Specialisation Options in the Master’s Programme in Mathematics Minimum Set
In the following, you will find the concrete planning for courses at specialisation level. The Master’s seminars in the respective specialisations will always be scheduled so that they do not clash but are not included here for space reasons. The same is true of the relevant core modules in the Bachelor’s Programme in Mathematics.
Please note that details may change.
A complete overview of course planning can be found on this page .
All the specialisation offers in our Master's programmes up until summer semester 2027 can be found here (opens in new tab) .
The specialisation courses in the study field Data Science can be found in this table (opens in new tab) .
SuSe 2024
 Algebraic Number Theory (4+2 ger, Wedhorn)
 Automorphic Forms (4+2 en, Bruinier/Scheithauer)
WiSe 2024/25
 padic geometry (2+1 en, Wedhorn)
 Complex Manifolds (2+1 en, Zufetti)
SuSe 2025
 Algebraic Geometry (4+2 en, Richarz/Pauli)
 Specialisation Algebra (4+2 en, Scheithauer)
WiSe 2025/26
 Algebraic Geometry II (2+1 en, Richarz)
SuSe 2026
 Automorphic Forms (4+2 en, Bruinier)
WiSe 2026/27
 Specialisation Algebra (NN)
Requirements for a specialisation in Algebra:
 Attending the third year course “Algebra” resp. courses with similar contents, e.g. in former studies
 The prerequisites for a specialisation in algebra are the following:
 Lang, Algebra, GTM 211, Revised third edition, Springer
 Chapter I Groups: Sections 1 to 11
 Chapter II Rings
 Chapter III Modules
 Chapter IV Polynomials: Sections 1 to 6
 Chapter V Algebraic extensions: Sections 1 to 5
 Capter VI Galois theory: Sections 1 to 7
 Chapter VII Extensions of rings: Section 1
 Chapter X Noetherian rings and modules: Section 1
 Chapter XIII Matrices and linear maps: Sections 1 to 6
 Chapter XIV Representation of one endomorphism
 Chapter XV Structure of bilinear forms: Sections 1 to 8
 Chapter XVI The tensor product: Sections 1 and 2
 Lang, Algebra, GTM 211, Revised third edition, Springer
For additional information visit Algebra.
The specialisation in Analysis (focus: PDE) comprises two lectures (4+2 each), a seminar and, potentially, other special classes. It can be completed in three semesters. The Research Group guarantees that it will begin in every Summer Semester as well as every Winter Semester. You must have existing knowledge of functional analysis. (It is thus essential to attend the course in Functional Analysis if you want to specialise in Analysis; the relevant course is NOT included in the three semesters mentioned above).
The specialisation in Analysis (focus: Banach Algebra – Roch) can only be offered sporadically.
SuSe 2024
 Partial Differential Equations II (4+2 ger, Hieber)
 ReactionDiffusion Systems (2+1 en, Bothe)
 Mathematical Modelling of Fluid Interfaces I (2+1 ger, Bothe)
 Fourier Analysis and Applications (2+1 en, Roy)
WiSe 2024/25
 Partial Differential Equations I (4+2 en, Hieber)
 Internet Seminar (9 CP en, Haller/Egert)
 Mathematical Modelling of Fluid Interfaces II (2+1 en, Bothe)
 Parabolic PDEs (2+1 en, Stinner)
SuSe 2025
 Mathematical Modelling of Fluid Interfaces I (2+1 en, Bothe)
 PDE II/2 Data Assimilation for Fluid Dynamics (2+1 en, Hieber)
 PDE II/2 (2+1 en, Hieber)
 Machine Learning for Fluid Dynamics (2/1 en, Bothe/Maric)
WiSe 2025/26
 PDE I (4+2 en, Stinner)
 Mathematical Modelling of Fluid Interfaces II (2+1 en, Bothe)
 Internet Seminar (9 CP, en, Haller/Egert)
SuSe 2026
 PDE II (4+2 en, Stinner)
 PDE II/2 (2+1 en, NN)
 Mathematical Modelling of Fluid Interfaces I (2+1 en, Bothe)
WiSe 2026/27
 PDE I (4+2 en, NN)
 Internet Seminar (9 CP, en, Haller/Egert)
 Parabolic PDEs (2+1 en, Stinner)
SuSe 2027
 PDE II/2 Data Assimilation for Fluid Dynamics (2+1 en, NN)
 PDE II/2 (2+1 en, NN)
 Machine Learning for Fluid Dynamics (2/1 en, Bothe/Maric)
 Mathematical Modelling of Fluid Interfaces I (2+1 en, Bothe)
WiSe 2027/28
 PDE I (4+2 en, Egert)
 Internet Seminar (9 CP, en, Haller/Egert)
Requirements for a specialisation in Analysis:
 Attending the third year course “Funktionalanalysis” resp. courses with similar contents, e.g. in former studies
 Recommended reading:
 Bühler, Salamon: Functional Analysis, Graduate Studies in Mathematics (opens in new tab), 191. American Mathematical Society. Providence, RI, 2018. Paragraphs 1.1 – 1.3, 1.5, 2 (w/o 2.4.4), 3.1 – 3.2.1.
