WiSe 2024/25

• p-adic geometry (2+1 en, Wedhorn)
• Complex Manifolds (2+1 en, Zufetti)

SuSe 2025

• Algebraic Geometry (4+2 en, Richarz/Pauli)
• Automorphic Forms (4+2 en, Scheithauer)

WiSe 2025/26

• Algebraic Geometry II (2+1 en, Richarz)

SuSe 2026

• Automorphic Forms I (4+2 en, Bruinier)
• Specialisation Algebra (2+1 en, Richarz)

WiSe 2026/27

• Automorphic Forms II (2+1 en, Bruinier)

Suse 2027

• Algebraic Geometry I (4+2 en, Wedhorn)

WiSe 27/28

• Algebraic Geometry II (4+2 en, Wedhorn)

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

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.

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)
• 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)
• Mathematical Modelling of Fluid Interfaces II (2+1 en, Bothe)
• Internet Seminar (9 CP, en, Haller/Egert)

SuSe 2028

• PDE II (2+1 en, Egert)
• Machine Learning for Fluid Dynamics (2+1 en, Bothe/Maric)
• Mathematical Modelling of Fluid Interfaces I (2+1 en, Bothe)

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 2025

• Variations of geometric energies (4+2 en, Mäder-Baumdicker)

WiSe 2025/26

• Riemannian Geometry (4+2 en, Große-Brauckmann)

SuSe 2026

• Specialisation Geometry (4+2 en, Reif)

WiSe 2026/27

• Specialisation Geometry (4+2 en, Reif)

SuSe 2028

• Specialisation Geometry (4+2 en, Mäder-Baumdicker)

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 Prentice-Hall 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.

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)
• Algorithms and Symmetry (4+2 en, Schweitzer)

SuSe 2026

• Introduction to Computability Theory (2+1 en, Kohlenbach)
• Computational Group Theory (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)

SuSe 2028

• Applied Proof Theory (4+2 en, Kohlenbach)
• Computational Complexity (4+2 en, Eickmeyer)

• 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.

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 1-7 and 10-14 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
  • 04-10-0013/de Einführung in die Numerische Mathematik 9 CP
  • 04-10-0393/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 Non-Linear Optimisation, can be started in any semester and completed within a year. Moreover, at irregular intervals, additional classes are offered at specialisation level.

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 en, 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)
• First-order 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 for Machine Learning (2+1 en, Ulbrich)

SuSe 2027

• Discrete Optimization (4+2 en, Pfetsch)
• Optimization in Data Science (2+1 en, Pfetsch/Ulbrich)

WiSe 27/28

• Nonlinear Optimization (4+2 en, NN)
• Optimization Methods for Machine Learning (2+1 en, Pfetsch)
• Nonsmooth Optimization (2+1 en, Ulbrich)

SuSe 2028

• Discrete Optimization (4+2 en, Pfetsch)
• Geometric Combinatorics (2+1 en, Paffenholz)

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.

WiSe 2024/25

• Stochastic processes (4+2 en, Betz)

SuSe 2025

• Spin Systems and Statistical Mechanics (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)

WiSe 27/28

• Stochastic processes I (4+2 en, Betz)

SuSe 2028

• Specialisation in Stochastics (4+2 en, Betz)
• Mathematical Statistics (4+2 en, Wichelhaus)

WiSe 28/29

• Stochastic processes I (4+2 en, Aurzada)
• Statistical Theory of Deep Learning (4+2 en, Wichelhaus)

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)
• In the study programme M.Sc. Mathematics a specialisation in Statistics is not possible.

For additional information visit Stochastics.