciplinesIn this module you will learn deep-learning methods and numerical simulation algorithms for physical materials such as fluids and deformable bodies. By the end you will be able to apply concepts such as generative models, time-series prediction, and numerical methods for partial differential equations, and select suitable network architectures and solvers for concrete tasks.6 ECTSno date this semesterIN2298Advanced Finite ElementsNo ratings for this module yet.Mathematical ModulesYou will learn advanced finite element techniques and apply them to concrete applications. In the end, you will be able to independently explore current research topics, work on Fachliteratur, and use modern open-source frameworks to solve complex PDE problems.7 ECTSno date this semesterMA5337Advanced Machine Learning: Deep Generative ModelsNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will engage with advanced methods of machine learning, with a focus on deep generative models. In the end you will know the theoretical foundations and be able to apply and implement the key building blocks (Normalizing Flows, VAEs, GANs, diffusion models) in a modern programming language and qualitatively compare them.3 ECTSno date this semesterCIT4230003Advanced Natural Language ProcessingNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou engage with current, advanced topics in Natural Language Processing: modern transformer models and explainability, machine translation for resource-poor languages, argument mining and ethical aspects, dialogue-oriented AI, quantum NLP, automatic text summarization as well as multimodal models (text + images). In the end you will be able to understand research work on these methods, combine technical building blocks and design and evaluate own architectural variants for research or practical application.5 ECTSno date this semesterCIT4230002Advanced Topics in Algebraic TopologyNo ratings for this module yet.Mathematical ModulesYou will learn algebraic methods for the study of smooth manifolds, in particular De‑Rham theory, cohomology and characteristic classes. By the end you will be able to understand, prove and apply the techniques for calculating examples of central theorems (e.g. Poincaré duality, Stokes, Poincaré–Hopf).5 ECTSno date this semesterMA5123Advanced Topics in Uncertainty QuantificationNo ratings for this module yet.Mathematical ModulesYou will learn methods for uncertainties quantification for sensitivity analyses, estimation of rare events, and the Bayesian approach to inverse problems. In the end you will be able to select appropriate numerical and statistical solution procedures and critically assess their foundations as well as their limitations.6 ECTSno date this semesterCIT4130021Algebraic GeometryNo ratings for this module yet.Mathematical ModulesYou will learn central terms and techniques of algebraic geometry: dimension theory of schemes, products of schemes, separated and genuine morphisms, coherent sheaves as well as differentials and smoothness. In the end you will be able to apply these algebraic and geometric concepts to fundamental questions of algebraic geometry.9 ECTSno date this semesterMA5107Algebraic Number TheoryNo ratings for this module yet.Mathematical ModulesYou deal with number fields (finite extensions of Q) and their rings of integers. You learn central concepts such as integral dependence, Dedekind domains, ideal class groups, ramification and étale algebras as well as classical analytical results such as the Hermite–Minkowski theorem and Dirichlet’s theorems on class groups and unit groups. In the end you will be able to apply the main theorems and solve problems on number fields, integers and simple diophantine equations.9 ECTSno date this semesterMA5111Algebraic Number Theory 2No ratings for this module yet.Mathematical ModulesYou will learn p-adic numbers Q_p and their finite field extensions (local fields) and their parallels to global algebraic number theory. A focus is the local class field theory, which relates abelian finite Galois extensions of a local field to suitable subgroups of the field. In the end you can apply properties of extensions of local fields (ramified, unramified, tam) and use simple statements of local class field theory.5 ECTSno date this semesterCIT4130023Algebraic Number Theory 3No ratings for this module yet.Mathematical ModulesYou will learn the fundamentals of class field theory, both locally and globally. The focus is on local class field theory (including the invariant map, reciprocity law and existence theorem) and applications such as the local Kronecker–Weber theorem; in addition you will get an introduction to global class field theory and selected applications. In the end you will be able to apply the central theorems and methods of class field theory and transfer them to concrete problems in number theory.5 ECTSno date this semesterCIT413025Algebraic SurfacesNo ratings for this module yet.Mathematical ModulesYou deal with algebraic curves and surfaces, their classifications and the birational geometry of surfaces. In the end you know the classification (Kodaira–Enriques), minimal models, blow-ups, and important surfaces classes such as rational, elliptic, del Pezzo, K3 and Enriques surfaces; you can apply theoretical statements and compute invariants in concrete examples.9 ECTSno date this semesterMA5132Algebraische ZahlentheorieNo ratings for this module yet.Mathematical ModulesYou will learn the basic concepts and main theorems of algebraic number theory for number fields and their rings of integers. In the end you will be able to compute the norm, trace and discriminant, investigate the structure of ideals and the class group, and apply the theory to concrete examples such as quadratic and cyclotomic number fields.6 ECTSno date this semesterMA5110Algorithmen für Uncertainty QuantificationNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn methods for quantifying uncertainties in computer-based simulations. In the end you will be able to place central algorithms for Forward Uncertainty Quantification, assess their complexity, and evaluate when which procedures (e.g., Monte Carlo, Quasi-Monte Carlo, stochastic collocation, stochastic Galerkin) are suitable.5 ECTSno date this semesterIN2345Algorithmic Game TheoryNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn the fundamentals of algorithmic game theory at the intersection of computer science, mathematics, and economics. In this module you will deal with algorithmic aspects of game-theoretic solution concepts such as Nash equilibria and with the design of economic mechanisms; in the end you will be able to analyze these concepts algorithmically and in terms of complexity theory.5 ECTSno date this semesterIN2239Algorithms for Scientific ComputingNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn efficient, hierarchical algorithms and data structures for scientific computing and how to implement them. The focus is on fast discrete Fourier and related transforms (FFT, DCT/DST), space-filling curves (Peano, Hilbert) for organizing multi-dimensional data, as well as hierarchical methods such as Sparse Grids and adaptive representations. In the end you will be able to explain such procedures, analyze them, and implement them if needed.8 ECTSno date this semesterIN2001Algorithms for Scientific Computing IINo ratings for this module yet.C Mathematical Theories in other DisciplinesYou engage with advanced numerical methods and their application in scientific computing. Depending on the lecture focus, you learn e.g. efficient procedures for sparsely populated matrices, numerical techniques for quantum systems, or methods such as molecular dynamics, sparse grids and algebraic multigrid. In the end you can apply suitable methods to demanding application problems and explain and utilize their hierarchical aspects.4 ECTSno date this semesterIN2002An Introduction to the Regularity Theory of Elliptic Partial Differential EquationsNo ratings for this module yet.Mathematical ModulesYou will get an introduction to the regularity theory of elliptic partial differential equations. You will learn classical and modern methods for deriving regularity results for linear and nonlinear problems as well as for systems, and you will be able to apply the most important proof techniques, e.g. De Giorgi's solution of Hilbert's XIX. In the end you will understand the basics of Nirenberg's methods, Schauder theory and partial regularity for systems.5 ECTSno date this semesterMA5081An Introduction to the Theory of Functions of Bounded VariationsNo ratings for this module yet.Mathematical ModulesYou learn the theory of functions of bounded variation (BV functions) and important tools from geometric measure theory. In the end you will be able to apply structural and compactness properties, traces and extensions as well as fine point properties of BV functions and sets with finite perimeter.5 ECTSno date this semesterMA5948Analyse und Design zellulärer NetzwerkeNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn analysis techniques for system-biological models and the structural principles (design) of biochemical networks. In the end you will be able to determine time hierarchies and sensitivities as well as analyze stability properties and control-loop behavior and derive proposals for biotechnological modifications from these results.5 ECTSno date this semesterMW2242Analysis of Three-Dimensional ShapesNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn methods for the representation, analysis, and comparison of three-dimensional shapes. The module covers both the underlying mathematics (e.g., differential geometry, spectral and conformal methods) and practical implementation aspects, so that you can understand and implement procedures for analyzing and comparing 3D shapes.8 ECTSno date this semesterIN2238Angewandte QuantenmechanikNo ratings for this module yet.C Mathematical Theories in other DisciplinesThis module covers applied quantum mechanics with a focus on fundamentals and applications in quantum information. By the end of the module you will be able to understand the central concepts of quantum mechanics and apply them to problems of quantum computation and information.5 ECTSno date this semesterPH2205Ansätze der theoretischen Physik in den Klima- und ErdsystemwissenschaftenNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn how the Earth system and its climate can be described with concepts from theoretical physics. Based on selected works from dynamical systems theory, statistical mechanics and stochastic processes you understand central principles of climate dynamics and can classify them critically.3 ECTSno date this semesterED110116Applications of Mathematical BiologyNo ratings for this module yet.Mathematical ModulesYou will learn fundamental mathematical methods of biology, including nonlinear dynamics, bifurcation and singular perturbation theory, as well as fundamental stochastic processes. These methods will be applied to important models from ecology, biochemistry, regulatory pathways, neuroscience and population genetics, so that you can understand research articles and adapt standard models to problems in the end.9 ECTSno date this semesterMA3602Applied Discrete OptimizationNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn how discrete optimization problems are modeled and solved. The course covers polyhedral foundations, exact procedures (e.g., Branch-and-Bound, Branch-and-Cut, Branch-and-Price, Dantzig–Wolfe, Benders, Lagrange-Relaxation) and heuristic/metaheuristic approaches. In the end you can apply suitable methods (exact or heuristic) to solve complex, large-scale models.6 ECTSno date this semesterWI000819Applied Introduction to Differential GeometryNo ratings for this module yet.Mathematical ModulesYou receive an application-oriented introduction to the fundamentals of differential geometry. By the end you can recognise manifolds and vector bundles and compute with simple geometric objects (Lie derivatives, exterior derivatives, integration of differential forms) as well as apply Lie groups to describe symmetries in physical systems.5 ECTSno date this semesterMA5228Applied Numerical ModelingNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn the fundamentals of numerical modeling with a focus on application and practical implementation. In the end, you can select, apply, and interpret the results of suitable numerical procedures for questions of Earth system processes.3 ECTSno date this semesterED110237Applied Reinforcement LearningNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn practical methods of reinforcement learning (RL) for sequential decision problems and how to apply them. In the end you will be able to model typical RL scenarios, implement common algorithms, and solve and assess simple robotics tasks (e.g. on the e-Puck) with RL.6 ECTSno date this semesterEI7641Applied Risk ManagementNo ratings for this module yet.Mathematical ModulesYou analyze five historical risk management cases from different asset classes (Fixed Income, Equity, Commodities, Credit, Hedge funds). You will learn to apply the underlying historical events, the mathematical concepts, and their implementation in simple risk management tools in standard software.5 ECTSno date this semesterMA5730Approximation AlgorithmsNo ratings for this module yet.Mathematical ModulesYou learn how to design and analyze efficient approximation algorithms for combinatorial optimization problems. In the end you can assess the running time and approximation guarantees of algorithms, apply known techniques (e.g. Greedy, LP-Rounding, Primal-Dual), and prove limits of approximability.9 ECTSno date this semesterCIT4100003Artificial Intelligence in Medicine IINo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will gain an overview of advanced prediction and classification tasks in medicine. You will learn methods for prognosis and diagnostics (e.g., risk scores, survival models, differential diagnosis, population stratification), specialized ML techniques (geometric deep learning methods for point clouds/networks, transformers, reinforcement learning) as well as topics on trustworthiness and clinical implementation of AI (bias, fairness, generalizability, data harmonization, evaluation). By the end you can apply the concepts in your own AI projects and assess their social and ethical implications.5 ECTSno date this semesterIN2408Astroteilchenphysik 2No ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn the connections between cosmology and particle physics: from the fundamentals of the Standard Model and cosmology to observable properties of the universe and current questions such as dark matter, neutrino physics, cosmic radiation and gravitational waves. In the end you will be able to link key observations (CMB, primordial nucleosynthesis, large-scale structure) with particle physics and discuss candidates as well as detection methods for dark matter.5 ECTSno date this semesterPH2074Auction Theory and Market DesignNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn game-theoretic fundamentals and mechanism design as well as the theory and practical realization of various auction and matching formats. In the end you will be able to explain properties and payment rules of open and closed auctions, model strategic interactions, and justify the selection of auction formats with regard to efficiency or revenue goals.5 ECTSno date this semesterIN2211Augmented RealityNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn the fundamentals of augmented reality (AR): geometric transformations, projection geometry, representation of 3D information, display and tracking devices, as well as mathematical foundations of optical tracking, sensor fusion, and calibration. In the end you can describe, analyze and extend the mathematical and programming aspects of AR systems for your own solution approaches, and evaluate input/output devices for suitability to application scenarios.6 ECTSno date this semesterIN2018Ausgewählte Themen aus dem Bereich Computergrafik und -visionNo ratings for this module yet.C Mathematical Theories in other DisciplinesIn this module selected current topics from computer graphics and image understanding are presented. You will learn the state of research and technology in these areas and can engage with current research projects.5 ECTSno date this semesterIN3200Ausgewählte Themen aus dem Bereich Künstliche Intelligenz und RobotikNo ratings for this module yet.C Mathematical Theories in other DisciplinesIn this module, current topics from artificial intelligence and robotics are introduced. By the end you will know the state of research and technology in selected areas and be able to critically engage with newer research projects.5 ECTSno date this semesterIN3150Autonomes FahrenNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn the fundamentals and central questions of automated driving. The module provides an overview of perception, decision-making, lane and trajectory planning, as well as sensor models, multisensor fusion and mapping. In the end you will be able to apply exemplar solutions to typical traffic scenarios and you will have both scientific and practical relevance to the current development.3 ECTSno date this semesterIN2356AV Artificial IntelligenceNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will obtain a comprehensive overview of methods of artificial intelligence and machine learning with practical relevance to vehicle technology. In the end you will be able to select appropriate ML methods for various questions in vehicle technology and implement them in code (e.g., for autonomous driving tasks).5 ECTSno date this semesterMW2378Basic Mathematical Methods for Imaging and VisualizationNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn fundamental mathematical methods that are applied in imaging and visualization, and you can subsequently use them to formulate, analyze and solve concrete problems. Topics include, among others, linear algebra, analysis, optimization and probability theory and their applications in image processing and computer vision. In the end you will be able to select appropriate methods, optimize them and transfer them to related engineering disciplines.5 ECTSno date this semesterIN2124Bildverstehen II: Robot VisionNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn practice-relevant methods and algorithms of robot vision and machine vision. The lecture explains fundamentals, data structures and implementation aspects of central procedures and shows typical applications, so that you can analyze, evaluate and develop practical applications for image processing tasks.4 ECTSno date this semesterIN2016Biofluid MechanicsNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn how fluid mechanics is applied to biological systems, in particular blood flow in vessels and flow in the lungs. By the end you will be able to use fluid-mechanical principles and mathematical as well as numerical methods to describe and simulate biological processes.5 ECTSno date this semesterMW0376Blockchain-based Systems EngineeringNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn about the structure, properties and applications of blockchain and distributed ledger technologies (DLT). By the end you will be able to analyze blockchain-based application systems, select technologies suitable for concrete use cases, and justify fundamental architecture and design decisions.5 ECTSno date this semesterIN2359Bordisms and Topological Field TheoriesNo ratings for this module yet.Mathematical ModulesYou will learn the theory of bordisms (Cobordisms) and their algebraic structures as well as the formulation of topological field theories as functors according to Atiyah and Segal. In the end you will be able to justify basic results, compute bordism rings, and follow and understand the connections to topological field theories as well as simple examples.6 ECTSno date this semesterMA5133Branching Random WalksNo ratings for this module yet.Mathematical ModulesYou will learn the basics and advanced aspects of branching random walks. In the end you will know the classical theory of branching processes and Galton‑Watson trees as well as the connections to partial differential equations and relevant application areas.3 ECTSno date this semesterCIT413035Calculus of VariationsNo ratings for this module yet.Mathematical ModulesYou will learn methods of variational calculus, both indirect and direct approaches for scalar and vector-valued problems. This includes relaxation theory and Gamma-convergence as well as their application to model problems of nonlinear continuum mechanics. In the end you can apply direct and indirect methods and investigate various linear and nonlinear optimization problems.9 ECTSno date this semesterMA5074Case Studies in Scientific ComputingNo ratings for this module yet.Mathematical ModulesYou work in small, interdisciplinary teams on concrete application problems from research or industry. In doing so, you create the entire solution chain from modeling through analysis and numerical solution to presentation, and you can ultimately develop mathematical models, select and implement suitable numerical methods, and present the results scientifically.7 ECTSno date this semesterCIT4130015Case Studies Life Science MathematicsNo ratings for this module yet.Mathematical ModulesYou work in small teams on concrete problems from the Life Sciences. You formulate questions mathematically, develop models (deterministic or stochastic), solve and implement suitable methods, evaluate the results and present them scientifically and for a general audience.10 ECTSno date this semesterCIT413052Case Studies OptimizationNo ratings for this module yet.Mathematical ModulesYou work in small teams on concrete optimization tasks from discrete and non-linear optimization. You model real problems, select and implement suitable solution procedures with modern optimization tools, and present and assess the results both for a disciplinary