For additional information visit Analysis.
SuSe 2024
 Riemannian Geometry (Reading course, GroßeBrauckmann)
SuSe 2025
 Specialisation Geometry (4+2 en, MäderBaumdicker)
WiSe 2025/26
 Riemannian Geometry (4+2 en, GroßeBrauckmann)
SuSe 2026
 Specialisation Geometry (4+2 en, Reif)
WiSe 2026/27
 Specialisation Geometry (4+2 en, Reif)
Requirements for a specialisation in Geometry and Approximation:
 Attending the third year course “Differentialgeometrie” resp. courses with similar contents, e.g. in former studies
 Recommended reading:
 do Carmo, Manfredo P.: Differential geometry of curves and surfaces, Dover 2016, relevant are Chapter 1 to 4.
 Oprea, John: Differential geometry and its applications, Pearson Education 2007 (or PrenticeHall 1997), relevant are Chapter 1 to 6.
For additional information visit Geometry and Approximation.
Specialisation lecture courses are offered in four fields of specialisation that can be combined (see this page); specialisation cycles can be started every semester.
SuSe 2024
 Model Theory (2+1 en, Otto)
 Computability Theory (4+2 en, Kohlenbach)
 Specialisation in Logic: Graph Theory (2+1 en, Eickmeyer/Schweitzer)
WiSe 2024/25
 Proof Mining (2+1 en, Pinto)
 Algorithmic Metatheorems (2+1 en, Eickmeyer)
SuSe 2025
 Basic Applied Proof Theory (2+1 en, Kohlenbach)
 Logics of Knowledge and Information (4+2 en, Otto)
 Computational Complexity (4+2 en, Eickmeyer)
WiSe 2025/26
 Specialisation Logic (2+1 en, Otto)
 Advanced Applied Proof Theory (2+1 en, Kohlenbach)
SuSe 2026
 Introduction to Computability Theory (2+1 en, Kohlenbach)
 Algorithms and Symmetry (4+2 en, Schweitzer)
WiSe 2026/27
 Applied Proof Theory (4+2 en, Kohlenbach)
 Specialisation Logic (2+1 en, Otto)
SuSe 2027
 Specialisation Logic (4+2 en, Otto)
 Computational Complexity (4+2 en, Schweitzer)
WiSe 2027/28
 Specialisation Logic (4+2 en, Schweitzer)
 Attending the third year course “Introduction to Mathematical Logic” resp. courses with similar contents, e.g. in former studies
 Recommended reading:
 Forster, T.: Logic, Induction and Sets. Cambridge University Press, 234pp., 2003
For additional information visit Logic.
The modules can be taken in any order so that over a period of two years you can complete an entire specialisation in numerics (with or without a Master’s dissertation), irrespective of the semester in which you begin your Master’s programme.
SuSe 2024
 Efficient Methods for Data Assimilation (2+1 ger/en, Giesselmann)
 Discontinous Galerkin Methods (2+1 ger/en, Giesselmann)
WiSe 2024/25
 Numerics for PDEs with Uncertain Data (4+2 en, Tscherpel)
 Asymptotic Analysis and Numerical Methods for Singular Perturbed Differential Equations (2+1 en, Schmidt)
SuSe 2025
 Numerics for Hyperbolic Equations (2+1 en, Giesselmann)
 Numerics for Fluid Dynamics (2+1 de/en, Tscherpel)
WiSe 2025/26
 Numerics for PDEs with Uncertain Data (4+2 en, Lang)
 Computational Electromagnetics (2+1 de/en, Schmidt)
SuSe 2026
 Efficient Methods for Data Assimilation (2+1 en, Giesselmann)
 Scalable Linear Solvers for Data Science (2+1 en, Lang)
WiSe 2026/27
 Numerics for PDEs with Uncertain Data (4+2 de/en, Giesselmann)
SuSe 2027
 Computational Electromagnetics (2+1 de/en, Schmidt)
 Mathematical Biology (2+1 de/en, Gerisch)
Requirements for a specialisation in Numerics and Scientific Computing:
 For specialized courses in numerical analysis of the master program, we require knowledge from the preceeding bachelor programm, that compares to chapter 17 and 1014 of the following textbook:

 Endre Süli, University of Oxford, David F. Mayers, University of Oxford: An Introduction to Numerical Analysis, 2003, Cambridge University Press ISBN: 9780511801181
 The content of these chapters are taught at TU Darmstadt in the two German taught modules
 04100013/de Einführung in die Numerische Mathematik 9 CP
 04100393/de Numerik gewöhnlicher Differentialgleichungen 9 CP
For additional information visit Numerics and Scientific Computing.
