Planning of specialisation courses

Specialisation options in Master's programmes

In the following you will find the concrete planning of courses at the specialisation level. The Master seminars that are suitable for the specialisations are always offered at specific times that do not collide with lectures, and are not listed separately for reasons of clarity. The same applies to the corresponding elective compulsory modules from the Bachelor of Mathematics.

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 on the English-language Master’s programme up to the Summer Semester 2024 can be found here (opens in new tab).

WiSe 2022/23

  • Modulformen (4+2 de, Bruinier)
  • Lie-Algebren und Vertex-Algebren (4+2 de, Scheithauer)

SuSe 2023

  • Algebraische Geometrie (4+2 de, Wedhorn)
  • Vertiefung Algebra (2+1 de oder en, Scheithauer)

WiSe 2023/24

  • Algebraische Geometrie II (2+1 de oder en, Wedhorn)
  • Vertiefung Algebra (2+1 de oder en, Scheithauer)

SuSe 2024

  • Algebraische Zahlentheorie (4+2 de, 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 2022/23

  • Partial differential equations (4+2 en, Egert)
  • Internet Seminar (9 CP, en, Haller-Dintelmann/Egert)
  • Optimal Transport (2+1 en, Modena)
  • Lagrange/Euler Interfac Advektionsmethoden II (2+1 de, Maric)

SuSe 2023

  • Partial differential equations II (4+2 en, Hieber)
  • Banachalgebren und Numerische Analysis (4+2 de, Roch)
  • Reaktions-Diffusions-Systeme (2+1 de, Bothe)
  • Mathematische Modellierung fluider Grenzflächen (2+1 de, Bothe)

WiSe 2023/24

  • Partielle Differentialgleichungen (4+2 de, Haller)
  • Parabolic PDEs (2+1 en, Stinner)
  • Mathematische Modellierung fluider Grenzflächen II (2+1 de, Bothe)
  • Internet Seminar (9 CP, en, Haller/Egert)

SuSe 2024

  • Partielle Differentialgleichungen (4+2 de, Hieber)
  • Reaction-Diffusion Systems (2+1 en, Bothe)
  • Mathematische Modellierung fluider Grenzflächen (2+1 de, Bothe)

Requirements for a specialisation in Analysis:

For additional information visit Analysis.

WiSe 2022/23

  • Approximationstheorie (4+2 ger, Reif)

SuSe 2023

  • Vertiefung Geometrie (4+2 en, Mäder-Baumdicker)

WiSe 2023/24

  • Vertiefung Geometrie (4+2 en, Große-Brauckmann)

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 2023/24

  • Algorithms and Symmetries (4+2 en, Schweitzer)
  • Classical and Non-Classical Model Theory (4+2 en, Otto)
  • Incompleteness of Formal Systems (2+1 en, Streicher)
  • Proof Mining (2+1 en, Pinto)

SuSe 2023

  • Mathematische Grundlagen der funktionalen Programmierung 1 (2+1 de, Streicher)
  • Logics of Knowledge and Information (4+2 en, Otto)
  • Algorithmic Group Theory (4+2 en, Schweitzer)

WiSe 2023/24

  • Applied Proof Theory (4+2 en, Kohlenbach)
  • Mathematische Grundlagen der funktionalen Programmierung 2 (2+1 de, Streicher)

SuSe 2024

  • Vertiefung Logik (4+2 en, Otto)
  • Vertiefung Logik (4+2 en, Kohlenbach)
  • Vertiefung Logik (2+1 en, Eickmeyer/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.

WiSe 2023/24

  • Numerical Methods for PDEs (4+2 en, Lang)
  • Computational Electromagnetics (2+1 de, Schmidt)

SuSe 2023

  • Stochastic Finite Elements (2+1 en, Lang)
  • Deep Neural Networks (Approximation) (2+1 en, Lang)
  • Numerik Hyperbolischer PDGLS (2+1 de, Sikstel)

WiSe 2023/24

  • Numerical Methods for PDEs (4+2 de, Giesselmann)
  • Computational Electromagnetics (2+1 en, Schmidt)

SuSe 2024

  • Vertiefung Numerik (4+2 en, Giesselmann)
  • Deep Neural Networks (Approximation) (2+1 de, NN)

Requirements for a specialisation in Numerics and Scientific Computing:

  • Attending the third year course “Numerik gewöhnlicher Differentialgleichungen” resp. courses with similar contents, e.g. in former studies
  • 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:
  • 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 von 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 2022/23

  • Nichtlineare Optimierung (4+2 de, Ulbrich)
  • Diskrete Mathematik (4+2 de, Paffenholz)
  • Optimierungsmethoden für Maschinelles Lernen (2+1 de, Ulbrich)
  • Optimierung in Transport und Verkehr (2+1 de, Pfetsch)

SuSe 2023

  • Diskrete Optimierung (4+2 de, Pfetsch)
  • Geometric Combinatorics (2+1 en, Paffenholz)
  • Online Optimization (2+1 en, Disser)

WiSe 223/24

  • Nonlinear Optimization (4+2 en, NN)
  • Diskrete Mathematik (4+2 de, Pfetsch)
  • Optimierungsmethoden für Maschinelles Lernen (2+1 de, Pfetsch)
  • Combinatorial Optimization (2+1 en, Disser)

SuSe 2024

  • Discrete Optimization (4+2 en, Disser)
  • Nichtglatte Optimierung (2+1 de, NN)
  • Gemischt-Ganzzahlige Nichtlineare Optimierung (2+1 de, 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:

For additional information visit Optimisation.

A specialisation cycle in Stochastics lasting two semesters is offered every Winter Semester.

WiSe 2022/23

  • Stochastische Prozesse 1 (4+2 de, Aurzada)

SuSe 2023

  • Specialisation: Stochastics (4+2 en, Aurzada)
  • Specialisation: Stochastics (4+2 ger, Wichelhaus)

WiSe 2023/24

  • Mathematische Statistik (4+2 de, Kohler)

SuSe 2024

  • Statistik (4+2 de, 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)
  • In the study programme M.Sc. Mathematics a specialisation in Statistics is not possible.

For additional information visit Stochastics.