audience and for a non-scientific audience.10 ECTSno date this semesterCIT413042Catastrophe TheoryNo ratings for this module yet.Mathematical ModulesYou will learn the theory of critical points and their local classifications, in particular nondegenerate and certain degenerate singularities such as fold and cusp. In the end you will be familiar with classification theorems for germs and with stable unfoldings (unfoldings) up to codimension 4.5 ECTSno date this semesterCIT4130016Category TheoryNo ratings for this module yet.Mathematical ModulesYou will learn the basic concepts of category theory: categories, functors and natural transformations as well as central concepts such as universal properties, representability and the Yoneda lemma. You will also become familiar with limits, colimits and adjunctions and will subsequently be able to analyze properties of categories from different mathematical areas.5 ECTSno date this semesterMA5144Causal Inference in Time SeriesNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn methods of causal inference for time series and apply them. By the end you will be able to identify causal structures in dynamic networks, apply suitable algorithms and implement results practically on real data sets.5 ECTSno date this semesterCIT4230006CausalityNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou engage with concepts and methods of causal inference: from probabilistic and graph-theoretic foundations through structural models to modern algorithms for causal discovery and estimation of causal effects. In the end you can judge whether and how causal conclusions are possible from given data and assumptions, select appropriate methods and apply them in practice.8 ECTSno date this semesterIN2410Code-based CryptographyNo ratings for this module yet.Mathematical ModulesYou will learn the fundamentals of coded cryptography: relevant terms from algebraic coding theory, cryptographic basic concepts and complexity theory as well as central problems and systems such as Syndrome Decoding, Information Set Decoding, Code Equivalence, McEliece and Niederreiter. In the end you will be able to name several code-based cryptosystems and attacks, analyze a system and estimate the costs of an attack, as well as evaluate the use cases and apply the knowledge to examples.9 ECTSno date this semesterCIT413062Coding TheoryNo ratings for this module yet.Mathematical ModulesYou will learn the fundamentals of algebraic coding theory: important bounds, constructions and decoding procedures for various code classes as well as applications, e.g. in cryptography. In the end you will be able to apply the central theorems and transfer methods to concrete problems and examples.9 ECTSno date this semesterCIT413045Cognitive SystemsNo ratings for this module yet.C Mathematical Theories in other DisciplinesIn this module you will learn fundamental concepts of human cognition (perception, cognition, action) and how these abilities can be transferred to technical systems, especially in robotics. In the end you will be able to apply mathematical and algorithmic methods as well as architectures for cognitive systems to realize perception, planning and action execution in technical systems.5 ECTSno date this semesterIN2222CombinatoricsNo ratings for this module yet.Mathematical ModulesYou will learn central methods and structures of combinatorics and practice transferring them to concrete problems — with a special focus on applications in cryptography. In the end you will be able to formulate combinatorial models, solve structured counting problems, and present combinatorial arguments clearly.9 ECTSno date this semesterCIT413068Complex Function Theory 2No ratings for this module yet.Mathematical ModulesYou deal with the continuation of holomorphic functions, meromorphic functions on the Riemann sphere, and fundamental constructions in function theory (infinite products, Weierstrass and Mittag-Leffler theorems). You will also learn descriptive Riemann surfaces, homology and holomorphic differential forms, and apply the Riemann mapping theorem. In the end you will be able to construct holomorphic or meromorphic functions with prescribed zeros/poles and practically use the Riemann mapping.5 ECTSno date this semesterMA5005Complexity TheoryNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn formal computational models (in particular Turing machines and circuits) as well as the most important complexity classes (e.g. L, NL, P, NP, PSPACE, EXP, NEXP, PH). By the end you will be able to analyze problems with respect to time and space complexity, apply reductions and completeness proofs, and classify advanced concepts such as alternation, randomized methods, and interactive proof systems.8 ECTSno date this semesterIN2007Compressed SensingNo ratings for this module yet.Mathematical ModulesYou learn how to reconstruct sparse signals from a few structured linear measurements and which measurement matrices guarantee reliable recovery. In the end you can formulate important recovery statements, apply the Restricted Isometry Property (RIP) to random matrices, and use the underlying probabilistic proof techniques.5 ECTSno date this semesterMA5352Computational Complexity in OptimizationNo ratings for this module yet.Mathematical ModulesYou learn the fundamentals of complexity theory with a focus on optimization problems: formal models, classes such as P and NP, NP-completeness and typical NP-hard optimization tasks. In the end you will be able to assess the difficulty of optimization problems, apply appropriate modeling guidelines, and analyze practical examples.5 ECTSno date this semesterMA5222Computational Convexity - Optimal ContainmentNo ratings for this module yet.Mathematical ModulesYou deal with algorithmic questions on convex problems in arbitrary dimensions and, to some extent, in generalized normed spaces. In the module you will learn typical problems such as optimal containment, the underlying concepts of convex analysis and techniques from linear optimization, as well as their algorithmic solution and analysis.9 ECTSno date this semesterMA5206Computational Integer ProgrammingNo ratings for this module yet.Mathematical ModulesIn this module you learn the computational methods for solving mixed-integer optimization problems (MIP). You understand fundamental algorithms such as Simplex, Branch-and-Bound and Cutting-Plane-Separation as well as practical improvements and heuristics that make MIP solvers applicable to real problems. By the end you can explain these procedures, justify their correctness, and use your modeling knowledge to improve MIP models.3 ECTSno date this semesterMA8034Computational Inverse ProblemsNo ratings for this module yet.Mathematical ModulesYou will learn mathematical and numerical methods for solving mainly linear inverse problems. In the end you will know the theory (ill-posedness, regularization, SVD, generalized Tikhonov) and common numerical procedures (direct and iterative regularization) as well as criteria for stability, convergence and stopping.6 ECTSno date this semesterMA4302Computational Social ChoiceNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will become familiar with methods of collective decision making (Social Choice), with a focus on procedures that use majority relations and their algorithmic properties. In the end you will be able to analyze, compare, and assess the computational complexity of various election procedures.6 ECTSno date this semesterIN2229Computational StatisticsNo ratings for this module yet.Mathematical ModulesYou will learn methods of computational statistics for high-dimensional, hierarchical, and latent data structures and how to apply them. The focus is on simulation (univariate and multivariate), Bayesian inference with MCMC (Gibbs, Metropolis-Hastings, Hamiltonian MC), bootstrap procedures and the EM algorithm for missing or latent data. In the end you can theoretically understand the algorithms, implement them in R, and interpret results statistically.5 ECTSno date this semesterMA4402Computational TopologyNo ratings for this module yet.Mathematical ModulesYou will learn the basics of algebraic topology with a focus on homology and its computation as well as concepts of persistent homology. In the end you will be able to compute the homology of simplicial complexes, work with coefficients, apply the fundamental exact sequences, and understand and sketch the key results of persistent homology.6 ECTSno date this semesterMA5224Computer AlgebraNo ratings for this module yet.Mathematical ModulesYou learn fundamental algebraic structures and their representation on the computer (e.g., integers, rational numbers, field extensions, finite fields, polynomials, rational functions). You also cover fundamental algorithms such as primality tests, prime factorization, gcd computation and polynomial factorization; optionally formal summation/integration as well as basics on varieties, ideals and Gröbner bases are offered. In the end you will understand concepts and methods of computer algebra and design, analyze, implement and apply algebraic algorithms.9 ECTSno date this semesterMA3101Computer Vision I: Variational MethodsNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn how many tasks of image processing (e.g. denoising, desmearing, segmentation, optical flow, stereo depth estimation, 3D reconstruction) are formulated and solved as variational problems. In the end you know the Euler–Lagrange approach and PDEs, efficient solution methods as well as convex formulations and relaxations and you can implement central concepts in Matlab.8 ECTSno date this semesterIN2246Computer Vision II: Multiple View Geometry (3D Computer Vision)No ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn the mathematical foundations of multiple-view geometry in order to reconstruct camera motion and 3D geometry from several images. In the end you will understand image formation, epipolar geometry, camera calibration, rank conditions and bundle adjustment and you will be able to implement central algorithms in Matlab.8 ECTSno date this semesterIN2228Computerbasierte MaterialphysikNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn modern theoretical methods of computer-based materials physics and how to apply them. The focus is on density functional theory and ab initio molecular dynamics for the microscopic description of physical and chemical properties of real materials. In the end you can assess the fundamentals, possibilities and limitations of these methods and independently perform and interpret simple calculations on material systems.5 ECTSno date this semesterPH2289Computergestützte Methoden in der VielteilchenphysikNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn computer-based methods for investigating many-particle systems, from numerical algorithms to machine learning techniques. In the end you will be able to apply typical algorithms and understand and assess the underlying concepts.10 ECTSno date this semesterPH2264Concentration of MeasureNo ratings for this module yet.Mathematical ModulesYou will learn fundamental inequalities and techniques of Concentration of Measure (e.g., Chernoff, Hoeffding, Bernstein inequalities, isoperimetry, Johnson–Lindenstrauss, Martingale methods, Poincaré and Gromov–Milman theorems). In the end you will be able to understand these inequalities and apply them to simple examples from applications.5 ECTSno date this semesterCIT4100004Conformal Mapping and ProbabilityNo ratings for this module yet.Mathematical ModulesThe module covers conformal mappings and their connection with stochastic processes in the plane. You will learn how conformal methods can solve probabilistic problems, and gain insight into two-dimensional critical systems and their scaling limits (e.g., percolation, loop-erased random walks, Ising model) as well as SLE and loop ensembles.5 ECTSno date this semesterMA5432Corporate FinanceNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn the fundamental concepts of corporate finance: valuation of firms and options, capital structure, dividend policy, market efficiency, as well as transactions such as IPOs and M&A. In the end you will be able to critically discuss these concepts, value financial and real options, and make decisions on financing and valuation questions (e.g., DCF, option valuation).6 ECTSno date this semesterWI000091Cost AccountingNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn the fundamentals of managerial cost accounting and how to apply them. The module covers cost accounting methods such as job costing, activity-based costing, and process costing as well as cost allocation, inventory valuation, capacity analysis and cost behavior. By the end you can select appropriate procedures and apply them to practical cost accounting problems.6 ECTSno date this semesterWI001130Coxeter GroupsNo ratings for this module yet.Mathematical ModulesYou learn the definition and fundamental properties of Coxeter groups as well as central theorems and methods of the theory. In the second, shorter part you apply the theory to a concrete topic (e.g. finite reflection groups, Iwahori–Hecke algebras and knot theory, root systems and Lie theory, or computations for Coxeter groups). At the end you can explain the terms, apply the theorems to examples and work on new examples.3 ECTSno date this semesterMA5138Credit-Equity ModelingNo ratings for this module yet.Mathematical ModulesYou will learn models for credit and equity risks and deepen the fundamentals of Credit-Equity modeling. At the end you will be able to apply theoretical models (e.g., defaultable Markov-diffusion processes, reduced-form and firm-value models) and numerically value derivative products such as convertible bonds within these models.5 ECTSno date this semesterCIT413034Cryptography and CryptanalysisNo ratings for this module yet.Mathematical ModulesYou learn the fundamentals of modern symmetric and asymmetric cryptography as well as common attack and cryptanalysis techniques. In the end you will be able to assess secure parameters and implementations, develop cryptographic solutions yourself, and implement practical attacks against intentionally insecure systems.5 ECTSno date this semesterCIT413046CryptologyNo ratings for this module yet.Mathematical ModulesYou engage with fundamental concepts of modern cryptology: secrecy, complexity-theoretic foundations and concrete encryption methods such as RSA, Diffie–Hellman, ElGamal, Rabin as well as elliptic curves. In the end you will be able to describe the presented systems, discuss their advantages and disadvantages and apply the necessary algebraic foundations.5 ECTSno date this semesterMA5104Cyber-Physical SystemsNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn how to model and analyze systems in which computing elements are tightly linked to physical processes (Cyber‑Physical Systems). The focus is on continuous, discrete and hybrid dynamics as well as fundamental methods for simulation, stability analysis and control of such systems.6 ECTSno date this semesterIN2305DatenanalyseNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn the fundamentals and methods of data analysis and how to apply them, in particular statistical concepts and probabilistic approaches for evaluating measurement and experimental data. In the end you will be able to present data analysis results and discuss the underlying insights independently.5 ECTSno date this semesterPH2221Datenanalyse und VersuchsplanungNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn fundamentals of statistics and probability theory as well as methods of experimental design. Building on this, procedures of data analysis (e.g., cluster methods, principal component analysis, exploratory factor analysis) and model types for structure optimization such as Bayesian networks are covered. In the end you can analyze data from large data sets and create simple model structures for parameter identification in biomechanical/biochemical networks.5 ECTSno date this semesterMW2248Delay Differential Equations with ApplicationsNo ratings for this module yet.Mathematical ModulesYou will learn the theory and numerics of delay differential equations (in particular with constant delays). You can formulate models with delays, analyze their existence, uniqueness and stability properties, as well as apply suitable numerical procedures and interpret results.5 ECTSno date this semesterMA5062Dependence Models Generated via Line Integrals and Actuarial ApplicationsNo ratings for this module yet.Mathematical ModulesYou learn how multivariate lifetime models can be constructed with the help of line integrals and hazard vector fields. In the end you will be able to generate such models, adapt them, and apply them in actuarial applications, as well as understand discrete and continuous cases with physical interpretation.5 ECTSno date this semesterMA5734DerivativesNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn how standardized financial derivatives (forwards, futures, swaps, options) work and how to practically apply them. In the end you will be able to assess payoff and profit profiles as well as risk characteristics, value derivatives, develop arbitrage and hedging strategies, analyze and construct swaps.6 ECTSno date this semesterWI000232Design and Analysis of ExperimentsNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn principles and methods for planning and evaluating experiments as well as fundamental statistical procedures. By the end you will be able to choose appropriate experimental designs, analyze data in R (descriptively and inferentially), and interpret and communicate results correctly.5 ECTSno date this semesterWZ3223Differential FormsNo ratings for this module yet.Mathematical ModulesYou learn the foundations and tools of differential forms on smooth manifolds: construction, exterior product, exterior derivative, integration and Stokes’ theorem. In the end you can differentiate, integrate and apply differential forms in contexts of geometry, topology, analysis and physics.5 ECTSno date this semesterCIT4130022Differential Forms 2No ratings for this module yet.Mathematical ModulesYou will learn how differential forms are applied in algebraic and differential topology as well as in differential geometry. In the end you will be able to apply and interrelate concepts such as de-Rham cohomology, Poincaré duality, Mayer-Vietoris, the Künneth formula, fixed-point and degree theory as well as basics on fiber bundles, characteristic classes, Lie groups and Riemannian manifolds.5 ECTSno date this semesterCIT413033Diffusion ProcessesNo ratings for this module yet.Mathematical ModulesYou will learn the mathematical theory of diffusion processes: Gaussian processes, stochastic integrals (Itô, Stratonovich, Klimontovich) and their transformation, Langevin equations to describe diffusions, and the analysis of diffusion operators using semigroup theory. You will also receive an introduction to log-Sobolev inequalities and to stochastic partial differential equations, so that you can formally analyze the models and treat them with semigroup-theoretic methods.9 ECTSno date this semesterCIT413069Direct Methods in the Calculus of VariationsNo ratings for this module yet.Mathematical ModulesYou engage with the fundamentals and modern methods of the calculus of variations. By the end you can understand central terms such as coercivity, sublevelness, relaxation and Γ-convergence and apply them to problems in e.g. mathematical physics and materials science.9 ECTSno date this semesterMA5917Discontinuous Galerkin MethodsNo ratings for this module yet.Mathematical ModulesYou will obtain an introduction to Discontinuous Galerkin (DG) methods for the numerical solution of partial differential equations. In the end you will be able to derive DG formulations for elliptic, parabolic and hyperbolic problems, evaluate their stability and convergence properties, and practically implement DG schemes.9 ECTSno date this semesterMA5343Discrete Harmonic AnalysisNo ratings for this module yet.Mathematical ModulesYou deal with harmonic analysis in discrete, finite structures. The module covers Fourier transforms on finite (abelian and non-abelian) groups, discrete Fourier and fast Fourier transforms, and applications e.g. in signal processing, graph theory, and number theory. In the end you will be able to formulate the fundamental methods of discrete harmonic analysis and apply them to examples and applications.6 ECTSno date this semesterMA5911Diskontinuierliche Galerkin-Verfahren in der Numerischen SimulationNo ratings for this module yet.C Mathematical Theories in other DisciplinesIn this module you will learn about and apply discontinuous (Discontinuous) Galerkin methods for the numerical solution of partial differential equations. You can explain various variants (including higher order), their properties compared to finite differences, finite volumes and continuous finite elements, and implement and evaluate simple simulations in fluid dynamics and acoustics.5 ECTSno date this semesterMW2453Diskrete FlächentheorieNo ratings for this module yet.Mathematical ModulesYou will become familiar with discrete models of surfaces in R^3 and R^4 as well as in projective and Möbius geometry. The module introduces discrete (integrable and non-integrable) surface theory, discrete curvature concepts and transformation theories, so that you can practically work with discrete differential geometry methods afterwards.5 ECTSno date this semesterMA5229Dynamics of Democratic ElectionsNo ratings for this module yet.Mathematical ModulesYou will learn models from socio-physics and mathematical social sciences that describe the behavior of voters and the dynamics of democratic elections. In the end you will be able to explain these models, apply them, and perform and interpret simple data-based analyses of voting processes.6 ECTSno date this semesterMA5619Dynamics of Infectious DiseasesNo ratings for this module yet.Mathematical ModulesYou will learn standard models and central