Modules

50 results

A1.4 Mathematics50

Computational Plasma PhysicsNo ratings for this module yet.A1.4.1 Modules in NumericsYou 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 semesterMA4304Mathematical EcologyNo ratings for this module yet.A1.4.1 Modules in NumericsYou 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.A1.4.1 Modules in NumericsYou 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 semesterMA3601Mathematische Methoden zur Unsicherheitsquantifizierung in der HydrologieNo ratings for this module yet.A1.4.1 Modules in NumericsYou 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 semesterBGU54027Nonconvex Global OptimizationNo ratings for this module yet.A1.4.1 Modules in NumericsYou 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 semesterCIT4130019
45 more in A1.4 MathematicsNumerik der DifferentialgleichungenNo ratings for this module yet.A1.4.1 Modules in NumericsYou 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 semesterMA3301Advanced Finite ElementsNo ratings for this module yet.A1.4.1 Modules in NumericsYou 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 Numerical Linear AlgebraNo ratings for this module yet.A1.4.1 Modules in NumericsIn this module you will learn methods of numerical linear algebra with applications in data assimilation, model reduction and the solution of matrix equations. In the end you will be able to formulate and interpret variational and statistical data assimilation problems, understand and implement common model reduction procedures for linear systems, and apply theory and numerical methods for Lyapunov and Sylvester equations.1 ECTSno date this semesterMA5922Advanced Topics in Uncertainty QuantificationNo ratings for this module yet.A1.4.1 Modules in NumericsYou 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 semesterCIT4130021Applications of Mathematical BiologyNo ratings for this module yet.A1.4.1 Modules in NumericsYou 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 semesterMA3602Case Studies in Scientific ComputingNo ratings for this module yet.A1.4.1 Modules in NumericsYou 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 in Scientific ComputingNo ratings for this module yet.A1.4.1 Modules in NumericsYou work in small interdisciplinary teams on real application problems from science or industry. You model, analyze and solve these problems with modern numerical methods and present the results scientifically (poster, talk, short paper). In the end you can mathematically model complex applications, select appropriate algorithms, implement them and communicate scientifically.10 ECTSno date this semesterCIT413058Case Studies Life Science MathematicsNo ratings for this module yet.A1.4.1 Modules in NumericsYou 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 semesterCIT413052Compressed SensingNo ratings for this module yet.A1.4.1 Modules in NumericsYou 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 Inverse ProblemsNo ratings for this module yet.A1.4.1 Modules in NumericsYou 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 semesterMA4302Delay Differential Equations with ApplicationsNo ratings for this module yet.A1.4.1 Modules in NumericsYou 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 semesterMA5062Discontinuous Galerkin MethodsNo ratings for this module yet.A1.4.1 Modules in NumericsYou 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 semesterMA5343Dynamics of Democratic ElectionsNo ratings for this module yet.A1.4.1 Modules in NumericsYou 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 semesterMA5619Geometric Methods for Physics of Magnetized PlasmasNo ratings for this module yet.A1.4.1 Modules in NumericsYou 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 semesterMA5333Geometric Numerical Integration 1No ratings for this module yet.A1.4.1 Modules in NumericsYou learn the fundamentals of geometric (structure-preserving) numerical integration for ordinary differential equations. In the end you can recognize different geometric structures in differential equations and select and apply suitable numerical methods that preserve these structures.5 ECTSno date this semesterMA5341Geometrische Numerische Verfahren für gewöhnliche DifferentialgleichungenNo ratings for this module yet.A1.4.1 Modules in NumericsYou learn fundamental techniques of geometric (structure-preserving) numerics for ordinary differential equations. In the end you recognize geometric structures in ODEs, know modern integrators that preserve these structures, and can select and implement appropriate procedures.6 ECTSno date this semesterMA5329Gitterfreie VerfahrenNo ratings for this module yet.A1.4.1 Modules in NumericsYou 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 semesterMA5324Identification of Artificial Neural Networks: from the Analysis of one Neuron to Deep Neural NetworksNo ratings for this module yet.A1.4.1 Modules in NumericsYou 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 semesterMA5929Introduction to Conservation LawsNo ratings for this module yet.A1.4.1 Modules in NumericsYou 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 Stochastic Differential Equations: Theory and NumericsNo ratings for this module yet.A1.4.1 Modules in NumericsYou 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 semesterMA5950Isogeometric Analysis: Theory and PracticeNo ratings for this module yet.A1.4.1 Modules in NumericsYou learn B-Splines/NURBS from the CAD side through approximation theory to application in isogeometric finite element methods. In the end you will be able to derive weak formulations for elliptic, Maxwell, and Stokes problems, explain their properties, and implement corresponding finite-element solvers in Python.5 ECTSno date this semesterMA5938Lattice Boltzmann methodsNo ratings for this module yet.A1.4.1 Modules in NumericsYou 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 semesterCIT4130009Low Rank ApproximationNo ratings for this module yet.A1.4.1 Modules in NumericsYou will learn methods for low-rank approximation of matrices and tensors, including singular value decomposition