Lecture notes

(mostly in German)

Nonsmooth analysis and optimization

(Convex analysis, proximal point and splitting methods, Clarke subdifferential, semismooth Newton method)

Stochastic optimization

(Optimization under uncertainty: Minimization of expected value functionals, Monte Carlo approximation, stochastic subgradient method, robust optimization and risk measures; basics of convex optimization and probability theory)

Nonlinear optimization

(Theory and numerical methods for optimization problems with constraints: Tangent cones, KKT constraints, penalty methods, barrier and interior-point methods, SQP methods; convex optimization: subdifferentials, Fenchel duality, subgradient methods)

(Theory and numerical methods for optimization problems with and without constraints)

Optimization 1

(Unrestricted nonlinear optimization; linear optimization)

(Linear optimization: duality theory and simplex methods)

Numerical partial differential equations

(Finite element method for elliptic and parabolic differential equations)

Krylov space methods

(Krylov space methods for linear systems of equations, eigenvalue problems and balancing problems; accompanying: short introduction to MATLAB)

Numerical mathematics 2

(Iterative methods for systems of linear equations and eigenvalue problems; introduction to numerical methods for ordinary differential equations)

Numerical mathematics 1

(numerical representation and error analysis, direct methods for linear systems of equations and balancing, polynomial and spline interpolation, FFT, numerical integration, nonlinear equations)

Stochastics for teacher training

(Introduction for teacher candidates: Probability spaces, discrete random variables, expected value and variance, conditional probability and independence, real-valued random variables, statistics, point estimators, set estimators, hypothesis tests)

Functional analysis I

(Linear operators in Banach and Hilbert spaces, spectral theory for compact operators)

Mathematical image processing

(Variation methods and proximal point methods in image processing)

Inverse problems

(Regularization theory for linear and nonlinear ill-posed operator equations)

Fundamentals of mathematics

(Introduction to elementary logic, set theory and proof strategies)

Applied Numerical Mathematics I

(Introduction to numerical linear algebra, analysis and differential equations for computational scientists)

Numerics for teacher candidates

(Introduction to numerical linear algebra and analysis for teacher candidates)