results on the spread and control of infectious diseases. You will set up classical models (e.g., Kermack–McKendrick) and variants, estimate the basic reproduction number R0, consider stochastic modeling, contact tracing, control measures, and evolutionary aspects of pathogens. In the end you will be able to adapt models to concrete disease cases and recognize the driving evolutionary forces and their consequences.6 ECTSno date this semesterCIT413056Dynamische SystemeNo ratings for this module yet.Mathematical ModulesYou learn the theory of dynamical systems for ordinary differential equations and mappings in finite-dimensional phase spaces. The module provides tools for analyzing stable and unstable solutions, bifurcations, chaos and ergodic properties; at the end you can analyze geometric and topological properties of trajectories and attractors and transfer the methods to differentiable manifolds and infinite-dimensional spaces.9 ECTSno date this semesterMA3081Economics of Uncertainty and Asymmetric InformationNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn how to analyze economic decisions under uncertainty and asymmetric information. By the end you will be able to apply expected utility-based models, identify market failures due to information asymmetries, and assess measures to solve incentive and information problems (e.g., in insurance markets or in the principal-agent context).6 ECTSno date this semesterWI000100Effiziente Algorithmen und Datenstrukturen IINo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn advanced algorithmic methods focusing on linear optimization and techniques for solving combinatorial problems. In the end you will be able to formulate linear models, apply classical solution methods such as the Simplex method and advanced methods like Ellipsoid and Karmarkar methods, and use approximation and rounding approaches for NP-complete problems.8 ECTSno date this semesterIN2004Einführung in die Algebraische ZahlentheorieNo ratings for this module yet.Mathematical ModulesYou will learn the foundations of algebraic number theory: number fields, rings of algebraic numbers and their ideal theory. In the end you can understand central concepts such as norm, trace, integrality, discriminant and units and apply the fundamental theorems to concrete problems and simple diophantine questions.5 ECTSno date this semesterMA5129Einführung in die digitale SignalverarbeitungNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn the fundamentals of digital signal processing: signals and systems in the time and frequency domain, discretization, filter operations, frequency transformations, compression techniques and initial aspects of digital image processing. You also learn how the algorithms are implemented on a digital signal processor (DSP) and apply these implementations in the lab. In the end you can analyze theoretical concepts and practically implement suitable algorithms.7 ECTSno date this semesterIN2061Einführung in die KernenergieNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn the technical and physical foundations of electricity generation with nuclear reactors, including fission, energy conversion, and reactor designs. You will also gain an overview of radiation, radiation protection, the nuclear fuel cycle, nuclear waste, and the principles of nuclear safety, as well as historical and economic aspects of nuclear energy.5 ECTSno date this semesterMW0799Einführung in die nichtlineare Dynamik und ChaostheorieNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou receive an illustrative introduction to nonlinear dynamical systems and chaos theory. You will learn to derive ordinary differential equations for classical systems, identify equilibrium points and qualitatively assess their stability. In the end you will be able to analyze phase portraits, limit cycles and simple chaotic systems geometrically and without formal proofs.3 ECTSno date this semesterMW2373Einführung in die QCDNo ratings for this module yet.C Mathematical Theories in other Disciplines5 ECTSno date this semesterPH2042Einführung in die theoretische AstrophysikNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn fundamental concepts of theoretical astrophysics, from the structure and dynamics of compact objects to stars and up to galaxies and galaxy clusters. In the end you will be able to apply physical principles (gravitation, hydrodynamics, radiative transfer, equations of state), derive simple scaling relations, and describe astrophysical examples such as white dwarfs, stellar evolution, accretion, and shock fronts.5 ECTSno date this semesterPH2080Elements of Harmonic AnalysisNo ratings for this module yet.Mathematical ModulesYou will learn the fundamentals of harmonic analysis for different groups: finite groups, the torus and the real line. Topics include Fourier analysis in more abstract settings, convolution operations, representation theory of finite type, as well as central theorems such as Plancherel, inversion, Bochner and duality theorems; at the end you will be able to understand classical results of Fourier analysis in the context of locally compact (abelian) groups and to give elementary proofs.5 ECTSno date this semesterMA5021Elements of the Theory of DistributionsNo ratings for this module yet.Mathematical ModulesYou learn the fundamentals of distribution theory: test functions, the delta distribution, distributions on D and S, as well as operations such as convolution, derivatives, integration and Fourier transforms of distributions. By the end you can perform calculations with distributions and apply them in various applications.5 ECTSno date this semesterMA5319Elliptic CurvesNo ratings for this module yet.Mathematical ModulesYou will learn the foundations of the theory of elliptic curves: from algebraic curves and their invariants to the arithmetic structure of the points on elliptic curves. In the end you will know definitions, important theorems (e.g. Bezout, Mordell, Hasse) and you can compute invariants, differentials, the genus and the group structure for curves in Weierstrass form.9 ECTSno date this semesterMA5114Energie InformatikNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn how modern energy systems are formally modeled, simulated and operated with data-driven informatics methods. In the end you will be able to apply forecasting, optimization and control approaches (e.g., ML, optimization, MPC) to energy generation, networks, storage and flexible loads and assess their role in energy management systems.5 ECTSno date this semesterED180013Energy EconomicsNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn economic fundamentals and methods for analyzing energy markets (e.g., gas, oil, coal, electricity). In the end you will be able to distinguish market structures and behaviors of producers and consumers, assess network regulation, and apply theoretical as well as empirical methods to current developments such as the energy transition.6 ECTSno date this semesterWI001145Energy TradingNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn the value chain of energy trading: from market structures through trading venues to products for electricity, gas and additionally coal, crude oil and emission allowances. In the end you will understand how energy markets work, be able to assess risks, design trading portfolios and hedging strategies, and analyze price and clearing mechanisms.6 ECTSno date this semesterWI000992ErdsystemmodellierungNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou deepen your methods of Earth system modelling and learn how the atmosphere, oceans, biosphere and cryosphere are simulated together. You acquire the ability to develop simple to complex climate and Earth system models, to understand nonlinear feedbacks, and to validate models with observational data. In the end you can select suitable Earth system models for specific questions and critically evaluate their results.5 ECTSno date this semesterED110011Fallstudien in Risikomanagement, Finanz- und VersicherungsmathematikNo ratings for this module yet.Mathematical ModulesYou work on practice-oriented questions from financial mathematics, actuarial science and risk management. You model suitable stochastic approaches, implement numerical algorithms and adapt models to market data; in the end you can evaluate solutions and present your results.6 ECTSno date this semesterMA5727Financial Mathematics 2No ratings for this module yet.Mathematical ModulesYou learn stochastic processes and Ito calculus for modeling financial markets and understand the concepts of arbitrage, completeness and risk-neutral valuation. You can price derivatives (including exotic options) in continuous models, especially Black-Scholes and its generalizations, and implement various numerical methods.9 ECTSno date this semesterMA3408First Order Primal-Dual Optimization MethodsNo ratings for this module yet.Mathematical ModulesIn this module you will learn modern First-Order Primal-Dual optimization methods. You will understand how simple iterative schemes with primal-dual decompositions can be combined to design efficient, structure-exploiting algorithms for large-scale problems, and you will be able to apply and further investigate these methods.5 ECTSno date this semesterCIT413065Fortgeschrittene Allgemeine RelativitätstheorieNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn the theoretical foundations of general relativity, the main methods for describing curved spacetimes, and selected physical phenomena. In the end you can follow the basic calculations of the field equations and examples of physical applications and apply them independently to exercise problems.5 ECTSno date this semesterNAT3046Fortgeschrittene Konzepte des Quantum ComputingNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn advanced concepts and algorithms of Quantum Computing, with a focus on the quantum Fourier transform, the Shor algorithm and quantum error correction. In the end you will be able to distinguish these techniques, apply the quantum Fourier transform in new scenarios and understand the mathematical formalism of error correction, including the stabilizer formalism.5 ECTSno date this semesterIN2400Fortgeschrittene Methoden in der Quanten-VielteilchenphysikNo ratings for this module yet.C Mathematical Theories in other DisciplinesIn this module you will learn advanced theoretical methods of quantum many-body physics. By the end you will be able to apply and assess central techniques for exactly solvable models, topological phases, and quantum-dynamic representations.10 ECTSno date this semesterPH2297Fortgeschrittene Netzwerk- und Graph-AlgorithmenNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou deepen knowledge of graph and network algorithms: the focus is on centrality measures, density measurement algorithms in (sub)graphs, connectivity problems, and the assignment problem (Hungarian method). At the end you can analyze complex network problems, assess their complexity, and develop or apply suitable efficient algorithms.8 ECTSno date this semesterIN2158Fortgeschrittene QuantenfeldtheorieNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou deal with advanced methods of quantum field theory: unitarity, renormalization of non-abelian gauge theories, infrared divergences, effective actions, spontaneous symmetry breaking and anomalies, as well as quantized spin-1 and spin-2 fields. In the end you can apply these concepts and calculation methods, e.g. to compute scattering processes, loop corrections and effective field theories.10 ECTSno date this semesterPH2185Fortgeschrittene rechnergestützte Methoden in der BiotechnologieNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn numerical methods and modeling techniques used in biotechnology, bioprocess engineering and systems biology. In the end you will be able to develop complex MATLAB programs and simulate and analyze various model types of cellular networks – both stochastic and deterministic.4 ECTSno date this semesterMW2424Fortgeschrittene theoretische PhysikNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou engage with advanced aspects of theoretical physics. In the end you will be able to analyze complex case studies from theory and reproduce the developed solutions in written exams.10 ECTSno date this semesterPH1004Foundations of Data AnalysisNo ratings for this module yet.Mathematical ModulesIn this module you will learn mathematical methods of data analysis, in particular linear and nonlinear procedures for data dimensionality reduction as well as techniques for reconstructive restoration of structured signals. By the end you will be able to apply and assess singular value decomposition, random matrices, compressive methods and manifold-based procedures.8 ECTSno date this semesterMA4800Fourier- und Laplace-TransformationNo ratings for this module yet.Mathematical ModulesYou learn the theory and applications of Fourier and Laplace transforms: Fourier series, Fourier analysis (integral transform), Gabor transform and Laplace transform. In the end you can understand the interaction between a function and its Fourier transform and use it for optimized approximations.9 ECTSno date this semesterMA5039FourieranalysisNo ratings for this module yet.Mathematical ModulesYou learn the fundamentals of Fourier analysis on Euclidean spaces: Fourier series on period intervals and the Fourier transform on R^n, including generalizations to L^2 and distributions. In the end you will be able to assess convergence and regularity questions and apply Fourier techniques to applications such as PDEs, signal processing and sampling.5 ECTSno date this semesterMA4064Fraktale GeometrieNo ratings for this module yet.Mathematical ModulesYou will learn how to construct fractal sets with iterated function systems, analyze their fundamental properties and dimensions, and relate them to dynamical systems. You will also learn how to create approximation models with fractal functions and fractal surfaces.5 ECTSno date this semesterMA5207Functions of Bounded Variations and ApplicationsNo ratings for this module yet.Mathematical ModulesYou will learn the fundamentals and important tools of the theory of functions of bounded variation as well as geometric measure theory. You will understand measures such as Hausdorff measures, area and Coarea formulas, concepts of sets of finite perimeter and special BV functions. In the end you will be able to apply these terms to the treatment of relaxation problems in W^{1,1} and understand the mathematics behind the Mumford–Shah functional.9 ECTSno date this semesterCIT4130001Fundamentals of Climate ChangeNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will gain an overview of the physical foundations of climate change, observed changes in physical, biological and biogeochemical systems, and the attribution of anthropogenic causes. In addition, measures for mitigation will be introduced. At the end you will be able to explain causes and impacts of climate change and to recognize and evaluate observations in natural systems.3 ECTSno date this semesterWZ8100Fundamentals of Optimization for Machine LearningNo ratings for this module yet.Mathematical ModulesYou will learn fundamentals and advanced techniques of optimization, both convex and nonconvex as well as combinatorial and continuous, with a focus on applications in machine learning. In the end you will be able to understand optimization problems from ML research and approach research questions in this area.5 ECTSno date this semesterCIT413031Funktional-DifferentialgleichungenNo ratings for this module yet.Mathematical ModulesYou will be introduced to the theory of functional differential equations, in particular delay differential equations and further types (e.g., mixed type). At the end you will be able to understand and assess fundamental questions on existence, uniqueness, and stability of solutions.3 ECTSno date this semesterMA5006FusionsforschungNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will receive an introduction to fusion research with a focus on magnetic fusion. The module explains the fundamentals of nuclear fusion, different magnetic confinement concepts (e.g., mirror, pinch, tokamak, stellarator), heating and diagnostics of plasmas, as well as current research results. By the end you will be able to describe the basic fusion processes, the most important confinement concepts, and the relevant methods for heating and diagnostics.5 ECTSno date this semesterPH2196GasdynamikNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn the fundamentals of compressible flow theory: from the compressible Navier–Stokes equations and thermodynamic principles through stationary flow line theory and shock relations to linear and nonlinear wave dynamics. In the end you will be able to treat stationary and unsteady gas-dynamic problems in sub- and supersonic regimes with analytical methods and to estimate simple multidimensional effects in supersonic flows.5 ECTSno date this semesterMW0357Generalized Linear ModelsNo ratings for this module yet.Mathematical ModulesYou learn methods of regression for non-normally distributed target variables (e.g., binary, count data, nominal, positive values). In addition to classical GLMs such as logistic, Probit-, Poisson-, Gamma-, and log-linear models, extensions (e.g., overdispersion, random effects) are covered. By the end you will be able to estimate models, validate them, and analyze and interpret the results with R.9 ECTSno date this semesterMA3403Geometric Measure Theory and ApplicationsNo ratings for this module yet.Mathematical ModulesYou will learn the fundamentals of Geometric Measure Theory and how to transfer classical geometric properties of smooth sets to non-smooth situations. In the end you will be able to understand and apply central concepts such as tangent measures, Hausdorff measures, rectifiability, as well as area- and co-area-formulas, and follow the modern analysis of the Plateau problem.no date this semesterMA5925Geometric Methods for Physics of Magnetized PlasmasNo ratings for this module yet.Mathematical ModulesYou will learn to apply geometric methods (Hamiltonian and Lagrangian formalism) for the systematic reduction of complex multi-scale dynamical systems based on magnetized plasmas. You understand perturbative Lie-Transform methods, the derivation of field and kinetic equations from variational principles as well as the associated conservation laws; in addition you will see how continuous variational descriptions can be transferred to discrete formulations and implemented numerically, e.g. in Particle-In-Cell Monte-Carlo simulations.5 ECTSno date this semesterMA5333Geometrie und Topologie für die DatenanalyseNo ratings for this module yet.Mathematical ModulesYou will learn fundamental methods of geometric and topological data analysis. This includes constructions such as Voronoi and Delaunay diagrams, Alpha Shapes, as well as concepts from topology such as simplicial complexes and homology and their application to filtrations and persistent homology to investigate the topological properties of point sets.6 ECTSno date this semesterMA4804Geometry of Finite-dimensional Normed SpacesNo ratings for this module yet.Mathematical ModulesYou deal with the geometry of finite-dimensional normed spaces and convex bodies. You learn fundamental theorems of convex and discrete geometry as well as tools (e.g. Helly, Carathéodory, Radon, John ellipsoid, Banach–Mazur distance) and apply these to concrete problems in finite normed spaces.3 ECTSno date this semesterCIT413057Gitterfreie VerfahrenNo ratings for this module yet.Mathematical ModulesYou will learn methods for mesh-free approximation and interpolation of multivariate, scattered data, in particular Radial Basis Functions (RBF) and Moving Least Squares (MLS). In the end you can apply the fundamental principles, analyze them and implement the algorithms in Matlab.5 ECTSno date this semesterMA5324Gleichungslogik und Lambda-KalkülNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn the fundamentals of equation logic, term rewriting systems and untyped as well as typed lambda calculus. In the end you will be able to apply semantics and proof systems of equation logic, analyze term rewrites for correctness (termination, confluence) and program and type lambda terms as well.8 ECTSno date this semesterIN2048GPU ComputingNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn the basics of parallel programming on GPUs, the structure and use of GPU hardware, as well as programming models and optimization techniques. In the end you will be able to write GPU kernels in CUDA/HIP/SYCL, integrate them into C/C++ programs, debug and profile programs, and design and implement simple GPU applications.6 ECTSno date this semesterCITHN4015Gradient Flows in Metric SpacesNo ratings for this module yet.Mathematical ModulesYou will learn the analytical and geometric foundations of the metric theory of gradient flows. In the end you will be able to investigate existence, regularity and long-term behavior of such flows and qualitatively analyze solutions of the associated class of partial differential equations.5 ECTSno date this semesterMA5059Graph TheoryNo ratings for this module yet.Mathematical ModulesYou learn the fundamentals of graph theory: paths and cycles, connectivity, trees, matchings, k-connectivity and Menger's theorem, as well as planar graphs and colorings. In the end you can apply central definitions and theorems, carry out proofs, and transfer the concepts presented to concrete problems and simple applications (including from data analysis).6 ECTSno date this semesterCIT413051Graphical Models in StatisticsNo ratings for this module yet.Mathematical ModulesIn this module you will learn statistical models whose conditional independencies are described by graphs. The focus is on continuous distributions (in particular the multivariate normal distribution), undirected graphical models (Gaussian models) and directed acyclic graphs (Bayesian networks). By the end you will be able to