# Course of Study "Mathematics International" (M.Sc.)

## [MAT-88.706-SG]

## Section Pure Mathematics

WP | MAT-40-11-M-4 |
Commutative Algebra
Not possible if the chosen specialisation is "Algebra and Number Theory" or "Algebraic Geometry and Computer Algebra".
| in WiSe | EN | 9.0 CP |
---|---|---|---|---|---|

WP | MAT-40-14-M-4 | Cryptography | in SuSe | EN | 9.0 CP |

WP | MAT-40-28-M-4 |
Plane Algebraic Curves
Not possible if the chosen specialisation is "Algebraic Geometry and Computer Algebra".
| in SuSe | EN | 4.5 CP |

WP | MAT-60-11-M-4 |
Probability Theory
Not possible if the chosen specialisation is "Financial Mathematics", "Statistics" or "Stochastic Analysis".
| in WiSe | EN | 9.0 CP |

WP | MAT-70-11-M-4 |
Functional Analysis
Not possible if the chosen specialisation is "Stochastic Analysis".
| in SuSe | EN | 9.0 CP |

WP | MAT-80-11B-M-4 |
Introduction to PDE
Not possible if the chosen specialisation is "Modelling and Scientific Computing", "Partial Differential Equations", or "Systems and Control Theory".
| in WiSe | EN | 4.5 CP |

WP | MAT-40-24-M-4 |
p-adic Numbers
Not possible if the chosen specialisation is "Algebra and Number Theory".
| irreg. SuSe | EN | 4.5 CP |

WP | MAT-40-25-M-4 |
Character Theory of Finite Groups
Not possible if the chosen specialisation is "Algebra and Number Theory".
| irreg. SuSe | EN | 4.5 CP |

WP | MAT-40-29-M-4 |
Quadratic Number Fields
Not possible if the chosen specialisation is "Algebra and Number Theory".
| irreg. SuSe | EN | 4.5 CP |

WP | MAT-40-16-M-6 | Algebraic Topology | irreg. | EN | 9.0 CP |

WP | MAT-40-19-M-6 | Elliptic Functions and Elliptic Curves | irreg. | EN | 3.0 CP |

WP | MAT-40-20-M-6 | Multilinear Algebra | irreg. | EN | 3.0 CP |

WP | MAT-40-21-M-6 | Manifolds | irreg. | EN | 9.0 CP |

WP | MAT-40-26-M-6 | Riemannian Surfaces | irreg. | EN | 3.0 CP |

WP | MAT-40-27-M-6 | Elliptic Curves in Positive Characteristics | irreg. | EN | 3.0 CP |

WP | MAT-49-11-M-6 | Categories | irreg. | EN | 3.0 CP |

WP | MAT-49-15-M-6 | Introduction to Tensor Categories | irreg. | EN | 3.0 CP |

WP | MAT-RM-MPOOL-7 | Pure Mathematics (Advanced Modules M.Sc.) | [4.5 - 9.0] CP |

## Section Applied Mathematics

The choice of the modules is limited by the chosen mathematical specialisation:

- Modules that are directly attributable to the chosen specialisation may not be included in the section "Applied Mathematics".
- In the sections "Pure Mathematics" and "Applied Mathematics", a total of modules amounting to at least 18 CP must be provided outside the focus area which the specialisation belongs to.
- When choosing a specialisation that is wholly or partially attributable to the field of stochastics (e.g. "Stochastic Analysis", "Financial Mathematics" or "Statistics"), at least 24 CP must be provided in the sections "Pure Mathematics", "Applied Mathematics" and "Specialisation" outside of stochastics.

WP | MAT-40-14-M-4 | Cryptography | in SuSe | EN | 9.0 CP |
---|---|---|---|---|---|

WP | MAT-50-11-M-4 |
Integer Programming: Polyhedral Theory and Algorithms
Not possible if the chosen specialisation is "Optimisation".
| in WiSe | EN | 9.0 CP |

WP | MAT-50-12-M-4 |
Nonlinear Optimization
Not possible if the chosen specialisation is "Optimisation".
| in SuSe | EN | 9.0 CP |

WP | MAT-60-11-M-4 |
Probability Theory
| in WiSe | EN | 9.0 CP |

WP | MAT-60-12-M-4 |
Regression and Time Series Analysis
Not possible if the chosen specialisation is "Financial Mathematics" or "Statistics".
| in SuSe | EN | 9.0 CP |

WP | MAT-60-14-M-6 |
Monte Carlo Algorithms
Not possible if the chosen specialisation is "Financial Mathematics" or "Statistics".
| irreg. SuSe | EN | 9.0 CP |

WP | MAT-60-15-M-4 |
Foundations in Financial Mathematics
Not possible if the chosen specialisation is "Financial Mathematics" or "Statistics".
| in SuSe | DE | 3.0 CP |

WP | MAT-70-11-M-4 |
Functional Analysis
Not possible if the chosen specialisation is "Stochastic Analysis".
| in SuSe | EN | 9.0 CP |

WP | MAT-80-11-M-4 |
Differential Equations: Numerics of ODE & Introduction to PDE
| in WiSe | EN | 9.0 CP |