and various tensor factorizations. In the end you will be able to assess which approximation is suitable for a given application and apply and implement it for data compression or analysis.3 ECTSno date this semesterMA5328Mathematical Foundations of ImagingNo ratings for this module yet.A1.4.1 Modules in NumericsYou 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 semesterMA5063Mathematische Einführung in die MagnetohydrodynamikNo ratings for this module yet.A1.4.1 Modules in NumericsYou 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 semesterMA5902Mathematische Grundlagen der Neuronalen NetzeNo ratings for this module yet.A1.4.1 Modules in NumericsThe module conveys selected mathematical foundations for the analysis of artificial neural networks. You will learn how approximation properties, stability with respect to input perturbations, and the learnability of networks are studied using various mathematical tools. In the end you will understand the central theoretical results and the analytical methods used.6 ECTSno date this semesterMA5913Mechanics and SymmetryNo ratings for this module yet.A1.4.1 Modules in NumericsYou will learn mathematical foundations of mechanics with a focus on symmetries: multilinear algebra, differential geometry and Lie groups, variational principles and reduction (Euler–Poincaré), as well as related structures such as symplectic geometry and Lie–Poisson brackets. In the end you will be able to apply variational principles, perform reduction for symmetric systems, and assess conservation laws using momentum maps/Noether arguments.3 ECTSno date this semesterMA5940Methods for Inverse ProblemsNo ratings for this module yet.A1.4.1 Modules in NumericsYou 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 semesterMA5931Models and Numerical Methods for Eulerian and Lagrangian Hyperbolic EquationsNo ratings for this module yet.A1.4.1 Modules in NumericsIn this module you will learn mathematical models and numerical methods for hyperbolic conservation laws in Eulerian and Lagrangian representations. You will engage with fundamentals such as Burgers’, shallow-water and gas dynamics, learn concepts such as weak solutions, shock and rarefaction structure as well as entropy conditions, and implement robust finite-volume methods, also for moving meshes.3 ECTSno date this semesterMA5928Modern Approximation TheoryNo ratings for this module yet.A1.4.1 Modules in NumericsYou 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 semesterMA5952Numerical Analysis for High-dimensional Quantum DynamicsNo ratings for this module yet.A1.4.1 Modules in NumericsYou 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 and Kinetic EquationsNo ratings for this module yet.A1.4.1 Modules in NumericsYou will learn numerical methods for hyperbolic and kinetic partial differential equations. The module covers fundamental discretization procedures (e.g., finite differences, finite volumes, semi-Lagrangian) for hyperbolic conservation laws and methods for high-dimensional kinetic equations as well as asymptotic-preserving methods and applications in control and uncertainty quantification. In the end you will understand the connections between mathematical structure and practical implementation and will be able to apply selected methods to applications.3 ECTSno date this semesterMA5932Numerical Methods for Hyperbolic SystemsNo ratings for this module yet.A1.4.1 Modules in NumericsYou 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.A1.4.1 Modules in NumericsYou 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.A1.4.1 Modules in NumericsYou 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 semesterMA5348Particle in Cell Methods for the Vlasov-Maxwell EquationsNo ratings for this module yet.A1.4.1 Modules in NumericsIn 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 semesterCIT413049Quantum Dynamics 3No ratings for this module yet.A1.4.1 Modules in NumericsYou 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 semesterMA5926Structure Preserving Discretisation on Staggered GridsNo ratings for this module yet.A1.4.1 Modules in NumericsYou will learn principles and methods of structure-preserving discretisations for partial differential equations. Using finite differences on staggered grids and finite element methods, you will learn to design procedures such that fundamental properties of the PDEs (e.g., invariants or Hamiltonian structures) are preserved. In the end you will be able to apply these procedures to classical PDEs such as Maxwell’s or Euler’s equations and assess their advantages and limitations.5 ECTSno date this semesterMA5936Structure-preserving Finite Elements for Computational ElectromagnetismNo ratings for this module yet.A1.4.1 Modules in NumericsIn 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 semesterCIT413044Time-Frequency AnalysisNo ratings for this module yet.A1.4.1 Modules in NumericsYou 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 Dynamical Systems: Computational DynamicsNo ratings for this module yet.A1.4.1 Modules in NumericsYou 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 semesterCIT415303TUM Data Innovation LabNo ratings for this module yet.A1.4.1 Modules in NumericsIn 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 semesterMA8113Variational Inequalities with Applications in Porous MediaNo ratings for this module yet.A1.4.1 Modules in NumericsYou 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.A1.4.1 Modules in NumericsYou 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 semesterCIT4130010Weiterführende Finite-Elemente MethodenNo ratings for this module yet.A1.4.1 Modules in NumericsYou will learn about advanced finite element techniques (e.g. Mixed/Hybrid Elements, Discontinuous Galerkin, Non-conforming methods, adaptive procedures, Isogeometric Analysis) as well as modern iterative solvers and preconditioners. In the end you will be able to analyze these methods, apply them to examples from solid mechanics and incompressible flow, and independently access further specialist literature.5 ECTSno date this semesterMA4303