represent dependency structures in data with graphical models and select appropriate model classes.9 ECTSno date this semesterMA5439Gruppentheorie in der PhysikNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou receive an introduction to group theory with a focus on applications in particle physics. By the end you will be able to apply central concepts and statements of group theory, classify representations of SU(2), SU(3) and the Lorentz group, and construct character tables and weight diagrams.10 ECTSno date this semesterPH2116Harmonic AnalysisNo ratings for this module yet.Mathematical ModulesYou will learn core techniques of harmonic analysis such as Fourier transformation, singular integrals and function spaces. In the end you will be able to apply these methods to the study of partial differential equations, in the theory of function spaces and in applications such as signal processing.3 ECTSno date this semesterMA5954Harmonic Analysis on Commutative SpacesNo ratings for this module yet.Mathematical ModulesYou will learn the fundamentals of harmonic analysis on topological groups and on their coset spaces. You will practice integration and convolution on groups, fundamentals of representation theory and specific techniques for Abelian, compact as well as homogeneous spaces and double coset spaces. In the end you will be able to analyze functions on these spaces and understand the connections to geometric analysis.9 ECTSno date this semesterCIT413026High-Dimensional Partial Differential EquationsNo ratings for this module yet.Mathematical ModulesYou learn how partial differential equations appear in very high dimensions, what theoretical peculiarities and numerical difficulties (e.g., Curse of Dimensionality) arise, and which modern solution approaches exist. In the end you will be able to analyze theoretical properties of solutions and implement and apply various numerical methods (sparse grids, tensor decompositions, neural networks) to applications.5 ECTSno date this semesterCIT413060High-dimensional StatisticsNo ratings for this module yet.Mathematical ModulesYou learn methods for the analysis of data where the number of variables is large. After the module you can apply procedures for controlling false discoveries in large-scale multiple testing, use sparse regression methods (e.g., Lasso) and methods for group-specific or low-dimensional structured signals, as well as use regularization approaches for matrix parameters and graph models.5 ECTSno date this semesterMA5442HomogenizationNo ratings for this module yet.Mathematical ModulesYou learn methods of homogenization for partial differential equations with rapidly oscillating coefficients as well as for PDEs in domains with periodically distributed small holes. In the end you will be able to apply fundamental homogenization techniques such as asymptotic expansions and two-scale convergence and describe the concepts behind stochastic homogenization problems.3 ECTSno date this semesterMA5921Homological AlgebraNo ratings for this module yet.Mathematical ModulesYou will learn the fundamental tools of homological algebra, which are applied in topology, geometry and representation theory. In the end you can work with categorical vocabulary, compute with chain complexes and homology, and compute derived functors such as Ext and Tor.6 ECTSno date this semesterMA5140Identification of Artificial Neural Networks: from the Analysis of one Neuron to Deep Neural NetworksNo ratings for this module yet.Mathematical ModulesYou will learn mathematical methods for the analysis and identification of feed-forward neural networks — from individual neurons to flat networks up to deep networks. The focus is on linear algebra, probability (in particular concentration inequalities) and optimization to determine weights and activation functions efficiently and robustly.6 ECTSno date this semesterMA5929Infinity CategoriesNo ratings for this module yet.Mathematical ModulesYou will learn the fundamentals and central concepts of ∞-category theory, especially in the presentation as quasi-categories (simplicial sets with certain lifting properties). In the end you can apply the key constructions such as fibrations, limits/colimits, adjunctions and the Grothendieck construction and you will be able to familiarize yourself with further literature and research.5 ECTSno date this semesterCIT413047Informatikanwendungen in der Medizin IINo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn advanced methods of medical image processing, segmentation and registration as well as the fundamentals of machine learning and 3D volume visualization. In the end you will be able to distinguish the most important algorithm types, assess when they are applied, implement central procedures in Python, and apply them to clinical questions.5 ECTSno date this semesterIN2022Insurance Mathematics 2No ratings for this module yet.Mathematical ModulesYou learn the fundamentals of personal insurance: life insurance, occupational pension provision, and health insurance. You can calculate expected values and present values of insurance benefits, determine premiums and reserves according to classical and modern models, and apply valuation methods for pension obligations and specific questions of private health insurance.9 ECTSno date this semesterMA3406International Capital Markets and Investment PracticeNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou engage with global financial markets and with strategies, procedures, as well as best practices in asset management. By the end you will know the sources of risk and return, various asset classes and philosophies, as well as methods for portfolio construction, risk management and asset allocation, and you will be able to apply models for risk analysis and forecasting.3 ECTSno date this semesterWI001157Introduction to Conservation LawsNo ratings for this module yet.Mathematical ModulesYou learn the fundamentals and properties of hyperbolic conservation laws, in particular the occurrence and handling of discontinuities (e.g. shock waves). By the end you can solve the Riemann problems for simple systems, apply the entropy condition to select physically relevant weak solutions, and assess and develop basic finite-difference and finite-volume methods along with modern Riemann solvers for compressible flows.5 ECTSno date this semesterMA5935Introduction to Group Representation TheoryNo ratings for this module yet.Mathematical ModulesYou will receive an introduction to the representation theory of groups and algebras with a view to applications in mathematics and the natural sciences. In the end you will be able to apply fundamental techniques such as complete reducibility, character theory and the representation of symmetric groups (or alternatively Hecke algebras and braid groups) and to explore further areas.5 ECTSno date this semesterMA5134Introduction to Quantum NetworksNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn the fundamentals of quantum communication and how entangled particle pairs can be used as a resource in communication networks. In the end you will be able to use theoretical models and practical exercises with the Python-based network simulator QuNetSim to analyze and optimize TCP/IP networks with quantum communication.5 ECTSno date this semesterEI71064Introduction to R for Data ScienceNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn the fundamentals of the R programming language for data preparation, analysis and visualization. In the end you will master the basic functions and important packages (e.g. tidyverse) and be able to independently import, format, analyze and visualize data.6 ECTSno date this semesterMGT001367Introduction to Regularization and Learning Methods for Inverse ProblemsNo ratings for this module yet.Mathematical ModulesYou will learn the mathematical foundations of inverse problems and regularization as well as modern data-driven solution approaches. In the end you will be able to analyze inverse problems, apply classical regularization methods and classify data-based reconstruction methods.5 ECTSno date this semesterCIT413070Introduction to Stochastic Differential Equations: Theory and NumericsNo ratings for this module yet.Mathematical ModulesYou learn the fundamentals of stochastic differential equations (SDEs) as well as their numerical treatment. By the end you will know the most important stochastic processes, the construction of stochastic integrals, and solution methods for SDEs, and you can analytically solve simple SDEs and apply numerical schemes to approximate general SDEs.3 ECTSno date this semesterMA5950Introduction to Variational and Level Set Methods for Geometric FlowsNo ratings for this module yet.Mathematical ModulesYou learn analytical and variational methods for the study of geometric flows. The focus is on Level-Set methods, viscosity solutions of degenerate parabolic equations, and variational formulations of the Mean-Curvature Flow. In the end you will be able to understand existence and uniqueness statements for generalized Level-Set Flows and cope with concepts such as Weak–Strong-Uniqueness, Fattening, and Minimising Movements.5 ECTSno date this semesterCIT413066Invariant TheoryNo ratings for this module yet.Mathematical ModulesYou learn the foundations and methods of invariant theory: behavior of orbits, generation and structure of invariants as well as classical and modern results for finite and reductive groups. In the end you can work on examples, connect algebraic and geometric perspectives, and practically apply methods to concrete problems.6 ECTSno date this semesterMA5131Inventory ManagementNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn fundamental models and methods of inventory management for one- and multi-period, multi-echelon, and multi-product systems. In the end you will be able to select appropriate control rules, calculate parameters, analyze the effects of costs and service parameters, and implement simple data-driven inventory decisions.6 ECTSno date this semesterWI000979Investment and Financial Management (MiM)No ratings for this module yet.C Mathematical Theories in other DisciplinesYou will gain a broad understanding of the instruments for analyzing and evaluating investment opportunities and learn how companies make financial decisions. In the end you will be able to apply performance metrics of companies, create investment and capital budgeting plans, and evaluate optimal capital structures (with and without taxes).6 ECTSno date this semesterWI001138Investment StrategiesNo ratings for this module yet.Mathematical ModulesYou will gain an overview of important static and dynamic investment strategies and their mathematical foundations. The module is complemented by an introduction to stochastic control methods and utility maximization. In the end you will be able to develop new investment strategies, calculate their net present value, and analyze their risk.5 ECTSno date this semesterMA5709Konvexe Optimierung für Computer VisionNo ratings for this module yet.Mathematical ModulesYou will learn the fundamentals of convex analysis and their application to optimization problems in image processing and computer vision. After the module you will be able to understand, apply and implement common first-order and proximal methods for typical CV tasks (e.g., image reconstruction, segmentation, matrix factorization).6 ECTSno date this semesterIN2330Lambda CalculusNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn the fundamentals of the lambda calculus as a model of programming languages. First you treat untyped lambda calculus, its reduction rules, evaluation strategies (e.g., call-by-value, call-by-name) and its Turing completeness. In the second part you learn typed lambda calculi, common type systems in functional languages and the connection between types and logic (Curry–Howard). In the end you can use lambda terms, translate them and prove their properties.5 ECTSno date this semesterIN2358Lattice Boltzmann methodsNo ratings for this module yet.Mathematical ModulesYou will learn the Lattice-Boltzmann Method (LBM) as an alternative to classical CFD methods: how the method is derived from kinetic models, how streaming and collision steps work, and which advantages LBM offers for complex geometries, microscopic interactions, and parallelization. In the end you will be able to theoretically classify, implement, and apply the method to selected model problems from science and engineering.9 ECTSno date this semesterCIT4130009Lattices and CodesNo ratings for this module yet.Mathematical ModulesYou will learn fundamental types of lattices (e.g., even/odd, unimodular, root lattices) and important properties of root lattices as well as the connection between (binary) linear codes and certain integer lattices. In the end you will be able to geometrically construct codes and derive their properties from the lattice structure and associated theta functions or modular forms.6 ECTSno date this semesterCIT4130014Linear Algebraic GroupsNo ratings for this module yet.Mathematical ModulesYou will learn the theory of linear algebraic groups: structure, core concepts and central structural results such as connected components, Lie algebras, quotients and Jordan decomposition. In the end you will be able to apply these results and analyze examples as well as transfer the concepts to connections with representation theory, arithmetic geometry and invariant theory.9 ECTSno date this semesterCIT4130018Logic Synthesis and Physical DesignNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn algorithms and data structures to automatically generate digital circuits from specifications and physically place them. In the end, you will understand logic synthesis, optimization, as well as partitioning, floorplanning, placement and routing, and you will be able to practically use tools such as ABC, Yosys or OpenROAD.6 ECTSno date this semesterCIT433032LogikNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn the basics of propositional and predicate logic: syntax, semantics and formal proof systems. In the end you will be able to conduct proofs in deductive systems, demonstrate soundness and completeness, formalize problems and apply simple decision or semi-decision procedures such as resolution.8 ECTSno date this semesterIN2049Machine Learning for Graphs and Sequential DataNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn methods of machine learning for graph data and sequential data. You understand models for texts and temporal sequences as well as techniques for networks and graphs and can apply and evaluate them to real tasks. In the end you can select suitable procedures and assess their strengths/weaknesses for non-independent data.5 ECTSno date this semesterIN2323Machine Learning for Regulatory GenomicsNo ratings for this module yet.C Mathematical Theories in other DisciplinesIn this module you will learn biological fundamentals of gene regulation and modern deep learning methods for modeling sequence-based regulatory processes. After completion you will be able to apply genome-wide experimental procedures and deep learning models for different stages of gene expression and biologically interpret the model predictions.6 ECTSno date this semesterIN2393Magnetohydrodynamische Phänomene - eine EinführungNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will receive an introduction to magnetohydrodynamic phenomena. In the end you will be able to understand and apply the fundamental principles and typical problems of magnetohydrodynamics.5 ECTSno date this semesterPH2037Marker-assisted SelectionNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn the technical and genetic fundamentals of molecular markers, the construction of genetic and physical maps, as well as the concepts of QTL and association analyses. You will also acquire knowledge on genomic prediction and marker-assisted selection and will be able to apply the methods later in breeding programs.5 ECTSno date this semesterWZ1589Marketing and Innovation ManagementNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn how innovations can be market-oriented, organized, and implemented, as well as the basics and tools of marketing. In the end you can apply models of innovation processes and technology acquisition and assess marketing strategies as well as the marketing mix.6 ECTSno date this semesterWI000820Markov ProcessesNo ratings for this module yet.Mathematical ModulesYou will learn theory and methods of continuous-time Markov processes: continuous-time Markov chains, the Markov property, Feller processes as well as properties of transition semigroups and their generators. In the end you can analyze the long-term behavior of processes, apply ergodic theorems and use them in examples (e.g. queueing theory, interacting particle systems, time series).9 ECTSno date this semesterMA4408Maschinelles Lernen für ComputersehenNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn fundamental machine learning methods that are frequently used in computer vision (e.g., object classification, segmentation, denoising, camera calibration). In the end you will be able to explain the mathematical formulation of central procedures, create simple implementations, and apply them to concrete datasets from the field of computer vision.5 ECTSno date this semesterIN2357Mathematical Data AnalysisNo ratings for this module yet.Mathematical ModulesYou will learn methods for analyzing complex and unstructured data, including regression and classification tasks. The module provides fundamentals such as loss functions, positive definite kernels and reproducing kernel Hilbert spaces as well as regularization strategies (e.g. Tikhonov) and SVM regression. In addition, summation procedures and manifold learning are covered.6 ECTSno date this semesterMA5098Mathematical Foundations of ImagingNo ratings for this module yet.Mathematical ModulesYou will learn mathematical foundations and models of imaging — from Fourier series and -transforms through frame theory and time-frequency analysis to wavelet transforms and variational methods. In the end you can compare different imaging models, apply their mathematical analysis, and employ suitable tools to solve concrete imaging problems.9 ECTSno date this semesterMA5063Mathematical Foundations of Machine LearningNo ratings for this module yet.Mathematical ModulesYou will learn the mathematical foundations of modern machine learning methods: structure, learning algorithms and approximation properties of neural networks, theory and application of kernel methods in reproducing kernel Hilbert spaces as well as qualitative aspects such as loss functions, risk and complexity questions. By the end you will be able to construct networks, discuss their approximation properties, apply kernel methods and assess the statistical efficiency of procedures.6 ECTSno date this semesterMA4801Mathematical Foundations of Machine LearningNo ratings for this module yet.Mathematical ModulesYou will learn the mathematical foundations of modern methods of machine learning. By the end you can design neural networks and discuss their approximation properties, apply kernel methods in Reproducing Kernel Hilbert Spaces, and assess the statistical efficiency of learning procedures.9 ECTSno date this semesterCIT413048Mathematical Introduction to Quantum Information ProcessingNo ratings for this module yet.Mathematical ModulesYou will learn the mathematical foundations of quantum information theory. The module covers abstract foundations of quantum mechanics, measurement and development theory, quantum statistics and tomography, as well as fundamental concepts regarding limits and resources of quantum information processing.9 ECTSno date this semesterMA5057Mathematics of Reinforcement LearningNo ratings for this module yet.Mathematical ModulesYou will learn the mathematical foundations of reinforcement learning: Markov decision processes (MDPs), tabular RL methods such as Monte Carlo, Temporal Difference, SARSA and Q-Learning, as well as basics of stochastic approximation to analyze the convergence of these algorithms. In the end you can formulate dynamic decision problems under uncertainty as MDPs and solve them with tabular RL algorithms.6 ECTSno date this semesterCIT413036Mathematische Einführung in die MagnetohydrodynamikNo ratings for this module yet.Mathematical ModulesYou will receive a mathematically focused introduction to magnetohydrodynamics (MHD) — the theory of electrically conducting fluids in a magnetic field. By the end you will be able to understand the fundamental MHD equations, their derivation from multi-fluid models, central conservation laws, as well as reduced and variational/Hamiltonian formulations, and place them in the scholarly literature.3 ECTSno date this semesterMA5902Medizintechnik 2 - ein organsystembasierter AnsatzNo ratings for this module yet.C Mathematical Theories in other DisciplinesIn this module you learn medical technology diagnostic and therapeutic principles along selected organ systems (e.g. respiratory system, nervous system, urogenital system, digestive system, sensory system/ear). You will gain fundamentals in anatomy, physiology and pathology of these systems and you will be able to assess medical-technical solutions and apply them in your own development projects.5 ECTSno date this semesterMW0017Meromorphic Functions on the Riemann SphereNo ratings for this module yet.Mathematical ModulesYou deal with meromorphic functions on the Riemann sphere, with covering mappings and Möbius transformations as well as with elliptic functions and their topology. In the end you will be able to construct meromorphic continuations, specify coverings and you will know the fundamentals of Riemann surfaces.5 ECTSno date this semesterMA5942Methods for Inverse ProblemsNo ratings for this module yet.Mathematical ModulesYou will learn mathematical foundations and numerical methods for solving inverse problems. The focus is on regularization techniques for linear and nonlinear problems as well