## Find the right courses

Below we have compiled a list of suitable English taught courses for exchange students. If you switch to the German version of the page, you will find the German taught courses. If you have any questions about the courses, please contact the International Coordinators.

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## Course selection for exchange students

Below you will find a list of the English taught courses that we recommend for exchange students.

Lineare Algebra 1 (eng) B.Sc. 1. Semester 9 graded algebraic structures (Groups, Rings, Fields); Vectorspaces, linear dependency, Bases, Dimension; linear and affine Subspaces, Products, Sums, Quotients, dual space; linear maps and Matrices; linear systems of equations; Determinants
Complex Analysis B.Sc. 1. Semester 5 graded Cauchy-Riemann Differential Equations; curve integral; Cauchy´s integral theorem/formula; power series; Liouville´s theorem; Laurentseries; Residue theorem
Proseminar (eng) B.Sc. 3. Semester 3 ungraded You must prepare a talk to a specific subject, that will be announced at the begining of the semester
Seminar (eng) B.Sc./M.Sc. 5 ungraded You must prepare a talk to a specific subject, that will be announced at the begining of the semester
Introduction to Mathematical Logic B.Sc. 5. Semester 9 graded Syntax and semantics of first level logic; formal proofs; Completeness; Compactness theorem; elementary recursion theory; Undecidability and Incompleteness
Probability Theory B.Sc. 5. Semester 9 graded Measure theory basics, Random variables, types of convergence, characteristic functions, independence, conditional expectation, martingales, limit theorems
Nonlinear Optimization M.Sc. 1. Semester 9 graded Modelling practical questions as Optimizationproblems; Optimality conditions, Duality theorie; methods for Problems without constraints: Linesearch-and Trust-Region-methods; methods for Problems with constraints: Penalty-, Inner-Point- and SQP-methods
Numerical Methods for PDEs M.Sc. 1. Semester 9 graded Examples of partial differential equations from practice; Elliptical problems; Galerkina approximation, finite element methods, error analysis; Parabolic problems; Semi and full discretization using Method of lines;
Analysis 2 (eng) B.Sc. 2. Semester 9 graded convergence of series of functions, Power series, Topology of metric spaces, Norms on R^n, Differentiation in multiple variables, partial derivatives, Gradient, Taylor's theorem in multiple variables, lokal Extrema, implicit functions, Integration in higher dimensions: curvs in R^n
Algorithmic Discrete Mathematics B.Sc. 4. Semester 5 graded Graph theorie, asymptotic complexity, algorithms to spanning trees, shortest paths, Matchings in bipartit graphs und flows in directet graphs, NP-Completness
Seminar (eng) B.Sc./M.Sc. 5 ungraded You must prepare a talk to a specific subject, that will be announced at the begining of the semester
Sobolev Spaces B.Sc. 6. Semester 5 graded Construction of Sobolev-Spaces, Embedding- und Trace theorems, application to Partial Differential Equations
Graph Theory B.Sc. 6. Semester 9 graded
Partial Differential Equations 2 M.Sc. 2. Semester 9 graded
existence, uniquness und regularity of solutions of linear/ nonlinearer partial differential equations, prefered are application to Fluid mechanics or Material sciences,
content differs depending on lecturer
Applied Proof Theory M.Sc. 2. Semester 9 graded Herbrand-Theorie, Kreisels no-counterexample Interpretation, Gödels Functional Interpretation, monotone Interpretations