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A1.2 Applied Mathematics7

FunktionalanalysisNo ratings for this module yet.You 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 semesterMA3001Numerik der DifferentialgleichungenNo ratings for this module yet.You 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 semesterMA3301Probability TheoryNo ratings for this module yet.You 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 semesterMA2409Computational StatisticsNo ratings for this module yet.You 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 semesterMA4402Numerical Methods for Partial Differential EquationsNo ratings for this module yet.You 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 semesterMA3303
2 more in A1.2 Applied MathematicsPartielle DifferentialgleichungenNo ratings for this module yet.In 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 semesterMA3005Stochastic AnalysisNo ratings for this module yet.You 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 semesterMA4405