as iterative solution methods (gradient-, Newton-, and Kaczmarz-type) and practical aspects such as adaptive discretization in PDE-based reconstruction tasks.3 ECTSno date this semesterMA5931Model CheckingNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn how to describe hardware and software systems with formal models and how to automatically verify these models using model checking methods to determine whether they satisfy desired properties. In the end you will be able to model simple systems, formulate properties in temporal logic, and explain basic model-checking algorithms as well as strategies against the state-space explosion problem and apply them to small examples.8 ECTSno date this semesterIN2050Modellierung und Maschinelles Lernen von dynamischen SystemenNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn to use the Julia programming language for the analysis and simulation of nonlinear and chaotic dynamical systems. In the end you can implement simple nonlinear models in Julia, analyze time series of dynamical systems, and apply data-driven modeling approaches — with examples from Earth system and climate modeling.5 ECTSno date this semesterED110068Modellierung zellulärer SystemeNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn to formulate, analyze and simulate mathematical models for cellular systems. The focus is on reaction kinetics, thermodynamics and stoichiometric networks; in the end you will be able to create balance equations for complex cellular networks, predict their behavior by means of simulations, and evaluate biotechnological processes with regard to temporal behavior and product yield.5 ECTSno date this semesterMW1141Modelling and SimulationNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn how to transfer real problems into formal models (mathematical or computational) and to process these models with suitable simulation strategies computationally. By the end of the module you will be able to distinguish model classes, develop simple solution procedures and select and apply simulation methods.8 ECTSno date this semesterIN2010Modelling Complexity in Energy and System ModelsNo ratings for this module yet.C Mathematical Theories in other DisciplinesIn this module you will learn how socio-economic aspects can be modeled in energy systems. You will be given methods (cellular automata, agent-based models, network and sociodynamics) and you can apply them to simple examples as well as write corresponding code.5 ECTSno date this semesterEI7490Models for Material Defects and Grain BoundariesNo ratings for this module yet.Mathematical ModulesYou are dealing with variational “semi-discrete” models for defects in metals and their significance for plastic deformation. The course covers multiscale analyses that lead to the formulation of line-energy models for dislocations and the modeling of grain boundaries. In the end you can apply mathematical techniques to analyze such models and understand the underlying energy estimates and asymptotics.3 ECTSno date this semesterMA5944Modern Approximation TheoryNo ratings for this module yet.Mathematical ModulesYou will learn tools of modern approximation theory: s-numbers (such as approximation, Gelfand and Kolmogorov numbers), entropy numbers as well as methods and bounds for sparse reconstruction (e.g., Prony methods, Restricted Isometry Property, iterative hard thresholding, CoSaMP). In the end you can apply these concepts to tasks for the approximation of vectors, functions and operators and you will recognize fundamental lower bounds in sampling theory.6 ECTSno date this semesterMA5952Modern Methods in Nonlinear OptimizationNo ratings for this module yet.Mathematical ModulesYou will learn selected modern methods of nonlinear optimization, e.g. convex and non-smooth optimization, interior-point methods, semidefinite programming, robustness concepts and duality. In the end you will be able to understand current research articles on the treated topics and you will be prepared to pursue your own research questions in nonlinear optimization.5 ECTSno date this semesterMA4503Moderne Methoden der Nichtlinearen Optimierung (2)No ratings for this module yet.Mathematical ModulesYou will learn selected modern methods of nonlinear optimization, such as convex methods, nonsmooth optimization, interior-point methods, semidefinite programming, robustness approaches, duality, or globalization techniques. In the end, you will be able to read current research articles on the treated topics and follow the presented methods independently further.5 ECTSno date this semesterMA4505Molekulardynamik-SimulationenNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn how molecular simulations are constructed, performed, and analyzed. After the module you will be able to plan, carry out independently, and evaluate thermodynamic as well as kinetic quantities from simulations using methods such as molecular dynamics, Monte Carlo, and Brownian dynamics.5 ECTSno date this semesterPH2019Netzwerke für den ZahlungsverkehrNo ratings for this module yet.C Mathematical Theories in other DisciplinesIn this module you will learn the system architecture, protocol layers and security aspects of networks used for national and international payments. In the end you will be able to assess fundamental architectures, security standards and authorization solutions and to evaluate types of attacks as well as mobile security concepts.3 ECTSno date this semesterIN2161NeuroAI and Machine Learning in NeuroscienceNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn modern methods of Computational Neuroscience and NeuroAI: from model-based approaches (dendrite models, mean-field, Fokker-Planck, linear response) through plasticity and stochastic processes to training methods for RNNs and SNNs as well as Reinforcement Learning and Predictive Coding. In the end you will be able to implement models at different levels, train RNNs/SNNs and analyze and reproduce NeuroAI papers in a professional manner.7 ECTSno date this semesterLS20057Nichtlineare Dynamik und komplexe Systeme 2No ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn how self-organization and pattern formation in spatially extended, dissipative systems can be described mathematically. The focus areas are reaction–diffusion systems (waves, pulses, spiral waves, Turing structures) and coupled oscillators (Kuramoto transition, complex Ginzburg–Landau equation) as well as the simulation and classification of the resulting patterns.5 ECTSno date this semesterPH2028Nichtlineare Dynamik: GrundlagenNo ratings for this module yet.Mathematical ModulesYou will learn the fundamentals of the theory of finite-dimensional continuous and discrete dynamical systems: phase space analysis, stability, bifurcations and initial insights into chaotic dynamics. In the end you will be able to apply these concepts to concrete examples and apply the most important analytical methods.5 ECTSno date this semesterMA3080Nonlinear AnalysisNo ratings for this module yet.Mathematical ModulesYou will learn fundamental methods of nonlinear analysis in infinite dimensions: Schauder degree theory regarding the question whether equations have zeros; generalized versions of inverse and implicit function theorems as well as Lagrange multipliers in the infinite-dimensional context; and bifurcation theory for the study of parameter-dependent solutions and their stability. In the end you will be able to apply these concepts to problems from partial and ordinary differential equations.9 ECTSno date this semesterMA5923Nonsmooth OptimizationNo ratings for this module yet.Mathematical ModulesYou will learn methods and concepts of nonsmooth optimization and how to apply them. The module conveys fundamentals of nonsmooth analysis, numerical procedures for minimization and for handling nonsmooth equations, as well as their convergence properties. At the end you will be able to select appropriate methods for concrete nonsmooth models and to assess their behavior theoretically.5 ECTSno date this semesterCIT4130020Numerical Analysis for High-dimensional Quantum DynamicsNo ratings for this module yet.Mathematical ModulesYou learn mathematical foundations and numerical methods for simulating quantum-dynamical systems in high dimensions. In the module you treat grid-based methods, the Truncated-Wigner Approximation, the time-dependent variational principle methodology, and the Gaussian wave packet approximation. In the end you will be able to understand and apply central approximations in phase-space formulation and methods from the time-dependent variational principle.6 ECTSno date this semesterCIT413027Numerical Methods for Hyperbolic SystemsNo ratings for this module yet.Mathematical ModulesYou engage with numerical methods for hyperbolic conservation laws as they occur in fluid and plasma physics. You will learn finite-volume and discontinuous-Galerkin methods in 1D and extend them to linear and nonlinear systems. In the end you can derive and implement a corresponding numerical scheme.5 ECTSno date this semesterMA5090Numerical Methods for Partial Differential EquationsNo ratings for this module yet.Mathematical ModulesYou will learn numerical solution methods for partial differential equations, in particular finite element methods for multi-dimensional elliptic boundary value problems. You will also learn error estimates, adaptive mesh refinement, fast solvers and an introduction to numerical methods for time-dependent problems. In the end you will be able to understand the methods, apply them and use the associated software.9 ECTSno date this semesterMA3303Numerical Methods for Uncertainty QuantificationNo ratings for this module yet.Mathematical ModulesYou learn how to formulate, analyze, and numerically approximate elliptic boundary value problems with random coefficients. This includes modeling and sampling of random fields as well as numerical methods such as Monte Carlo, stochastic collocation, and stochastic Galerkin methods.6 ECTSno date this semesterMA5348Numerics of Dynamical SystemsNo ratings for this module yet.Mathematical ModulesYou deal with numerical methods for dynamic systems: propagation and detection of bifurcations, computation and analysis of invariant sets (e.g. periodic orbits, invariant manifolds, attractors) as well as computational ergodic concepts such as Lyapunov exponents and invariant measures. In the end you will be able to apply these methods, implement them and evaluate their properties.5 ECTSno date this semesterMA3333Numerische Algorithmen für Computer Vision und Maschinelles LernenNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn numerical methods that are frequently used in computer vision and machine learning, including modeling of practical problems. In the end you will be able to implement basic algorithms, assess their strengths and weaknesses, and choose appropriate methods for solving concrete CV-/ML tasks.5 ECTSno date this semesterIN2384Online- und ApproximationsalgorithmenNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn fundamentals and advanced techniques of online and approximation algorithms. In the end you will know classical online problems (e.g., scheduling, paging, k-server), analysis tools such as amortized analysis and randomized algorithms, as well as design techniques for approximation algorithms including LP-relaxation and randomized rounding.8 ECTSno date this semesterIN2304Operator TheoryNo ratings for this module yet.Mathematical ModulesYou will learn the fundamentals of spectral theory of operators, in particular spectra of operators, spectral theory for normal operators and functional calculus for different classes of operators. In the end you will be able to analyze and apply these tools to integral and differential operators.9 ECTSno date this semesterMA5012Optimal TransportNo ratings for this module yet.Mathematical ModulesYou will learn the foundations of the mathematical theory of Optimal Transport (OT). By the end you will understand central concepts such as Monge and Kantorovich formulations, the Wasserstein distances and their role in analysis, physics, economics and machine learning, as well as methods for handling high-dimensional, multi-criterion problems.9 ECTSno date this semesterMA5934Optimal Transport for Stochastic Processes with Applications to Mathematical FinanceNo ratings for this module yet.Mathematical ModulesYou deal with modern methods of optimal transport and their applications in financial mathematics, probability, statistics and machine learning. A focus is on Optimal Transport for stochastic processes (causal/adapted OT), martingale OT, weak OT as well as on numerical procedures such as entropic regularization and estimation procedures. In the end you can understand the theoretical foundations (duality, regularity, geometric properties) and apply optimal-transport methods to problems of model-independent pricing and robust hedging in financial mathematics.3 ECTSno date this semesterCIT413071Optimal Transport, Numerics and SamplingNo ratings for this module yet.Mathematical ModulesIn this module you will learn the theory of optimal transport and methods for its numerical treatment. You will understand the fundamental models (Monge, Kantorovich), important properties of Wasserstein spaces and gain an overview of numerical procedures and applications in Data Science.3 ECTSno date this semesterMA5933Optimale Steuerung gewöhnlicher Differentialgleichungen 1No ratings for this module yet.Mathematical ModulesYou learn fundamental concepts and methods of optimal control for ordinary differential equations. In the end you will be able to formulate necessary optimality conditions (e.g., Euler–Lagrange, Legendre–Clebsch), distinguish different types of constraints and control restrictions, and convert control problems into boundary-value forms suitable for numerical treatment.5 ECTSno date this semesterMA3312Partial Differential Equations 2 - Nonlinear Evolution EquationsNo ratings for this module yet.Mathematical ModulesYou deal with qualitative properties of nonlinear evolution equations and learn methods to prove properties of solutions (e.g., regularity gain, convergence to stationary or self-similar profiles, contractivity). The main focuses are variational methods, Hamilton–Jacobi–Bellman equations, systems of conservation laws and degenerate parabolic equations.9 ECTSno date this semesterCIT4130024Partial Differential Equations 2 - Nonlinear Parabolic Evolution EquationsNo ratings for this module yet.Mathematical ModulesYou will learn methods of semigroup theory and gradient flows and apply them to investigate both linear and nonlinear parabolic evolution equations. By the end of the module you can analyze existence and qualitative properties of solutions using these techniques.5 ECTSno date this semesterMA5918Particle in Cell Methods for the Vlasov-Maxwell EquationsNo ratings for this module yet.Mathematical ModulesIn this module you will learn numerical Particle-in-Cell methods for the Vlasov–Maxwell equations. You will understand both deterministic and stochastic particle methods, structure-preserving discretizations with the discrete de-Rham complex, and you will be able to formulate and implement in Python geometric algorithms for Vlasov–Maxwell problems.5 ECTSno date this semesterCIT413049Partielle DifferentialgleichungenNo ratings for this module yet.Mathematical ModulesIn this module you will learn fundamental methods for the treatment of partial differential equations (PDEs). You will deal with classical representations of solutions for transport, Laplace, heat and wave equations, with conservation laws, Sobolev spaces, and with weak (variational) solutions of elliptic equations and their properties such as existence, uniqueness and regularity.9 ECTSno date this semesterMA3005PDE2 - Nonlinear Partial Differential EquationsNo ratings for this module yet.Mathematical ModulesYou learn methods for existence and qualitative analysis of nonlinear partial differential equations. The focus is on variational techniques (calculus of variations, Euler–Lagrange, existence of minimizers, regularity) as well as nonvariational methods (monotone, fixed-point iterations, sub- and supersolutions, methods for proving non-existence). In the end you can apply these tools to semilinear elliptic problems.9 ECTSno date this semesterMA5077PDE2: Dynamics of Nonlinear Evolution EquationsNo ratings for this module yet.Mathematical ModulesYou deal with nonlinear time-dependent partial differential equations (du/dt = Au + N(u)) and learn techniques to analyze their local and global behavior. In the end you will classify prototypes such as Burgers, nonlinear Schrödinger, KdV, or Nagumo equations and apply methods such as analytic semigroups, variation-of-constants (mild solutions), stability and invariant manifold theory.9 ECTSno date this semesterMA5946Perfect Simulation for Chains of Finite and Infinite OrderNo ratings for this module yet.Mathematical ModulesYou will learn about models of stochastic processes beyond finite Markov chains, in particular chains of infinite order, their properties and how to simulate them exactly (perfect simulation). In the end you will be able to assess existence and uniqueness questions, classify examples and apply perfect-simulation algorithms for such processes.5 ECTSno date this semesterCIT413043PetrinetzeNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will become acquainted with Petri nets as a formal model for describing and analyzing concurrent systems. In the end you will be able to model simple systems with Petri nets, analyze small nets by hand, and select suitable automatic analysis techniques and software tools for larger nets to assess behavior and properties.5 ECTSno date this semesterIN2052Philosophy of Artificial Intelligence: Key ReadingsNo ratings for this module yet.C Mathematical Theories in other Disciplines6 ECTSno date this semesterSOT56307Physik der GeneNo ratings for this module yet.C Mathematical Theories in other DisciplinesIn this module you will learn the physical properties of DNA and RNA — from thermodynamics and secondary structure to topology, polyelectrolyte behavior and the physical aspects of replication, transcription and translation. In the end you will be able to apply these concepts to biotechnological, genetic engineering and nanotechnological questions and perform simple calculations on DNA structure and thermodynamics.5 ECTSno date this semesterPH2277Planning and Scheduling of Complex Operations: Models, Methods and ApplicationsNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn to model and solve complex planning and scheduling problems with limited resources. In the end you will be able to formulate common scheduling models, apply suitable solution methods (exact, heuristic, metaheuristic) and implement simple implementations as well as linear programs to solve real problems.6 ECTSno date this semesterWI200541Plasmaphysik 2No ratings for this module yet.C Mathematical Theories in other DisciplinesYou will get an introduction to plasma physics: fundamentals, occurrences in nature and technical applications. The focus is on electrostatic and electromagnetic waves in plasmas, their use for diagnostics and heating, as well as nonlinear effects. You will also learn kinetic basics, derivation of fluid equations, transport processes, shock times, and ambipolar fields.5 ECTSno date this semesterPH2036Polyhedral CombinatoricsNo ratings for this module yet.Mathematical ModulesYou learn how to approach combinatorial optimization problems through the geometry of polyhedra: representation of polytopes, the connection between geometry and optimization of linear functions, as well as modern algorithms such as branch-and-cut and separation/optimization. In the end you will be able to apply the methods to typical problems (e.g., matching, TSP polytopes) and assess their limits in the context of NP-hardness.6 ECTSno date this semesterMA5225Population GeneticsNo ratings for this module yet.Mathematical ModulesYou will learn mathematical models of population genetics (e.g., Wright–Fisher, Moran, Kingman coalescent) and how evolutionary and ecological forces shape genomic variation. In the end you will be able to formulate models, analyze them, and interpret results as well as patterns in genomic polymorphism, including interspecific interactions such as cooperation or coevolution.6 ECTSno date this semesterMA5615Precise Point Positioning with GPS and GalileoNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn methods for highly accurate absolute position determination with GPS and Galileo. In the end you will be able to analyze, evaluate and implement methods such as Precise Point Positioning (PPP), ambiguity resolution and Kalman filter techniques in Matlab.5 ECTSno date this semesterEI7370Probabilistische Graphische Modelle in der Computer VisionNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn how probabilistic graphical models (directed and undirected) are used to model and solve typical computer vision problems. At the end you can understand MRF/CRF models, select appropriate inference and learning methods, and apply them to tasks such as segmentation, pose estimation, stereo or object recognition.5 ECTSno date this semesterIN2329Probability on GraphsNo ratings for this module yet.Mathematical ModulesYou will learn stochastic models on graphs, e.g. Random Walks, percolation and random graphs. In the end you will be able to analyse Random Walks on networks, use the connection to electrical networks to show recurrence/transience, and understand phase transitions and random spanning trees.5 ECTSno date this semesterMA4406Projektive Geometrie 2No ratings for this module yet.Mathematical ModulesYou explore selected topics of projective geometry and learn to apply algebraic and combinatorial methods to geometric problems. In the end you can, for example, purposefully use tensor or Clifford algebra, apply combinatorial tools such as oriented matroids or polytope theory, and explain the interplay between