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This entry is from Winter semester 2022/23 and might be obsolete. No current equivalent could be found.

LAaG Mathematics — Advanced Modules

Modules totaling 48 CP must be completed in this area of study. The modules Elementary Stochastics, Algebra, Mathematics Education: Teaching Algebra, Geometry, Mathematics Education: Teaching Geometry as well as ProfiWerk mathematics are mandatory.

In addition, a small advanced module (with 6 CP) and a large advanced module (with 9 CP) must be selected, of which at least one must be from pure mathematics. Advanced modules in pure mathematics are marked with an "R", advanced modules in applied mathematics are marked with an "A", respectively.

It should be noted that certain elective modules require, in addition to the competencies acquired in the course of study, further competencies that may have to be acquired extracurricularly (in self-study). This particularly concerns the module ''Statistics'' as well as the specialization modules.

List of modules in this area of study:

Sorted: alphabetical, by classification, by level and CP

• Algebra (Advanced module, 9 CP)
• Algebraic Equations and Varieties (Specialization module, 9 CP, R)
• Algebraic Geometry: Advanced 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 (Specialization module, 9 CP, R)
• Algebraic Topology (Small Specialization Module) (Specialization module, 6 CP, R)
• Analytic Number Theory (Specialization module, 9 CP, R)
• Applied Algebraic Geometry (Small Specialization Module) (Specialization module, 6 CP, R)
• Applied Functional Analysis (Specialization module, 9 CP, A)
• Approximation Theory (Specialization module, 9 CP, A)
• Combinatorics (Large Specialization Module) (Specialization module, 9 CP, R)
• Combinatorics (Small Specialization Module) (Specialization module, 6 CP, R)
• Commutative Algebra (Large Specialization Module) (Specialization module, 9 CP, R)
• Commutative Algebra (Small Specialization Module) (Specialization module, 6 CP, R)
• Complex Analysis (Advanced module, 9 CP, R)
• Complex Analysis and Vector Analysis (Advanced module, 9 CP, R)
• 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 Stochastics (Advanced module, 9 CP)
• Elementary Topology (Advanced module, 6 CP, R)
• Functional Analysis (Specialization module, 9 CP, R)
• Galois Theory (Specialization module, 9 CP, R)
• Geometry (Advanced module, 3 CP)
• Holomorphic Functions and Abelian Varieties (Specialization module, 9 CP, R)
• Introduction to Complex Geometry (Specialization module, 9 CP, R)
• Lie Groups and Lie Algebras (Advanced module, 9 CP, R)
• Linear Optimization (Advanced module, 9 CP, A)
• Mathematical Statistics (Specialization module, 9 CP, A)
• Mathematics Education: Teaching Algebra (Advanced module, 3 CP)
• Mathematics Education: Teaching Geometry (Advanced module, 3 CP)
• Measure and Integration Theory (Advanced module, 6 CP, R)
• Non-smooth Optimization (Specialization module, 6 CP, A)
• Noncommutative Algebra (Specialization module, 9 CP, R)
• Nonlinear Optimization (Specialization module, 9 CP, A)
• Number Theory (Advanced module, 9 CP, R)
• Numerical Analysis (Advanced module, 9 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)
• Partial Differential Equations (Specialization module, 9 CP, R)
• Probability Theory (Specialization module, 9 CP, A)
• ProfiWerk mathematics (Advanced module, 6 CP)
• Representation Theory (Advanced module, 9 CP, R)
• Small Advanced Module Algebra/Number Theory/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/Number Theory/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 Optimization (Specialization module, 6 CP, A)
• Small Specialization Module Stochastics (Specialization module, 6 CP, A)
• Spectral and Scattering Theory (Specialization module, 9 CP, R)
• Statistics (Advanced module, 6 CP, A)
• Stochastic Optimization (Specialization module, 6 CP, A)
• Stochastical Analysis (Specialization module, 9 CP, A)
• Topology (Advanced module, 9 CP, R)

Please note:

This page applies to the most current examination regulations in Winter semester 2022/23. 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
• Winter 2023/24 (no corresponding element)

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.