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M.Sc. Mathematics — Compulsory Elective Modules in Mathematics

In this field of study, modules of 51 or 69 CP must be completed, depending on whether an optional profile area of 18 CP is chosen. At least 18 CP in modules on pure mathematics (marked with an "R") and at least 12 CP in modules on applied mathematics ("A") must be acquired. In addition, at most two advanced modules may be taken.

List of modules in this area of study:

Sorted: alphabetical, by classification, by level and CP

• Algebraic Geometry: Modern Methods (Specialization module, 9 CP, R)
• Algebraic Geometry: Projective Varieties (Specialization module, 9 CP, R)
• Algebraic Lie Theory (Specialization module, 9 CP, R)
• Algebraic Topology I (Specialization module, 9 CP, R)
• Algebraic Topology II (Large Specialization Module) (Specialization module, 9 CP, R)
• Algebraic Topology II (Small Specialization Module) (Specialization module, 6 CP, R)
• Algebras and their Representations (Specialization module, 9 CP, R)
• Analytic Number Theory (Specialization module, 9 CP, R)
• Applied Harmonic Analysis I (Advanced module, 6 CP, A)
• Applied Harmonic Analysis II (Specialization module, 6 CP, A)
• Approximation Theory (Specialization module, 9 CP, A)
• Commutative Algebra (Large Specialization Module) (Specialization module, 9 CP, R)
• Commutative Algebra (Small Specialization Module) (Specialization module, 6 CP, R)
• Complex Geometry I (Specialization module, 9 CP, R)
• Complex Geometry II (Specialization module, 9 CP, R)
• Continuous Optimization (Advanced module, 9 CP, A)
• Differential Geometry I (Specialization module, 9 CP, R)
• Differential Geometry II (Specialization module, 9 CP, R)
• Discrete Geometry (Advanced module, 6 CP, R)
• Discrete Mathematics (Advanced module, 9 CP, R)
• Elementary Algebraic Geometry (Advanced module, 9 CP, R)
• Elementary Number Theory (Advanced module, 6 CP, R)
• Elementary Topology (Advanced module, 6 CP, R)
• Empirical processes (Specialization module, 6 CP, A)
• Financial Mathematics I (Advanced module, 6 CP, A)
• Financial Mathematics II (Specialization module, 6 CP, A)
• Financial Optimization (Specialization module, 6 CP, A)
• Fourier Integral Operators (Specialization module, 9 CP, R)
• Functional Analysis (Specialization module, 9 CP, A&R)
• Galois Theory (Specialization module, 9 CP, R)
• General Relativity (Specialization module, 3 CP, R)
• Group Theory (Advanced module, 6 CP, R)
• High-dimensional Statistics and Machine Learning (Specialization module, 6 CP, A)
• Holomorphic Functions and Abelian Varieties (Specialization module, 9 CP, R)
• Hopf Algebras (Specialization module, 9 CP, R)
• Hopf Algebras II (Specialization module, 9 CP, R)
• Large Advanced Module Algebra/Geometry (Advanced module, 9 CP, R)
• Large Advanced Module Analysis/Topology (Advanced module, 9 CP, R)
• Large Advanced Module Numerical Mathematics/Optimization (Advanced module, 9 CP, A)
• Large Advanced Module Stochastics (Advanced module, 9 CP, A)
• Large Specialization Module Algebra/Geometry (Specialization module, 9 CP, R)
• Large Specialization Module Analysis/Topology (Specialization module, 9 CP, R)
• Large Specialization Module Numerical Mathematics/Optimization (Specialization module, 9 CP, A)
• Large Specialization Module Stochastics (Specialization module, 9 CP, A)
• Lie Groups and Lie Algebras (Advanced module, 9 CP, R)
• Mathematical and Nonparametric Statistics (Specialization module, 9 CP, A)
• Matrix Methods in Data Analysis (Advanced module, 9 CP, A)
• Non-Life Insurance Mathematics (Specialization module, 3 CP, A)
• Noncommutative Algebra (Specialization module, 9 CP, R)
• Numerical Analysis I (Advanced module, 6 CP, A)
• Numerical Analysis II (Specialization module, 6 CP, A)
• Numerical Methods for Ordinary Differential Equations (Specialization module, 6 CP, A)
• Numerical Solution Methods for Differential Equations (Specialization module, 9 CP, A)
• Numerical Solution Methods for Finite Dimensional Problems (Specialization module, 9 CP, A)
• Operations Research (Advanced module, 9 CP, A)
• Optimization I (Advanced module, 6 CP, A)
• Optimization II (Specialization module, 6 CP, A)
• Partial Differential Equations (Specialization module, 9 CP, R)
• Personal Insurance Mathematics (Advanced module, 3 CP, A)
• Probabilistic Combinatorics (Specialization module, 9 CP, A)
• Probability Theory (Specialization module, 9 CP, A)
• Quantitative Risk Management (Specialization module, 6 CP, A)
• Representation Theory (Advanced module, 9 CP, R)
• Selected Topics in Numerical Analysis (Specialization module, 6 CP, A)
• Selected Topics on Financial Mathematics (Specialization module, 3 CP, A)
• Small Advanced Module Algebra/Geometry (Advanced module, 6 CP, R)
• Small Advanced Module Analysis/Topology (Advanced module, 6 CP, R)
• Small Advanced Module Numerical Mathematicss/Optimization (Advanced module, 6 CP, A)
• Small Advanced Module Stochastics (Advanced module, 6 CP, A)
• Small Specialization Module Algebra/Geometry (Specialization module, 6 CP, R)
• Small Specialization Module Analysis/Topology (Specialization module, 6 CP, R)
• Small Specialization Module Numerical Mathematics/Optimization (Specialization module, 6 CP, A)
• Small Specialization Module Stochastics (Specialization module, 6 CP, A)
• Small Specialization Module Stochastics without Tutorial (Specialization module, 3 CP, A)
• Special Topics of Insurance Mathematics (Specialization module, 3 CP, A)
• Spectral and Scattering Theory (Specialization module, 9 CP, R)
• Statistics (Advanced module, 9 CP, A)
• Stochastic Processes (Specialization module, 6 CP, A)
• Stochastical Analysis (Specialization module, 9 CP, A)
• Topological Methods in Data Analysis (Advanced module, 9 CP, A&R)

Please note:

This page applies to the most current examination regulations in Winter semester 2023/24. If you are studying according to an earlier or later examination regulation other provisions may apply:

• Winter 2016/17 (no corresponding element)
• Summer 2018 (no corresponding element)
• Winter 2018/19 (no corresponding element)
• Winter 2019/20 (no corresponding element)
• Winter 2020/21 (no corresponding element)
• Summer 2021 (no corresponding element)
• Winter 2021/22 (no corresponding element)
• Winter 2022/23 (no corresponding element)
• Winter 2023/24

The information in this online module guide was created automatically. Legally binding is only the information in the examination regulations (Prüfungsordnung). If you notice any discrepancies or errors, we would be grateful for any advice.