geometry, combinatorics and algebra in concrete examples.5 ECTSno date this semesterMA3204Quanten-Computing mit supraleitenden Qubits: von der Fabrikation zu AlgorithmenNo ratings for this module yet.C Mathematical Theories in other Disciplines5 ECTSno date this semesterNAT3033Quantendynamik und Spektroskopie, KlausurNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn methods of time-dependent quantum mechanics and their application in spectroscopy. The module conveys concepts such as density matrix formalism, response theory and light–matter interaction as well as dynamic spectroscopy. In the end you can qualitatively describe the methods, assess their applications and perform simple simulations.5 ECTSno date this semesterCH3335Quantenfehlerkorrektur und Fehlertoleranz für Computing und KommunikationNo ratings for this module yet.C Mathematical Theories in other Disciplines10 ECTSno date this semesterNAT3045QuanteninformationNo ratings for this module yet.C Mathematical Theories in other DisciplinesThe module covers fundamentals of quantum information. You will learn concepts and methods of quantum computation and quantum information theory and will be able to apply basic principles and formalisms of quantum information after completion.5 ECTSno date this semesterPH2237QuanteninformationNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn the fundamentals of quantum information theory: states and operations of qubits, entanglement, simple quantum algorithms, quantum measurement, quantum coding and elements of quantum error correction. In the end you will be able to apply fundamental concepts such as Schmidt decomposition, PPT criterion, Choi–Jamiołkowski isomorphism and simple quantum protocols and design simple circuits.10 ECTSno date this semesterNAT3035Quantenmechanik molekularer SystemeNo ratings for this module yet.C Mathematical Theories in other DisciplinesIn the module you will learn to apply quantum mechanical models to molecular systems to describe states and transitions. By the end you will be able to analyze, for example, pi-electron systems, harmonic and anharmonic vibrations, Born–Oppenheimer separation, as well as simple many-electron descriptions and transition rates for optical processes.5 ECTSno date this semesterPH2165QuantentechnologieNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn fundamental concepts and techniques of quantum technology, including quantum bits, control and decoherence. In the end you can explain and assess typical control sequences for qubits and how implementations on different platforms (e.g., superconducting qubits, spin-qubits in silicon) function and which error sources are relevant.5 ECTSno date this semesterPH2263Quantitative Risk ManagementNo ratings for this module yet.Mathematical ModulesYou learn basic probabilistic and statistical methods for assessing and modeling financial risks. By the end you can understand, derive and practically apply Risk Measures, Extreme-Value Methods and dependency models — especially in quantitative risk analysis scenarios.5 ECTSno date this semesterMA5415Quantum Dynamics 3No ratings for this module yet.Mathematical ModulesYou deal with mathematical methods for the analysis and numerical treatment of quantum-dynamical systems. In the module you will learn advanced approaches such as variational principles, Galerkin approximations and semiclassical models, and you can apply these to concrete model systems of medium to moderately high dimension.5 ECTSno date this semesterMA5926Quantum Entrepreneurship LaboratoryNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou work in interdisciplinary teams on real challenges from the Munich Quantum Valley: You develop relevant software prototypes for the quantum industry and work out marketing and business strategies. In the end you present the project at the Demo Day and create a Whitepaper describing the startup idea.3 ECTSno date this semesterWI001258Quantum GroupsNo ratings for this module yet.Mathematical ModulesYou learn the theory of quantum groups: Hopf algebras, q-deformations and quantized enveloping algebras. In the end you will be able to explain central constructions and examples, describe their representation theory and connections to classical Lie algebras as well as applications such as knot invariants.9 ECTSno date this semesterCIT413055Quantum Statistical InferenceNo ratings for this module yet.Mathematical ModulesYou will learn mathematical methods for hypothesis testing, parameter estimation, tomography, learning and predictive inference in quantum-statistical experiments. In the end you will be able to formally analyze, describe and design such experiments as well as apply suitable, advanced tools for inference about underlying quantum systems.5 ECTSno date this semesterCIT513009Quantum Theory for EngineersNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn the fundamentals and central concepts of quantum mechanics, from the wavefunction approach to the quantization of the electromagnetic field. In the end you will be able to explain the treated quantum theories and apply them to quantum systems relevant for engineers.5 ECTSno date this semesterCIT443036Quantum Tradeoff RelationsNo ratings for this module yet.Mathematical ModulesYou engage with various tradeoff relations in quantum mechanics and their applications in statistics, metrology and information theory. Starting with a short mathematical overview of density operators, POVMs, completely positive maps and instruments, you will learn to analyze and apply uncertainty relations, information-/disturbance as well as energy-/temperature tradeoffs and tradeoffs between speed, precision and sample size.5 ECTSno date this semesterCIT4130012Random Matrices: Theory, Numerical Methods, and ApplicationNo ratings for this module yet.Mathematical ModulesYou will receive an introduction to large random matrices, their eigenvalue distributions and eigenvalue spacings. At the end of the module you will know the fundamental methods (e.g. Stieltjes transform, orthogonal polynomials, Fredholm determinants, free probability) and you will be able to compute limit distributions and apply them to models in applications.3 ECTSno date this semesterMA5306Randomisierte AlgorithmenNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn fundamentals and techniques of randomized algorithms and how to estimate their running time and correctness with probabilistic methods. In the end you will be able to understand and analyze classical randomized algorithms (e.g., randomized Quicksort, Min-Cut, Treaps) and apply tools such as Markov, Chebyshev and Chernoff inequalities.8 ECTSno date this semesterIN2160Relativität, Teilchen und FelderNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn the foundations of special relativity and the field theory from the Lagrangian density to quantization. In the end you can quantize free and interacting fields, derive Feynman diagrams and rules, and calculate simple cross sections and decay rates.10 ECTSno date this semesterPH2040Representation Theory of Finite GroupsNo ratings for this module yet.Mathematical ModulesYou will learn fundamental concepts and methods of representation theory of finite groups. The topic covers representations, group algebras, module theory, semisimple algebras and modules, as well as characters and character tables; you can apply the developed statements and techniques to concrete problems.9 ECTSno date this semesterCIT413032Representations of Compact GroupsNo ratings for this module yet.Mathematical ModulesYou will learn the representation theory of compact groups. The module conveys the relationships between Lie groups and their Lie algebras, central results such as the Peter–Weyl theorem, the structure of maximal tori, roots, weights and the Weyl character formula as well as representations of the classical groups. In the end you will be able to construct, decompose and analyze representations from algebraic, differential-geometric and analytic perspectives.5 ECTSno date this semesterMA5054Resurgence in Geometry and PhysicsNo ratings for this module yet.Mathematical ModulesThe module covers methods for the analysis of divergent asymptotic series, their Borel sums, and the associated Stokes data. You will learn techniques of resurgence, Borel summability and applications in exact WKB analysis, cluster algebras, as well as in various areas of geometry and theoretical physics.6 ECTSno date this semesterCIT413050Robot Motion PlanningNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn methods for planning robot movements in different information scenarios: from planning procedures with complete environment knowledge to local, partially-known environments to probabilistic sampling methods for high-dimensional spaces. You will also learn data fusion and filtering procedures (Kalman filter, particle filter) with which maps are created and Simultaneous Localization and Mapping (SLAM) implemented, so you can plan collision-free trajectories.5 ECTSno date this semesterIN2138RoboterdynamikNo ratings for this module yet.C Mathematical Theories in other DisciplinesIn this module you will learn to systematically describe and analyze the kinematics and dynamics of stiff serial robots. At the end you will be able to model structure, motions and forces, and to evaluate and apply fundamentals of trajectory planning and control.5 ECTSno date this semesterMW0867Robust Machine LearningNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn the basics and current methods of robust machine learning (ML). The module covers types of attacks and threat models, practical attack methods, as well as empirical and certifiable defenses. In the end you will be able to assess methods for securing ML systems and select appropriate algorithms for concrete problems.3 ECTSno date this semesterCIT423004Scheduling: Theory and AlgorithmsNo ratings for this module yet.Mathematical ModulesYou will learn models and algorithms for the assignment of tasks to scarce resources. The module covers classical and modern scheduling problems (including stochastic, online, robust) as well as methods for their modeling, analysis and solution, so that you can, in the end, assess complexity, design exact or approximate algorithms and prove their quality.5 ECTSno date this semesterCIT413053Scientific Computing and Machine LearningNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn how methods of Machine Learning are applied in Scientific Computing to solve problems from the natural sciences and engineering. The focus is on numerical approximations of differential equations, inverse problems, model reduction and practical implementation on CPU/GPU. In the end you will be able to understand mathematical formulations of dynamic systems and select appropriate learning algorithms for specific problems.5 ECTSno date this semesterCIT423000Scientific Computing IINo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn the central steps of the simulation pipeline in Scientific Computing, with a focus on iterative solvers and efficient implementation of numerical methods. This is applied to examples from Computational Fluid Dynamics and to particle-based simulations (e.g., Molecular Dynamics). In the end you will be able to select, analyze and implement suitable iterative methods, as well as design and parallelize efficient algorithms for pairwise interactions.5 ECTSno date this semesterIN2141Security EngineeringNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn how to systematically design, analyze, evaluate, and operate secure IT applications. The focus is on system and threat analysis, derivation of security requirements, security architectures and measures, as well as methods for validation and a secure software development process.5 ECTSno date this semesterIN2178Selected Chapters from the Mathematical Continuum MechanicsNo ratings for this module yet.Mathematical ModulesYou will learn selected mathematically relevant methods of continuum mechanics and their applications in physical disciplines. From a range of topics (e.g., chemical/biological reactions, higher moments, Boltzmann equation and electrodynamics, introduction to relativity, self-gravitation of stars) you will deepen individual chapters and be able to understand and apply the underlying mathematical methods.5 ECTSno date this semesterMA5340Self-interacting Random Walks and Statistical PhysicsNo ratings for this module yet.Mathematical ModulesYou will learn methods for the analysis of self-interacting random walks and their connections to statistical physics. In the end you will be able to understand and apply central models (e.g. edge-/vertex-reinforced processes), proofs of localization/delocalization, and connections to supersymmetric sigma models and random Schrödinger operators.3 ECTSno date this semesterMA5941SemanticsNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn formal techniques for describing and analyzing the semantics of programming languages. In the end you will be able to understand and apply different semantics styles (operational, denotational, axiomatic) as well as define semantics for language constructs and prove properties such as type safety.8 ECTSno date this semesterIN2055Sensorgeführte Robotische Manipulation und LokomotionNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn how complex robotic systems (e.g., humanoid robots) can be modeled and motion-controlled, especially for manipulation and locomotion in unknown environments. In the end you will be able to distinguish the most important algorithmic methods for sensor-guided manipulation and movement and practically work on simple tasks.3 ECTSno date this semesterIN2068Service Operations ManagementNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn key planning problems in service systems (e.g., queues, facility location, resource and staff planning, appointment scheduling). In the end you will be able to formulate suitable optimization models and implement and interpret them in Python using the industrial solver Gurobi.6 ECTSno date this semesterMGT001034Signal Processing and Machine LearningNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn advanced mathematical methods, concepts and algorithms from signal processing and machine learning and apply them. The focus is on the integration of both paradigms with applications in communication and data processing. In the end, you can reformulate typical problem statements, apply suitable algorithms (e.g., for sparse signal processing or neural networks) and evaluate their results.5 ECTSno date this semesterEI70380Social ComputingNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn the basics and methods of Social Computing: concepts of social media, social networking and social contexts as well as sociometric methods (centrality, density, clustering), metrics of real networks, models of social relationships in space and time, Social Signal Processing and fundamentals of game theory. In the end you will be able to apply these concepts to the conception, implementation and research of Social Computing applications.5 ECTSno date this semesterIN2241SoftwarearchitekturenNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn how software architectures are described, constructed, reused and evolved over time. The module covers architectures of distributed systems, model-driven software development and current trends, so you can justify and apply architectural decisions in development projects.3 ECTSno date this semesterIN2088Special Topics in Ordinary Differential Equations: Symmetries and ReductionNo ratings for this module yet.Mathematical ModulesYou engage with parameter-dependent ordinary differential equations (analytic or polynomial), their symmetries and special reduction methods. A focus lies on algorithmic/reconstructive methods for determining symmetries and critical parameters as well as applications in simple biochemical reaction networks. In the end you will be able to recognize symmetries, perform reductions and identify critical parameters for singular perturbations.3 ECTSno date this semesterCIT4130011Stability of Nonlinear WavesNo ratings for this module yet.Mathematical ModulesYou learn what traveling waves (solutions that propagate with constant shape and speed) are and why their dynamic stability is important. By the end you can sketch the steps of a stability analysis, understand the associated spectral structure, and apply various tools to approximate spectra and infer (in)stability from spectral data.5 ECTSno date this semesterMA5945Statistical Analysis of CopulasNo ratings for this module yet.Mathematical ModulesYou learn to model multivariate dependency structures using Copulas and to understand, estimate, and apply Vine-Copula models (C-, D- and R-Vines). In the end you can select suitable vine models, implement them in R with VineCopula/CDVine, simulate, interpret and assess results.5 ECTSno date this semesterMA5408Statistical Inference for Dynamical SystemsNo ratings for this module yet.Mathematical ModulesIn this module you will learn how to model biological reaction networks with ordinary differential equations and how parameter values of these models can be reliably estimated from experimental data. You will acquire methods for parameter estimation (frequentist and Bayesian) as well as techniques for analyzing uncertainty and practicality of parameters and implement these in MATLAB.6 ECTSno date this semesterMA5612Statistical Inverse ProblemsNo ratings for this module yet.Mathematical ModulesYou learn fundamental methods for the statistical treatment of inverse problems. The course covers linear inverse problems with random noise, regularization, convergence rates, adaptive procedures and model selection; at the end you can compare the results and apply them to concrete examples.5 ECTSno date this semesterMA5428Statistical Signal ProcessingNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn the fundamentals of probability theory and stochastic processes and apply statistical methods to estimation and decision making. In the end you will be able to understand, evaluate and independently apply and develop mathematical concepts and numerical algorithms of statistical signal processing for communication and data processing applications.5 ECTSno date this semesterEI70240Stochastic AnalysisNo ratings for this module yet.Mathematical ModulesYou will learn the theory and fundamental applications of stochastic analysis. The focus is on Brownian motion (construction and properties), stochastic integrals and the Itô formula, as well as stochastic differential equations and methods such as Girsanov transformation and Donsker's invariance principle. In the end you will be able to formulate central statements and perform simple calculations with Itô integrals and SDEs.9 ECTSno date this semesterMA4405Stochastic Models for Tariff Calculation, Loss Reserving and Reinsurance and Their ApplicationsNo ratings for this module yet.Mathematical ModulesYou learn stochastic models and their application in property and casualty insurance: fundamentals, rating, reserve and reinsurance. By the end you can model tariffs and reserves and evaluate simple reinsurance contracts as well as practical constraints such as data or model risks.3 ECTSno date this semesterMA5736Stochastische OptimierungNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn the basics and methods of stochastic optimization and practice formulating and numerically solving real decision problems under uncertainty as stochastic optimization problems. In the end you can understand two- and multi-stage models, incorporate risk measures, and apply solution approaches with software (MATLAB + numerical solvers).6 ECTSno date this semesterWI001135StreuamplitudenNo ratings for this module yet.C Mathematical Theories in other DisciplinesIn this module you will learn modern methods for the calculation of scattering amplitudes in particle physics, from spinor-helicity formalism over on-shell recursion to techniques for loop amplitudes. In the end you will be able to apply on-shell methods to tree- and one-loop amplitudes and understand the fundamentals of modern multi-loop procedures as well as the underlying special functions.10 ECTSno date this semesterNAT3065Structural Research 1No ratings for this module yet.C Mathematical Theories in other DisciplinesYou work research-oriented on a current topic of the Chair of Structural Design. In the end you have submitted a scientific paper and can present the state of research, describe applied methods, and critically reflect on results.6 ECTSno date this semesterED120124Structure-preserving Finite Elements for Computational ElectromagnetismNo ratings for this module yet.Mathematical ModulesIn this module you will learn finite-element methods that preserve the underlying geometric and functional structure of electromagnetic problems. By the end you will be able to analyse the well-posedness of typical Maxwell model problems and apply stable, structure-preserving FEM approximations on geometrically non-trivial domains.5 ECTSno date this semesterCIT413044Systemtheorie und SignalverarbeitungNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn fundamentals and advanced content of systems theory and signal processing. This includes representation of signals in the time/space and frequency domain, convolution, linear time-invariant systems, as well as random signals, reconstruction and interpolation. In the end you will be able to evaluate the models and algorithms and process simple data with methods of signal processing.3 ECTSno date this semesterBV290010Techniken der ZellbiologieNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn methodological approaches to elucidating cellular signal transduction and discuss their potential and limits using case studies. In addition, you will address central aspects of cell cultures and their influence on experimental results. In the end you will be able to select suitable experimental strategies and assess their impact on cellular signaling pathways.5 ECTSno