WP | MAT-80-11A-M-4 |
Numerics of ODE
| in WiSe | EN | 4.5 CP |

WP | MAT-80-11B-M-4 |
Introduction to PDE
| in WiSe | EN | 4.5 CP |

WP | MAT-80-12A-M-4 |
Introduction to Systems and Control Theory
Not possible if the chosen specialisation is "Modelling and Scientific Computing" or "Systems and Control Theory".
| in SuSe | EN | 4.5 CP |

WP | MAT-59-14-M-6 | Mathematics of Quantum Computing | irreg. | EN | 4.5 CP |

WP | MAT-65-10-M-4 |
Foundations in Mathematical Image Processing
Not possible if the chosen specialisation is "Image Processing and Data Analysis".
| irreg. | EN | 9.0 CP |

WP | MAT-80-17-M-6 |
Dynamical Systems
Not possible if the chosen specialisation is "Modelling and Scientific Computing".
| irreg. SuSe | EN | 4.5 CP |

WP | MAT-80-18-M-4 |
Introduction to Systems and Control Theory & Dynamical Systems
| irreg. SuSe | EN | 9.0 CP |

WP | MAT-81-23-M-4 |
Differential-Algebraic Equations
Not possible if the chosen specialisation is "Modelling and Scientific Computing".
| irreg. SuSe | EN | 4.5 CP |

WP | INF-14-56-M-6 | Optimization in Fluid Mechanics | irreg. SuSe | EN | 4.5 CP |

WP | INF-14-55-M-6 | Topology Optimization | irreg. SuSe | DE/EN | 4.5 CP |

WP | MAT-70-10-M-6 | Spline Functions | irreg. | EN | 3.0 CP |

WP | MAT-80-13A-M-4 |
Introduction to Neural Networks
| irreg. | EN | 4.5 CP |

WP | MAT-80-12-M-6 |
Systems and Control Theory
| 2 Sem. from irreg. | EN | 9.0 CP |

WP | MAT-AM-MPOOL-7 | Applied Mathematics (Advanced Modules M.Sc.) | [4.5 - 13.5] CP |

## Section Specialisation

In addition, reading courses amounting to 12 CP have to be completed. The latter usually take place with semester-changing topics that are often based on current mathematical research. Towards the end of the lecture period of each semester, the reading courses offered in the following semester for the respective specialisation areas will be presented as part of the information sessions of the individual research focuses.

Modules associated to lectures (with or without exercise classes)
| |||||

WP | MAT-43-MPOOL-7 | Specialisation Algebra and Number Theory (M.Sc.) | [4.5 - 9.0] CP | ||
---|---|---|---|---|---|

WP | MAT-41-MPOOL-7 | Specialisation Algebraic Geometry and Computer Algebra (M.Sc.) | [4.5 - 9.0] CP | ||

WP | MAT-52-MPOOL-7 | Specialisation Mathematical Optimisation (M.Sc.) | [4.5 - 9.0] CP | ||

WP | MAT-61-MPOOL-7 | Specialisation Financial Mathematics (M.Sc.) | [4.5 - 13.5] CP | ||

WP | MAT-62-MPOOL-7 | Specialisation Statistics (M.Sc.) | [4.5 - 9.0] CP | ||

WP | MAT-65-MPOOL-7 | Specialisation Image Processing and Data Analysis (M.Sc.) | [4.5 - 9.0] CP | ||

WP | MAT-70-MPOOL-7 | Specialisation Stochastic Analysis (M.Sc.) | [4.5 - 13.5] CP | ||

WP | MAT-8x-MPOOL-7 | Specialisation Modelling and Scientific Computing (M.Sc.) | [4.5 - 9.0] CP | ||

WP | MAT-81-MPOOL-7 | Specialisation Partial Differential Equations (M.Sc.) | [4.5 - 9.0] CP | ||

WP | MAT-82-MPOOL-7 | Specialisation Systems and Control Theory (M.Sc.) | [4.5 - 9.0] CP | ||

Reading Courses
| |||||

P | MAT-RC-M-7 | Reading Course (Mathematics) | in WiSe/SuSe | DE/EN | 12.0 CP |

## Section Seminare

P | MAT-VSEM-M-7 | Seminar (Mathematical Specialisation) | in WiSe/SuSe | DE/EN | 3.0 CP |
---|---|---|---|---|---|

P | MAT-SEM-M-7 | Seminar (Mathematics) | in WiSe/SuSe | DE/EN | 3.0 CP |

## Section Master Thesis

P | MAT-MA-MAT-M-7 | Master Thesis (Mathematics, M.Sc.) | in WiSe/SuSe | DE/EN | 30.0 CP |
---|

## Section Non-mathematical Elective

Recommended are language courses, internships abroad or modules from non-mathematical subsidiary topics (minors) of the other mathematical study programmes are recommended. In the case of language courses, evidence must be provided by an examination recognised by a university or equivalent achievements.

If modules from other study programmes at TU Kaiserslautern are included, the achievements to be provided can be found in the examination regulations of the corresponding study programmes.

The choice of the modules is limited by the chosen mathematical specialisation: