Course selection for exchange students
Below you will find a list of the English taught courses that we recommend for exchange students.
Please note that proseminars and seminars are not graded. Should you nevertheless require a grade, please contact the lecturer directly in the first lesson unit.
Please contact us if you wish to take courses in other departments.
For the list of German taught courses please visit the German translation of this page.
| Course | Level | CP | Graded/ungraded | Description |
|---|---|---|---|---|
| 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; |
| Course | Level | CP | Graded/ungraded | Description |
|---|---|---|---|---|
| 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 |
| Course | Level | CP | Graded/ungraded | Description |
|---|---|---|---|---|
| Analysis 1 | B.Sc. 1. Semester | 9 | graded | Real/complex numbers; convergence of sequences and series; continous/differentiable functions; Mean value Theorem; Taylor's theorem; Integral |
| Complex Analysis | B.Sc. 3. Semester | 5 | graded | Cauchy-Riemann Differential Equations; curve integral; Cauchy´s integral theorem/formula; power series; Liouville´s theorem; Laurentseries; Residue theorem |
| Proseminar | B.Sc. 3. Semester | 3 | ungraded | You must prepare a talk to a specific subject, that will be announced at the beginning of the semester |
| Seminar | B.Sc./M.Sc. | 5 | ungraded | You must prepare a talk to a specific subject, that will be announced at the beginning 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 |
| Probabilty Theory | B.Sc. 5. Semester | 9 | graded | Measure theory basics, Random variables, types of convergence, characteristic functions, independence, conditional expectation, martingales, limit theorems |
| Partial Differential Equations 1 | M.Sc. 1. Semester | 9 | graded | Classical Laplace operator, elliptic boundary value problems, Sobolevspaces, embedding theorems and compactness, regularity theory, eigenvalues of elliptic operators |
| 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; |
| Mathematical Programs with Equilibrium Constraints | M.Sc. | 5 | graded | Eponymous class of optimization problems; Due to the special structure of equilibrium constraints, the optimality conditions known from nonlinear optimization are no longer applicable. Therefore, MPECs require their own optimality theory, in which methods from nonsmooth analysis are applied, and specialized solution algorithms. |