date this semesterWZ2388Technische DynamikNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn methods for deriving and analyzing motion equations of mechanical systems—from rigid multibody systems to one-dimensional continua. In the end you will be able to formulate models, linearize, analyze stability and vibration modes, and discretize and evaluate continuous systems with Rayleigh– Ritz and the Finite Element Method.5 ECTSno date this semesterMW2098Tensor Network MethodsNo ratings for this module yet.Mathematical ModulesYou learn modern methods for efficient approximation of high-dimensional functions (large N-tensors). The focus is on Tensor-Train (TT) approximation: its theory, numerical algorithms and applications. In the end you can analyze and simulate simple multidimensional problems with tensor-network methods.5 ECTSno date this semesterCIT413064The Economics of Firm CompetitionNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou learn how firms strategically operate in different market structures and what effects their behavior has on market performance and societal welfare. In the end you will be able to explain central models of strategic interaction and vertical relationships and analyze their consequences for efficiency and competition policy.6 ECTSno date this semesterWI001281Theoretische TeilchenphysikNo ratings for this module yet.C Mathematical Theories in other DisciplinesIn this module you will receive a structured overview of the Standard Model of particle physics and central current questions of field theory and phenomenology. In the end you will be able to describe the structure and symmetries of the Standard Model, calculate standard processes with Feynman rules up to one-loop corrections, and explain fundamental aspects of neutrino physics as well as possible extensions beyond the Standard Model.10 ECTSno date this semesterPH1005Theoretische Teilchenphysik im frühen UniversumNo ratings for this module yet.C Mathematical Theories in other Disciplines5 ECTSno date this semesterPH2298Theorie der ZufallsmatrizenNo ratings for this module yet.Mathematical ModulesYou learn non-asymptotic deviation estimates for random variables and vectors (in particular subgaussian and subexponential as well as isotropic vectors) and apply these concepts to random matrices with independent rows or columns. In the end you can formulate statements about the extreme singular values of such matrices, compare them and apply them to concrete examples as well as applications such as dimensionality reduction and Compressed Sensing.5 ECTSno date this semesterMA5346Theorie stochastischer ProzesseNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn the theory of stochastic processes and methods for their analysis. Using physical examples (predominantly from biophysics) you will acquire the tools to formulate, solve, and perform simple simulations of Master equations, Fokker-Planck, and Langevin equations, and to apply basic principles of stochastic thermodynamics.10 ECTSno date this semesterPH1006Time-Frequency AnalysisNo ratings for this module yet.Mathematical ModulesYou will learn the analysis of signals in time and frequency as well as methods for their approximation using frames. In the end you will know Fourier- and wavelet-like transformations, principles of uncertainty, the basics of frame theory and Gabor frames as well as frame-based reconstruction methods and you will be able to apply these to concrete signal and image analysis tasks.9 ECTSno date this semesterMA5916Topics in Computational BiologyNo ratings for this module yet.Mathematical ModulesYou will gain an overview of methods in Computational Biology, such as gene sequence analysis, image analysis, statistical network modeling, and dynamic path modeling. You will learn to assess the strengths and limitations of the different procedures and to select appropriate computational approaches for concrete biological or biomedical questions.6 ECTSno date this semesterMA5607Topics in Dynamical SystemsNo ratings for this module yet.Mathematical ModulesYou engage with a selected, advanced topic of the theory of dynamical systems (e.g., stochastic systems, multi-scale dynamics, numerical methods, special classes such as one-dimensional maps or infinite-dimensional systems). In the end you will be able to understand, apply, and assess the relevant concepts, methods, or numerical procedures for concrete systems.5 ECTSno date this semesterMA5300Topics in Dynamical Systems: Computational DynamicsNo ratings for this module yet.Mathematical ModulesYou study the numerical computation of objects and phenomena of dynamical systems (e.g. fixed/periodic points, invariant manifolds, limit and recurrent sets), with operators such as transfer and Koopman operators and with scalar metrics (e.g. Lyapunov exponents, entropy, dimensions). In the end you can develop, analyze and apply suitable algorithms and make qualitative and quantitative statements about the behavior of given dynamical systems.5 ECTSno date this semesterCIT415303Topics in Dynamical Systems: Network DynamicsNo ratings for this module yet.Mathematical ModulesThe module covers dynamic processes on and from networks. You will learn the basics, models (e.g., Kuramoto-type), random graphs, stochastic descriptions and applications such as epidemics or neural networks as well as related analytical methods. By the end you will be able to analyze given network dynamics with appropriate concepts or algorithms and make qualitative and quantitative statements about the dynamics.5 ECTSno date this semesterCIT415302Topics in Dynamical Systems: Stochastic DynamicsNo ratings for this module yet.Mathematical ModulesYou deal with stochastic or random dynamical systems. You will learn fundamentals, important methods (e.g. Fokker–Planck approach, large deviations, moment methods) as well as phenomena such as noise-induced behavior, synchronization by noise and stochastic bifurcations; at the end you will be able to analyze a given system with appropriate concepts/algorithms and make qualitative as well as quantitative statements about the dynamics.5 ECTSno date this semesterCIT415301Topics in Mathematical Statistical MechanicsNo ratings for this module yet.Mathematical ModulesYou will learn the mathematical foundations of statistical mechanics and acquire tools to treat thermodynamic limits, Gibbs states and large deviations. You will also examine phase transitions and symmetry breaking using concrete model examples such as the Ising and O(N) models.5 ECTSno date this semesterCIT413037Topological Quantum Field TheoryNo ratings for this module yet.Mathematical ModulesYou will learn the formal description of topological quantum field theories as functorial objects, with a focus on two-dimensional theories. In the end you can apply the fundamental definitions and examples, understand proofs, and perform simple calculations for 2D TQFTs.6 ECTSno date this semesterCIT413061Topologie und neue Arten der Ordnung in der Physik der kondensierten MaterieNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn theoretical concepts and experimental signatures of topological phases in solid-state physics. In the end you will be able to distinguish phases by symmetry and topology, derive topological invariants from band structures, and understand important examples such as quantum Hall states, topological insulators and metals, as well as topological superconductors.10 ECTSno date this semesterPH2246TopologyNo ratings for this module yet.Mathematical ModulesYou learn the fundamentals of set-theoretic topology and algebraic topology. In the first part you analyze topological and metric spaces as well as concepts such as continuity, compactness and connectedness; in the second part you deal with homotopies, fundamental groups and singular homology. At the end of the module you can assess topological properties as well as determine fundamental groups and homology of simple spaces.9 ECTSno date this semesterMA3241Transportation LogisticsNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou get an overview of central problems of goods and passenger transport logistics and learn basic modeling and solution approaches. In the end you will be able to formulate traffic, routing and network planning problems as mixed-integer linear programs and solve them practically with heuristics while interpreting the results.6 ECTSno date this semesterWI000978TUM Data Innovation LabNo ratings for this module yet.Mathematical ModulesIn the TUM Data Innovation Lab you work in your Master's program in small, interdisciplinary teams on real data-driven projects from science or industry. In the end you will be able to process, analyze and visualize data, implement numerical solutions, and present your results both technically and in an understandable way.10 ECTSno date this semesterMA8113Turbulente StrömungenNo ratings for this module yet.C Mathematical Theories in other DisciplinesIn this module you will learn the physical fundamentals and typical phenomena of turbulent flows as well as methods for their statistical description. You will learn how to formulate real flow problems with the basic equations, when turbulence modeling is necessary, and how to select appropriate models (including LES) to investigate flows numerically in an efficient and sufficiently accurate way.5 ECTSno date this semesterMW0595Value-based ManagementNo ratings for this module yet.C Mathematical Theories in other DisciplinesYou will learn the residual income concept as a central performance metric for maximizing shareholder value. You will be able to calculate Economic Value Added (EVA), make typical adjustments to accounting data, and analyze problems in cost of capital calculation, remuneration design, and implementation of value-oriented management, and develop solution proposals.6 ECTSno date this semesterWI000234Variational Analysis of the Ginzburg-Landau Functional: An IntroductionNo ratings for this module yet.Mathematical ModulesYou will learn the variational analytic foundations of Ginzburg–Landau energies. The module introduces Gamma-convergence, relaxation and the treatment of concentration phenomena on objects with co-dimension 1 and 2. By the end you can apply the fundamental concepts and follow the main results in proof lines.5 ECTSno date this semesterCIT413040Variational Analysis of Thin Elastic BodiesNo ratings for this module yet.Mathematical ModulesYou will learn the variational analysis of thin elastic bodies: from fundamentals of linear and nonlinear elasticity, through key inequalities and geometric rigidity, to dimension reduction. In the end you will be able to model variational problems for thin structures and apply the essential convergence and approximation results of the theory.5 ECTSno date this semesterCIT413029Variational Inequalities with Applications in Porous MediaNo ratings for this module yet.Mathematical ModulesYou engage with variational inequalities (elliptic, first- and second-order) and their applications in porous media. In the end you will know existence, uniqueness and a priori estimates, master solution methods and be able to apply the procedures in associated software.9 ECTSno date this semesterMA5356Variational Principles for Collective Plasma MotionNo ratings for this module yet.Mathematical ModulesYou will learn how models for collective motions in plasmas can be derived from variational principles. After the course you will be able to apply variational principles in Lagrangian and Eulerian descriptions and derive models such as MHD, Vlasov–Maxwell, drift-kinetics and hybrid variants, as well as understand the corresponding conserved quantities.3 ECTSno date this semesterCIT4130010
67 more modules match, but they are taught in German. Show themAircraft Trajectory OptimizationNo ratings for this module yet.C Mathematical Theories in other DisciplinesDu lernst, wie Flugzeugbewegungen modelliert, numerisch simuliert und durch optimale Steuerung verbessert werden. Am Ende kannst du Flugzeugmodelle unterschiedlicher Detailtiefe erstellen, Flugmanöver numerisch simulieren und optimale Flugbahnen mit Softwarepaketen berechnen.3 ECTSno date this semesterMW1669Algebraische Topologie in der PhysikNo ratings for this module yet.C Mathematical Theories in other DisciplinesDu erhältst grundlegende Kenntnisse in Algebra, Topologie und Kategorientheorie und lernst anschließend Methoden der Homotopie- und Homologietheorie sowie deren Anwendungen in der Physik. Außerdem werden Zusammenhänge zur Kohomologie auf differenzierbaren Mannigfaltigkeiten thematisiert. Am Ende kannst du zentrale Konzepte wie Fundamentalgruppe, singuläre Homologie und Poincaré-Dualität verstehen und anwenden.8 ECTSno date this semesterNAT3068Anorganische Festkörperchemie und OrganometallchemieNo ratings for this module yet.C Mathematical Theories in other DisciplinesDu lernst Grundlagen der anorganischen Festkörperchemie und der metallorganischen Molekülchemie. Teil I vermittelt Strukturtypen, Struktur-Beschreibungsprinzipien, Materialklassen, Synthese- und Reaktivitätsaspekte sowie Grundlagen zu Phasendiagrammen und Beugungsmethoden. Teil II führt in Ligandeneigenschaften, MO-Ansätze, das Isolobal-Prinzip und die Systematik sowie Synthesen, Struktur- und Reaktivitätsbeziehungen metallorganischer Verbindungen ein.5 ECTSruns this semesterCH4107Automatic Control Engineering (English Exam)No ratings for this module yet.C Mathematical Theories in other Disciplines5 ECTSno date this semesterLRG0081Axiomatische Mengentheorie und ihre logischen GrundlagenNo ratings for this module yet.Mathematical ModulesDu lernst die Grundlagen der formalen Logik und der axiomatischen Mengentheorie (Zermelo-Fraenkel). Am Ende kannst du formale Sprachen und Beweise verstehen und Methoden der Modelltheorie anwenden sowie natürliche Zahlen, Ordinal- und Kardinalzahlen innerhalb des Mengenuniversums konstruieren und mit transfiniter Rekursion umgehen.3 ECTSno date this semesterMA5075Bildverstehen I: Methoden der industriellen BildverarbeitungNo ratings for this module yet.C Mathematical Theories in other DisciplinesDu lernst praxisrelevante Methoden und Algorithmen der industriellen Bildverarbeitung kennen. Im Modul werden Verfahren zur Lageerkennung, Form- und Maßprüfung sowie Objekterkennung behandelt. Am Ende kannst du Bildverarbeitungsaufgaben analysieren, bewerten und mit geeigneter Hardware und Algorithmen umsetzen.3 ECTSno date this semesterIN2023Biologie für ChemikerNo ratings for this module yet.C Mathematical Theories in other DisciplinesDu erhältst eine kompakte Einführung in die Grundlagen der Biochemie und Zellbiologie mit Schwerpunkt auf für Chemiker relevanten Molekülen und Prozessen. Am Ende des Moduls kannst du die Struktur wichtiger Biomoleküle beschreiben, zentrale biochemische Vorgänge in der Zelle erklären und Zusammenhänge zwischen chemischer Struktur und biologischer Wirkung nachvollziehen.4 ECTSruns this semesterCH0106Biologie für Nebenfächer, 1. TeilNo ratings for this module yet.C Mathematical Theories in other DisciplinesDu erhältst grundlegendes Wissen der Zellbiologie, Genetik, Evolution und Biodiversität. Am Modulende kannst du den Aufbau und die Funktion von Zellen erklären, die Prinzipien genetischer Information und ihrer Regulation beschreiben sowie Grundlagen der Evolution und zoologischen Systematik nachvollziehen.3 ECTSruns this semesterWZ8057Biologie für Nebenfächer, 2. TeilNo ratings for this module yet.C Mathematical Theories in other DisciplinesDas Modul vermittelt grundlegende Kenntnisse zur Vielfalt des Lebens, zu Aufbau und Funktion von Pflanzen und Tieren sowie zu ökologischen und biogeografischen Zusammenhängen. Du lernst zentrale biologische Konzepte und Prozesse zu beschreiben, zu erklären und auf konkrete Fragestellungen anzuwenden.3 ECTSruns this semesterWZ8063Biomechanik - Grundlagen und ModellbildungNo ratings for this module yet.C Mathematical Theories in other DisciplinesDu lernst, wie mechanische Prinzipien auf biologische Systeme angewendet werden, um deren Funktion zu verstehen, krankhafte Veränderungen vorherzusagen und mögliche Therapieansätze zu erarbeiten. Anhand von Beispielen (z. B. Lunge, Knochen, kardiovaskuläres System) übst du Modellbildung: von anatomisch-physiologischen Grundlagen über Auswahl relevanter Effekte bis zur einfachen mathematischen Beschreibung. Schwerpunkte sind Gewebemechanik (passiv/aktiv, Wachstum, Remodelling) und Strömungs- bzw. Transportmodelle in Blutgefäßen und Atemwegen (Vergleich 3D/1D/0D).5 ECTSno date this semesterMW1817BiophysikNo ratings for this module yet.C Mathematical Theories in other DisciplinesDu lernst grundlegende Konzepte der theoretischen und experimentellen Biophysik. Das Modul vermittelt Bausteine lebender Systeme, Enzymkinetik, Struktur- und Musterbildung, Neurobiophysik, Bioenergetik, Nichtgleichgewichts-Thermodynamik, molekulare Wechselwirkungen sowie Simulations- und Modellierungsmethoden. Am Ende kannst Du diese Prozesse quantitativ beschreiben und physikalisch ableiten.10 ECTSno date this semesterPH0020Chemie in Alltag und Technik, KlausurNo ratings for this module yet.C Mathematical Theories in other DisciplinesDu lernst, wie aus Rohstoffen über die Value Chain vom Bohrloch zum Polymer industrielle Chemieprodukte entstehen und welche chemischen, physikalischen und prozesstechnischen Parameter dabei entscheidend sind. Schwerpunkte sind Grundlagen zu Polymerstruktur, Polymerisationen, Molmassenbestimmung, thermisches/mechanisches Verhalten von Kunststoffen sowie aktuelle Themen wie Biopolymere, CO2-basierte Verfahren, Recycling und Anwendungstechnik.5 ECTSno date this semesterCH0780Differentialformen in der PhysikNo ratings for this module yet.C Mathematical Theories in other DisciplinesDu lernst die Grundlagen der Differentialtopologie und Differentialformen kennen und kannst k-Formen auf Mannigfaltigkeiten integrieren. Du verstehst den allgemeinen Satz von Stokes, zentrale Verallgemeinerungen der klassischen Vektoranalysis (z. B. Poincaré-Lemma) und erhältst Einblicke in Anwendungen, etwa zur koordinatenfreien Formulierung der Maxwellgleichungen.5 ECTSno date this semesterNAT3043Differentialgeometrie in der PhysikNo ratings for this module yet.C Mathematical Theories in other DisciplinesIn diesem Modul lernst Du Grundlagen der Differentialgeometrie von Kurven und Flächen und ihre Übertragung auf gekrümmte Mannigfaltigkeiten. Am Ende kannst Du Konzepte wie Krümmung, Torsion, erste Fundamentalform, Riemannsche Metrik und grundlegende Krümmungsgrößen (z. B. Gauss-, Ricci- und Einstein-Tensor) anwenden und einfache Rechnungen dazu durchführen.8 ECTSno date this semesterNAT3020Einführung in die GenetikNo ratings for this module yet.C Mathematical Theories in other DisciplinesDu erhältst eine Einführung in die Grundlagen der Genetik von der Struktur einzelner Gene bis zur Organisation ganzer Genome. Du lernst molekulare Mechanismen der Vererbung, Mutationen, Rekombination und Genregulation kennen und bekommst Einblicke in rekombinante DNA‑Technologien sowie genomische Fragestellungen. Am Ende bist du in der Lage, genetische Zusammenhänge zu beschreiben, zu interpretieren und auf einfache Problemfälle anzuwenden.5 ECTSruns this semesterWZ2002Einführung in die HochfrequenztechnikNo ratings for this module yet.C Mathematical Theories in other DisciplinesDu lernst das Verhalten von Schaltungen, Bauelementen und Leitungen bei hohen Frequenzen kennen. Du kannst Ebene Wellen und Leitungswellen berechnen, grundlegende Antennenprinzipien verstehen und Funkverbindungen aus Sicht der Energieerhaltung beschreiben.5 ECTSruns this semesterEI0609Einführung in die Mikrobielle ÖkologieNo ratings for this module yet.C Mathematical Theories in other DisciplinesDu erhältst eine Einführung in die Mikrobielle Ökologie. Am Ende kennst du grundlegende Konzepte und Zusammenhänge mikrobieller Lebensgemeinschaften und ihre Bedeutung in ökologischen Prozessen.3 ECTSno date this semesterWZ0360Einführung in die Physik der kondensierten MaterieNo ratings for this module yet.C Mathematical Theories in other DisciplinesDu lernst die physikalischen Grundlagen von Festkörpern: von Bindungsarten und Kristallstrukturen über Gitterdynamik und thermische Eigenschaften bis zu Elektronenzuständen, Transport, Halbleitern, Supraleitern, Magnetismus und dielektrischen Eigenschaften. Am Ende kannst du diese Konzepte auf einfache Kristalle und typische Materialien anwenden und die zugrundeliegenden Experimente und Berechnungen verstehen.8 ECTSruns this semesterPH0019Einführung in die Theoretische InformatikNo ratings for this module yet.C Mathematical Theories in other DisciplinesDu erhältst eine systematische Einführung in die Theorie formaler Sprachen, Berechenbarkeit und Komplexität. Am Ende kannst du formale Sprachen mit passenden Beschreibungsmitteln (z. B. Automaten, Grammatiken, reguläre Ausdrücke) darstellen und analysieren, Unentscheidbarkeits- und Komplexitätseigenschaften nachweisen sowie grundlegende Reduktionen durchführen.8 ECTSno date this semesterIN0011Fahrzeugkonzepte: Entwicklung und SimulationNo ratings for this module yet.C Mathematical Theories in other DisciplinesDu lernst den Automobilentwicklungsprozess von der Planung bis zur Produktion kennen und übst, Fahrzeugkonzepte systematisch zu bewerten. Am Ende kannst du Prozessphasen, Meilensteine und gängige Simulationsmethoden erklären sowie Handlungsempfehlungen für frühe Entwicklungsphasen ableiten.5 ECTSruns this semesterMW1586Finite ElementeNo ratings for this module yet.C Mathematical Theories in other DisciplinesDu lernst, wie Strukturen des Ingenieurwesens mit der Finite-Elemente-Methode (FEM) modelliert, diskretisiert und numerisch gelöst werden. Am Ende kannst du passende Modell- und Elementtypen auswählen, FEM-Lösungen durchführen und deren Ergebnisse kritisch einschätzen.5 ECTSno date this semesterMW0612Finite Elemente in der FluidmechanikNo ratings for this module yet.C Mathematical Theories in other DisciplinesIn diesem Modul lernst Du, Finite-Elemente-Methoden für stationäre und zeitabhängige Konvektions‑Diffusions‑Probleme sowie für inkompressible