The specialisation cycle in Optimisation, which consists of Discrete Optimisation and NonLinear Optimisation, can be started in any semester and completed within a year. Moreover, at irregular intervals, additional classes are offered at specialisation level.
SuSe 2024
 Discrete Optimization (4+2 en, Disser)
 MixedInteger Nonlinear Optimization (2+1 ger, Pfetsch)
 Geometric Combinatorics (2+1 ger/en, Paffenholz)
WiSe 2024/25
 Nonlinear Optimization (4+2 ger, Ulbrich)
 Optimization in Machine Learning (2+1 en, Ulbrich)
 Optimization in Transport and Traffic (2+1 ger, Pfetsch)
SuSe 2025
 Discrete Optimization (4+2 en, Disser)
 Deep Learning Lab (1+2 en, Disser)
 Nonsmooth Optimization (2+1 ger, Ulbrich)
WiSe 2025/26
 Nonlinear Optimization (4+2 en, Ulbrich)
 Optimization in Machine Learning (2+1 en, Pfetsch)
 Online Optimization (2+1 en, Disser)
SuSe 2026
 Discrete Optimization (4+2 en, Pfetsch)
 Geometric Combinatorics (2+1 en, Paffenholz)
 Firstorder methods for optimization in data analytics (2+1 en, Ulbrich)
 Combinatorial Optimization (2+1 en, Disser)
WiSe 2026/27
 Nonlinear Optimization (4+2 en, Ulbrich)
 Optimization Methods in Data Science (2+1 en, Pfetsch/Ulbrich)
 Deep Learning Lab (1+2 en, Disser)
SuSe 2027
 Discrete Optimization (4+2 en, Pfetsch)
 Optimization in Machine Learning (2+1 en, Ulbrich)
 Optimization in Transport and Traffic (2+1 en, Pfetsch)
Requirements for a specialisation in Optimisation:
 Attending the third year course “Einführung in die Optimierung” resp. courses with similar contents, e.g. in former studies
 Recommended reading:
 V. Chvatal, Linear Programming, Freeman and Company (2003) (entirely)
 J. Nocedal and S. Wright, Numerical Optimization, Springer 1999, Chapter 12 to 12.3 (incl), Chapter 16 to 16.4 (incl)
 ADM (Algorithmic Discrete Mathematics) (opens in new tab)
For additional information visit Optimisation.
A specialisation cycle in Stochastics lasting two semesters is offered every Winter Semester.
SuSe 2024
 Statistics (4+2 ger, Kohler)
WiSe 2024/25
 Stochastic processes (4+2 en, Betz)
SuSe 2025
 Specialisation in Stochastics (4+2 en, Betz)
 Mathematical Statistics (4+2 en, Wichelhaus)
WiSe 2025/26
 Stochastic processes I (4+2 ger, Aurzada)
 Statistical Theory of Deep Learning (4+2 en, Wichelhaus)
SuSe 2026
 Specialisation in Stochastics (4+2 en, Aurzada)
WiSe 2026/27
 Mathematical Statistics (4+2 en, Kohler)
SuSe 2027
 Statistical Theory of Deep Learning (4+2 en, Kohler)
Requirements for a specialisation in Stochastics:
 Attending the third year course “Probability Theory” resp. courses with similar contents, e.g. in former studies
 Recommended reading:
 Durret, Rick: "Probability, Theory and Examples”, 4th edition. Please make sure you not only understand the contents of the following chapters but also do most of the exercises in the book.
 Chapter 1: Measure Theory
 Chapter 2: Laws of Large Numbers; sections 2.1 – 2.5.
 Chapter 3: Central Limit Theorems; sections 3.1 – 3.1 and section 3.9
 Chapter 4: Random walks; sections 4.1 and 4.2
 Chapter 5: Martingales
 Chapter 6: Markov Chains; knowledge of this chapter is not essential, but it would be good to have some ideas about Markov chains.
 Lecture Script of the course “Probability Theory” (opens in new tab)
 Durret, Rick: "Probability, Theory and Examples”, 4th edition. Please make sure you not only understand the contents of the following chapters but also do most of the exercises in the book.
 In the study programme M.Sc. Mathematics a specialisation in Statistics is not possible.
For additional information visit Stochastics.