Strömungen zu entwickeln und anzuwenden. Am Ende kannst Du die grundlegenden numerischen Herausforderungen solcher fluidmechanischen Probleme erkennen und geeignete FE‑Strategien zur Lösung einsetzen.3 ECTSno date this semesterMW2452Fluidmechanik 1No ratings for this module yet.C Mathematical Theories in other DisciplinesDu lernst die Grundlagen der Mechanik von Flüssigkeiten und Gasen: physikalische Eigenschaften, kinematische Beschreibung, Erhaltungssätze (Masse, Impuls, Energie), Bernoulli, Navier–Stokes, einfache kompressible Strömungen, Reibung, Turbulenz und technische Strömungen. Am Ende kannst du Strömungen kinematisch und dynamisch analysieren, einfache exakte Lösungen der Navier–Stokes-Gleichungen ermitteln und technische Strömungsprobleme beurteilen.6 ECTSno date this semesterMW2021Fluidmechanik 2No ratings for this module yet.C Mathematical Theories in other DisciplinesDu vertiefst die Mechanik von Gasen und Flüssigkeiten mit Schwerpunkt auf Wirbelströmungen, Potentialströmungen und Grenzschichten. Am Ende kannst du diese Strömungsarten beschreiben, mit Elementarwirbeln und Elementarpotentialen modellieren sowie Grenzschichtprobleme (theoretisch und näherungsweise) analysieren und abgelöste Strömungen sowie laminar-turbulente Transition phänomenologisch beschreiben.5 ECTSruns this semesterMW1910Fortgeschrittene Mathematische Physik: Konzepte und AnwendungenNo ratings for this module yet.C Mathematical Theories in other DisciplinesDu lernst fortgeschrittene Methoden der mathematischen Physik: von Wahrscheinlichkeitstheorie und statistischer Mechanik über mathematische Grundlagen der Quanteninformation bis zu grundlegenden Aspekten der Differentialtopologie. Am Ende kannst Du sowohl probabilistische Grenzwertsätze und grundlegende statistische-physikalische Modelle nachvollziehen als auch Quantenmechanische Zustände/Operationen und einfache topologische sowie differenzierbare Mannigfaltigkeiten formell behandeln.8 ECTSno date this semesterNAT3032Fortgeschrittene QuantenmechanikNo ratings for this module yet.C Mathematical Theories in other DisciplinesDu lernst fortgeschrittene Methoden der Quantenmechanik: zeitabhängige Störungstheorie, Streutheorie und Systeme identischer Teilchen. Am Ende kannst du Übergangswahrscheinlichkeiten (Fermis goldene Regel) ableiten und berechnen, Streuamplituden und Wirkungsquerschnitte bestimmen sowie Resonanzen und Lebensdauern von Zuständen analysieren.5 ECTSno date this semesterPH0024Fortgeschrittene Themen des SoftwaretestsNo ratings for this module yet.C Mathematical Theories in other DisciplinesDu lernst Methoden, Techniken und Managementaspekte des Softwaretestens kennen. Am Ende kannst du Testaktivitäten und -artefakte benennen, ihre Vor- und Nachteile einschätzen und in konkreten Kontexten Testfälle konzeptuell und beispielhaft erstellen und analysieren.5 ECTSno date this semesterIN2084GenetikNo ratings for this module yet.C Mathematical Theories in other DisciplinesDu lernst die grundlegenden Mechanismen der Vererbung und Genexpression im Kontext von Biochemie und Zellbiologie. Schwerpunkt ist die Genetik von Eukaryonten (mit Bezügen zu Anwendungen in Getränken, Pharmazeutika und Lebensmitteln). Am Ende kannst Du Abläufe der Genexpression beschreiben, die beteiligten Proteine erklären und DNA-Analysemethoden auswählen sowie Ergebnisse auswerten.5 ECTSno date this semesterWZ0703Genetische Übungen für Berufliche BildungNo ratings for this module yet.C Mathematical Theories in other DisciplinesDu führst grundlegende Experimente der klassischen und molekularen Genetik praktisch durch, lernst Versuchsaufbau, Durchführung und Auswertung und vertiefst dazu die theoretischen Grundlagen. Am Ende kannst du genetische Versuche handlungssicher durchführen, experimentelle Daten analysieren und die Ergebnisse kritisch beurteilen.4 ECTSno date this semesterWZ0015Grundlagen der IT-SicherheitNo ratings for this module yet.C Mathematical Theories in other DisciplinesIn diesem Modul erhältst du einen grundlegenden Überblick über zentrale Bereiche der IT-Sicherheit. Du lernst Bedrohungen und Angriffsarten kennen, verstehst kryptographische Verfahren sowie Authentifizierungs- und Zugriffskontrollen und kannst Sicherheitsmaßnahmen für Netzwerke, Systeme und organisatorische Abläufe einschätzen.5 ECTSruns this semesterEI04002Grundlagen der Makromolekularen Chemie, KlausurNo ratings for this module yet.C Mathematical Theories in other DisciplinesDu lernst die Einteilung, Synthesewege und Eigenschaften synthetischer Makromoleküle sowie die zugehörigen Herstellverfahren. Am Ende kannst du Polymere nach Herkunft, Struktur und Polymerisationsart einordnen, typische technische Synthesen der Monomere skizzieren und Grundbegriffe der Polymeranalyse, Polymerisationskinetik sowie Prozesstechnologie beschreiben.5 ECTSruns this semesterCH3211Grundlagen der numerischen StrömungsmechanikNo ratings for this module yet.C Mathematical Theories in other DisciplinesIn diesem Modul lernst Du die Grundgleichungen der Strömungsmechanik sowie deren Einordnung als hyperbolische, elliptische oder parabolische Differentialgleichungen kennen. Du übst räumliche und zeitliche Diskretisierungen (Finite Differenzen, Finite Volumen, gewichtete Residuen), analysierst Stabilität, Konsistenz und Genauigkeit und wendest Lösungsverfahren insbesondere für inkompressible Strömungen an.5 ECTSruns this semesterMW1913Grundlagen der ThermodynamikNo ratings for this module yet.C Mathematical Theories in other DisciplinesDu lernst die grundlegenden Konzepte der Thermodynamik und ihre Anwendung auf technische Systeme. Am Ende kannst du Energie-, Masse- und Entropiebilanzen aufstellen, einfache Zustandsänderungen und Kreisprozesse beschreiben sowie Wärme- und Arbeitsflüsse in Geräten berechnen und bewerten.6 ECTSruns this semesterMW2015Grundlagen Genetik und ZellbiologieNo ratings for this module yet.C Mathematical Theories in other DisciplinesIn diesem Modul lernst Du die grundlegenden Prinzipien der Genetik und Zellbiologie. Du verstehst molekulare Grundlagen von Vererbung und Genregulation sowie Aufbau und Funktion von Zellen und ihren Organellen. Am Ende kannst Du Wechselwirkungen zwischen Erbsubstanz, molekularen Strukturen und Zellphysiologie beschreiben.6 ECTSno date this semesterWZ0128Holomorphe Methoden in der PhysikNo ratings for this module yet.C Mathematical Theories in other DisciplinesDu erweiterst Deine Kenntnisse der Funktionentheorie und lernst, wie holomorphe Funktionenräume (z. B. Bergman, Segal–Bargmann, Hardy) als Banach- bzw. Hilberträume behandelt werden. Du lernst Verbindungen zur Funktionalanalysis und Geometrie sowie Methoden zur Quantisierung klassischer Theorien kennen und wendest Konzepte wie Toeplitz‑Operatoren und meromorphe Funktionen auf der Riemann‑Sphäre an. Am Ende kannst Du reproduzierende Kerne berechnen, Quantisierungsschemata erklären und holomorphe bzw. meromorphe Abbildungen unter geeigneten Voraussetzungen anwenden.5 ECTSno date this semesterNAT3062Human- und TierphysiologieNo ratings for this module yet.C Mathematical Theories in other DisciplinesDu lernst grundlegende Prinzipien der Physiologie von Tieren und Menschen: Energetik, Gleichgewichte, Erregungsphysiologie, Sinneswahrnehmung sowie die Organisation des Zentralnervensystems. Außerdem werden Atmung, Kreislauf, Thermoregulation, Ernährung, Stoffwechsel, Exkretion, Hormonsysteme, Immunologie und Grundlagen der Pathophysiologie behandelt. Am Ende kannst du physiologische Steuerungsprozesse erklären, Befunde einordnen und Wissen auf vertiefte Fragestellungen anwenden.6 ECTSno date this semesterWZ0022Instationäre Aerodynamik 1No ratings for this module yet.C Mathematical Theories in other DisciplinesIn diesem Modul untersuchst Du instationäre Vorgänge in der Aerodynamik von Tragflügeln und lernst, wie strömungs- und bewegungsbedingte zeitabhängige Kräfte entstehen und sich auswirken. Am Ende kannst Du die grundlegenden Ansätze der instationären Tragflügeltheorie anwenden und instationäre aerodynamische Kenngrößen sowie Derivativa für einfache Fragestellungen ermitteln.3 ECTSruns this semesterMW0183IT-SicherheitNo ratings for this module yet.C Mathematical Theories in other DisciplinesDu lernst grundlegende Konzepte, Verfahren und Protokolle zur Absicherung von Daten, Komponenten und Systemen. Das Modul vermittelt Ursachen heutiger Sicherheitsprobleme, gängige Angriffe, praxisrelevante Kryptographie sowie Konzepte zur Authentisierung, Zugriffskontrolle, Netzwerksicherheit und betriebliches IT-Sicherheitsmanagement. Am Ende kannst du Schutzmechanismen einordnen, auf Fallbeispiele anwenden und einfache Sicherheitsmaßnahmen beurteilen.5 ECTSruns this semesterIN0042Kern-, Teilchen- und Astrophysik 1No ratings for this module yet.C Mathematical Theories in other DisciplinesDu lernst die Grundlagen der Kern-, Teilchen- und Astrophysik: experimentelle Nachweismethoden, Prinzipien von Teilchenbeschleunigern, sowie die theoretischen Konzepte des Standardmodells (inkl. Klein‑Gordon/Dirac, QED, QCD). Am Ende verstehst Du Aufbau und Wechselwirkungen von Elementarteilchen und kannst einfache Phänomene mit den Grundlagen des Standardmodells erklären.9 ECTSruns this semesterPH0014Kern-, Teilchen- und Astrophysik 2No ratings for this module yet.C Mathematical Theories in other DisciplinesDu erhältst kompaktes Wissen zur Teilchen-, Kern- und Astrophysik: vom Standardmodell (insbesondere schwache Wechselwirkung, Yukawa-Kopplungen, CKM-Matrix, CP-Verletzung und Flavour-Oszillationen) über Kernphysik (NN-Wechselwirkungen, Kernmodelle, Radioaktivität, Reaktionen, kollektive Phänomene) bis zu Grundlagen der nuklearen Astrophysik und Kosmologie. Am Ende verstehst du die zentralen Modelle, Konzepte und Beispielrechnungen dieses Spektrums.9 ECTSno date this semesterPH0015Management AccountingNo ratings for this module yet.C Mathematical Theories in other DisciplinesDu lernst Methoden der Kostenplanung, Kostenkontrolle und der Kosten‑ und Erlösrechnung kennen und anwenden. Schwerpunkte sind Grenzplankosten‑ und Deckungsbeitragsrechnung, relative Einzelkostenrechnung, Prozesskostenrechnung/Activity Based Costing und Target Costing sowie die Abstimmung kurzfristiger Kostenrechnung mit Investitionsrechnung.6 ECTSruns this semesterWI000233MechanikNo ratings for this module yet.C Mathematical Theories in other DisciplinesDas Modul behandelt nichtlineare Kontinuumsmechanik und die Dynamik mechanischer Systeme. Du lernst Verfahren zur Beschreibung und Modellierung kontinuierlicher Körper (Deformation, Spannung etc.) sowie Methoden zur Analyse von Mehrkörpersystemen, Schwingungen und Stabilität.5 ECTSno date this semesterMW0002Meteorologie, Klimatologie und KlimawandelNo ratings for this module yet.C Mathematical Theories in other DisciplinesIn diesem Modul lernst Du die Grundlagen der Meteorologie, Klimatologie und des Klimawandels. Du verstehst meteorologische Grundbegriffe, Berechnung meteorologischer Parameter, großräumige und regionale Klimaprozesse sowie Wechselwirkungen zwischen Atmosphäre, Landnutzung und Städten und kannst Auswirkungen von Klimaveränderungen abschätzen.5 ECTSruns this semesterWZ0008Methoden komplexer SystemeNo ratings for this module yet.C Mathematical Theories in other DisciplinesDu lernst Methoden zur Analyse und Modellierung komplexer sozialer Systeme kennen. Dazu gehören Soziale Netzwerkanalyse, zentrale sozialwissenschaftliche Theorien, Simulations- und Visualisierungstechniken. Am Ende kannst Du diese Methoden auf eigene Forschungsfragen und Datensätze anwenden.6 ECTSno date this semesterPOL10200Methoden komplexer SystemeNo ratings for this module yet.C Mathematical Theories in other Disciplines3 ECTSno date this semesterPOL10200_2Methoden komplexer Systeme - ÜbungsleistungNo ratings for this module yet.C Mathematical Theories in other Disciplines3 ECTSno date this semesterPOL10200_1MikrobiologieNo ratings for this module yet.C Mathematical Theories in other DisciplinesDu erhältst grundlegendes Wissen über Mikroorganismen, mit Schwerpunkt auf prokaryotischen Arten (Bakterien und Archaeen). Du lernst Aufbau, Wachstum, Ernährung und Stoffwechsel dieser Organismen sowie ihre Rolle in Stoffkreisläufen, ihre Wechselwirkungen mit anderen Lebewesen und Anwendungen in biotechnologischen Verfahren.3 ECTSno date this semesterWZ0016Model Reference Adaptive ControlNo ratings for this module yet.C Mathematical Theories in other Disciplines3 ECTSruns this semesterMW2288Modellierung von EnergiesystemenNo ratings for this module yet.C Mathematical Theories in other DisciplinesIn dem Modul lernst Du, wie Energiesysteme mit unterschiedlichen mathematischen und ökonomischen Modellierungsansätzen beschrieben werden. Am Ende kannst Du geeignete Modelltypen auswählen, eigene vereinfachte Modelle aufstellen sowie bestehende Modelle aus der Praxis kritisch einordnen und bewerten.5 ECTSno date this semesterEI70870Moderne Methoden der Regelungstechnik 1No ratings for this module yet.C Mathematical Theories in other DisciplinesDu lernst moderne Zustandsraummethoden zur Auslegung von Mehrgrößenregelsystemen kennen und anzuwenden. Am Ende kannst du lineare Zustandsregler und Zustandsbeobachter entwerfen, Systemeigenschaften wie Stabilität, Steuer- und Beobachtbarkeit beurteilen und Maßnahmen zur Störunterdrückung sowie Ein-/Ausgangs-Linearisierung für ein- bzw. ein-/ausgangslineare Systeme entwerfen.5 ECTSno date this semesterMW0538Molekularbiologische MethodenNo ratings for this module yet.C Mathematical Theories in other DisciplinesDu lernst die molekularbiologischen und zellbiologischen Grundlagen, die für das Verständnis lebender Systeme und ihre biotechnologische Anwendung wichtig sind. Dazu gehören Aufbau und Funktion von Zellen, Membranen, Organellen, Stoffwechsel, Signaltransduktion sowie genetische Prozesse wie Genstruktur, Genexpression und rekombinante DNA-Techniken. Am Ende kannst du diese Grundlagen auf biotechnologische Fragestellungen anwenden und einfache Laborverfahren sicher durchführen und dokumentieren.6 ECTSruns this semesterWZ5425NeurobiologieNo ratings for this module yet.C Mathematical Theories in other DisciplinesDu erhältst einen systematischen Überblick über zentrale Themen der Neurobiologie und erwirbst Kompetenzen, neurobiologische Fragestellungen methodisch und kritisch zu beurteilen. Am Ende kannst du neurobiologische Prozesse aus ihren physikalischen und chemischen Randbedingungen ableiten, ihren Verlauf und ihre Steuerung im Organismus erklären und Befunde in ein Orientierungswissen der gesamten Neurobiologie einordnen.3 ECTSno date this semesterWZ2457Nichtlineare Finite-Element-MethodenNo ratings for this module yet.C Mathematical Theories in other DisciplinesIn diesem Modul lernst du, wie die Finite-Elemente-Methode auf technische Probleme mit geometrischer und materieller Nichtlinearität angewendet wird. Am Ende kannst du geeignete Dehnungs- und Spannungsmaße wählen, nichtlineare Gleichgewichtspfade berechnen und kritische Punkte bzw. Stabilitätsphänomene erkennen.5 ECTSno date this semesterMW0620Nichtlineare KontinuumsmechanikNo ratings for this module yet.C Mathematical Theories in other DisciplinesDu lernst die theoretischen Grundlagen zur Beschreibung des Verhaltens kontinuierlicher Körper unter Kräften. Dazu gehören Tensorrechnung, Kinematik, Bilanzgleichungen und konstitutive Beziehungen; am Ende kannst du quantitative Methoden zur Beschreibung beliebiger kontinuierlicher Systeme anwenden und erkennst, wie technische Mechanik und Fluidmechanik als Spezialfälle eingeordnet werden.5 ECTSno date this semesterMW0850PflanzenphysiologieNo ratings for this module yet.C Mathematical Theories in other DisciplinesDu lernst die grundlegenden physikalischen, chemischen und biologischen Prozesse, die das Funktionieren von Pflanzen steuern: Wasser- und Mineralhaushalt, Transport über Membranen sowie in Xylem und Phloem, Photosynthese und Respiration, Entwicklungsprozesse, Hormon- und Lichtwahrnehmung, Stressreaktionen und biotische Interaktionen. Am Ende kannst du pflanzenphysiologische Vorgänge auf ihre Grundlagen zurückführen, Netzwerke von Regulationsprozessen verstehen und Konsequenzen von Störungen ableiten sowie Ergebnisse der vergleichenden Pflanzenphysiologie kritisch einordnen und auf angewandte Fragestellungen übertragen.4 ECTSruns this semesterWZ0024Physik der kondensierten Materie 2No ratings for this module yet.C Mathematical Theories in other DisciplinesIm Modul lernst Du zentrale Konzepte der Festkörperphysik für Metalle, Halbleiter, Dielektrika, Magnetismus, Supraleitung sowie Oberflächen und Grenzflächen. Du kannst am Ende elektrische, magnetische und optische Eigenschaften unterschiedlicher Materialklassen mit Kristallstruktur, Bandstruktur und relevanten Modellen erklären und experimentelle Methoden zur Charakterisierung benennen.9 ECTSno date this semesterPH0018Praktikum Numerische StrömungssimulationNo ratings for this module yet.C Mathematical Theories in other DisciplinesDu arbeitest mit der kommerziellen CFD-Software ANSYS-CFX zur Lösung praktischer fluidmechanischer Fragestellungen. Am Ende kannst Du gegebene Rechengitter importieren, Rand- und Startbedingungen setzen, geeignete physikalische und numerische Modelle wählen, Simulationen durchführen, Ergebnisse per Postprocessing auswerten und deren Qualität kritisch beurteilen.4 ECTSruns this semesterMW1846RegelungstechnikNo ratings for this module yet.C Mathematical Theories in other DisciplinesIn diesem Modul lernst du, technische Systeme zu beschreiben, zu analysieren und durch Regler so zu beeinflussen, dass gewünschtes Verhalten am Ausgang entsteht. Du erwirbst Methoden zur Modellbildung, Zeit- und Frequenzbereichsanalyse, Reglerentwurf (inkl. Zustandsregelung) sowie zur digitalen Realisierung von Regelungen.5 ECTSruns this semesterMW2022Regelungstechnik (Prüfung in Deutsch)No ratings for this module yet.C Mathematical Theories in other DisciplinesDu lernst, wie technische Systeme modelliert, analysiert und durch Regelkreise so beeinflusst werden, dass sie gewünschtes dynamisches Verhalten zeigen. Am Ende kannst du lineare Modelle erstellen, Systemeigenschaften wie Stabilität und Übertragungsverhalten beurteilen sowie Regler entwerfen und digital implementieren.5 ECTSruns this semesterED140014Sichere Implementierung kryptographischer VerfahrenNo ratings for this module yet.C Mathematical Theories in other DisciplinesDu lernst, wie kryptographische Verfahren sicher in eingebetteten Systemen implementiert werden und wie typische praktische Angriffe (z. B. Timing-, Strom- und Fehlerangriffe) funktionieren. Am Ende bist du in der Lage, Implementierungen zu entwerfen, Angriffszenarien zu beurteilen und geeignete Schutzmaßnahmen praktisch anzuwenden.6 ECTSruns this semesterEI7243Stressbiologie und -physiologie der PflanzenNo ratings for this module yet.C Mathematical Theories in other DisciplinesDu lernst, wie Pflanzen auf biotische und abiotische Stressfaktoren reagieren – von Symptomen über molekulare Mechanismen bis zu physiologischen Folgen. Am Ende kannst du Stressauslöser benennen, die zugrunde liegenden Signalwege und Regulationsmechanismen erklären und physiologische Messgrößen zur Bewertung der Pflanzenleistung anwenden und beurteilen.5 ECTSno date this semesterWZ1036Symmetrie und GruppentheorieNo ratings for this module yet.C Mathematical Theories in other Disciplines4 ECTSno date this semesterCH0204Theoretische Physik 2 (Elektrodynamik)No ratings for this module yet.C Mathematical Theories in other DisciplinesDu lernst die klassische Elektrodynamik: Elektro- und Magnetostatik, Maxwellsche Gleichungen in Vakuum und in Materie, Potenziale und Eichtransformationen sowie Energie- und Impulssätze. Außerdem werden Wellen, Beugung, Multipolentwicklung, das Feld bewegter Punktladungen und Grundlagen der speziellen Relativitätstheorie behandelt.8 ECTSruns this semesterPH0006Theoretische Physik 3 (Quantenmechanik)No ratings for this module yet.C Mathematical Theories in other DisciplinesIn diesem Modul lernst du die Grundlagen der nichtrelativistischen Quantenmechanik: Beschreibung von Zuständen, Messprozessen, zeitlicher Entwicklung sowie wichtige Lösungsmethoden für Potentialprobleme. Am Ende kannst du typische ein- und dreidimensionale Probleme (z.B. Wasserstoff), Näherungsverfahren, Spinsysteme und Zwei-Niveau-Modelle rechnen und Quantenverschränkung sowie Dichtematrizen verstehen.9 ECTSno date this semesterPH0007Theoretische Physik 4A (Statistische Mechanik und Thermodynamik)No ratings for this module yet.C Mathematical Theories in other DisciplinesDu lernst Grundlagen der statistischen Mechanik und der Thermodynamik: von Ensemble-Theorie über thermodynamische Potentiale, Phasenübergänge und ideale/wechselwirkende Gase bis hin zu Elementen der Nichtgleichgewichts-Thermodynamik. Am Ende kannst du Temperatur, Wärme, Entropie und chemisches Potential formal beschreiben, ideale Quanten-Gase analysieren sowie grundlegende Aspekte von Phasenübergängen und Transportprozessen erklären.9 ECTSruns this semesterPH0008Theoretische Physik 4B (Thermodynamik und Elemente der statistischen Mechanik)No ratings for this module yet.C Mathematical Theories in other DisciplinesIn diesem Modul lernst Du Thermodynamik und elementare statistische Mechanik: von Temperatur, Wärme und Entropie über Ensemble- und Zustandssummen bis zu idealen Quanten- und wechselwirkenden Gasen sowie Phasenübergängen und einigen Nichtgleichgewichtsmechanismen. Am Ende kannst Du die Verbindung zwischen mikroskopischer Statistik und makroskopischer Thermodynamik erklären und typische Modelle und Rechnungen selbständig anwenden.9 ECTSno date this semesterPH0012ZellbiologieNo ratings for this module yet.C Mathematical Theories in other DisciplinesIn diesem Modul lernst Du Aufbau, Funktion und Zusammenspiel von pro- und eukaryotischen Zellen kennen. Du verstehst Organellen, molekulare Grundlagen (Proteine, DNA/RNA), Membranen und Transportprozesse sowie zentrale zelluläre Prozesse wie Teilung, Signaltransduktion, Differenzierung und Apoptose. Am Ende kannst Du Zellstrukturen und -funktionen erklären und Zusammenhänge zwischen Molekülen, Zellen und Organismen diskutieren.5 ECTSruns this semesterWZ0601