Course of Study "Mathematics" (M.Sc.)
Department  [MAT] Mathematik 

Degree  [M.Sc.] Master (M.Sc.)
(88)

Course of Study  Mathematics
(105)

State  [NORM] Active 
Short Name, Number  M.Sc. Mathematics
[MAT88.105SG]

Additional informations 
Section Pure Mathematics
WP  MAT4011M4 
Commutative Algebra
Not possible if the chosen specialisation is "Algebra and Number Theory" or "Algebraic Geometry and Computer Algebra".
 9.0 LP 

WP  MAT4014M4  Cryptography  9.0 LP 
WP  MAT4028M4 
Plane Algebraic Curves
Not possible if the chosen specialisation is "Algebraic Geometry and Computer Algebra".
 4.5 LP 
WP  MAT6011M4 
Probability Theory
Not possible if the chosen specialisation is "Financial Mathematics", "Statistics" or "Stochastic Analysis".
 9.0 LP 
WP  MAT7011M4 
Functional Analysis
Not possible if the chosen specialisation is "Stochastic Analysis".
 9.0 LP 
WP  MAT8011BM4 
Introduction to PDE
Not possible if the chosen specialisation is "Modelling and Scientific Computing", "Partial Differential Equations", or "Systems and Control Theory".
 4.5 LP 
WP  MAT4024M4 
padic Numbers
Not possible if the chosen specialisation is "Algebra and Number Theory".
 4.5 LP 
WP  MAT4025M4 
Character Theory of Finite Groups
Not possible if the chosen specialisation is "Algebra and Number Theory".
 4.5 LP 
WP  MAT4029M4 
Quadratic Number Fields
Not possible if the chosen specialisation is "Algebra and Number Theory".
 4.5 LP 
WP  MAT4016M6  Algebraic Topology  9.0 LP 
WP  MAT4019M6  Elliptic Functions and Elliptic Curves  3.0 LP 
WP  MAT4020M6  Multilinear Algebra  3.0 LP 
WP  MAT4021M6  Manifolds  9.0 LP 
WP  MAT4026M6  Riemannian Surfaces  3.0 LP 
WP  MAT4027M6  Elliptic Curves in Positive Characteristics  3.0 LP 
WP  MAT4911M6  Categories  3.0 LP 
WP  MAT4915M6  Introduction to Tensor Categories  3.0 LP 
WP  MATRMMPOOL7  Pure Mathematics (Advanced Modules M.Sc.)  [4.5  9.0] LP 
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  MAT4014M4  Cryptography  9.0 LP 

WP  MAT5011M4 
Integer Programming: Polyhedral Theory and Algorithms
Not possible if the chosen specialisation is "Optimisation".
 9.0 LP 
WP  MAT5012M4 
Nonlinear Optimization
Not possible if the chosen specialisation is "Optimisation".
 9.0 LP 
WP  MAT6011M4 
Probability Theory
Not possible if the chosen specialisation is "Financial Mathematics", "Statistics" or "Stochastic Analysis".
 9.0 LP 
WP  MAT6012M4 
Regression and Time Series Analysis
Not possible if the chosen specialisation is "Financial Mathematics" or "Statistics".
 9.0 LP 
WP  MAT6014M6 
Monte Carlo Algorithms
Not possible if the chosen specialisation is "Financial Mathematics" or "Statistics".
 9.0 LP 
WP  MAT6015M4 
Foundations in Financial Mathematics
Not possible if the chosen specialisation is "Financial Mathematics" or "Statistics".
 3.0 LP 
WP  MAT7011M4 
Functional Analysis
Not possible if the chosen specialisation is "Stochastic Analysis".
 9.0 LP 
WP  MAT8011M4 
Differential Equations: Numerics of ODE & Introduction to PDE
Not possible if the chosen specialisation is "Modelling and Scientific Computing", "Partial Differential Equations", or "Systems and Control Theory".
 9.0 LP 
WP  MAT8011AM4 
Numerics of ODE
Not possible if the chosen specialisation is "Modelling and Scientific Computing", "Partial Differential Equations", or "Systems and Control Theory".
 4.5 LP 
WP  MAT8011BM4 
Introduction to PDE
Not possible if the chosen specialisation is "Modelling and Scientific Computing", "Partial Differential Equations", or "Systems and Control Theory".
 4.5 LP 
WP  MAT8012AM4 
Introduction to Systems and Control Theory
Not possible if the chosen specialisation is "Modelling and Scientific Computing" or "Systems and Control Theory".
 4.5 LP 
WP  MAT5914M6  Mathematics of Quantum Computing  4.5 LP 
WP  MAT6510M4 
Foundations in Mathematical Image Processing
Not possible if the chosen specialisation is "Image Processing and Data Analysis".
 9.0 LP 
WP  MAT8017M6 
Dynamical Systems
Not possible if the chosen specialisation is "Modelling and Scientific Computing".
 4.5 LP 
WP  MAT8018M4 
Introduction to Systems and Control Theory & Dynamical Systems
Not possible if the chosen specialisation is "Modelling and Scientific Computing" or "Systems and Control Theory".
 9.0 LP 
WP  MAT8123M4 
DifferentialAlgebraic Equations
Not possible if the chosen specialisation is "Modelling and Scientific Computing".
 4.5 LP 
WP  INF1456M6  Optimization in Fluid Mechanics  4.5 LP 
WP  INF1455M6  Topology Optimization  4.5 LP 
WP  MAT7010M6  Spline Functions  3.0 LP 
WP  MAT8013AM4 
Introduction to Neural Networks
Not possible if the chosen specialisation is "Modelling and Scientific Computing" or "Systems and Control Theory".
 4.5 LP 
WP  MAT8012M6 
Systems and Control Theory
Not possible if the chosen specialisation is "Modelling and Scientific Computing" or "Systems and Control Theory".
 9.0 LP 
WP  MATAMMPOOL7  Applied Mathematics (Advanced Modules M.Sc.)  [4.5  13.5] LP 
Section Specialisation
In addition, reading courses amounting to 12 CP have to be completed. The latter usually take place with semesterchanging 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  MAT43MPOOL7  Specialisation Algebra and Number Theory (M.Sc.)  [4.5  9.0] LP 

WP  MAT41MPOOL7  Specialisation Algebraic Geometry and Computer Algebra (M.Sc.)  [4.5  9.0] LP 
WP  MAT52MPOOL7  Specialisation Mathematical Optimisation (M.Sc.)  [4.5  9.0] LP 
WP  MAT61MPOOL7  Specialisation Financial Mathematics (M.Sc.)  [4.5  13.5] LP 
WP  MAT62MPOOL7  Specialisation Statistics (M.Sc.)  [4.5  9.0] LP 
WP  MAT65MPOOL7  Specialisation Image Processing and Data Analysis (M.Sc.)  [4.5  9.0] LP 
WP  MAT70MPOOL7  Specialisation Stochastic Analysis (M.Sc.)  [4.5  13.5] LP 
WP  MAT8xMPOOL7  Specialisation Modelling and Scientific Computing (M.Sc.)  [4.5  9.0] LP 
WP  MAT81MPOOL7  Specialisation Partial Differential Equations (M.Sc.)  [4.5  9.0] LP 
WP  MAT82MPOOL7  Specialisation Systems and Control Theory (M.Sc.)  [4.5  9.0] LP 
Reading Courses
 
P  MATRCM7  Reading Course (Mathematics)  12.0 LP 
Section Seminare
P  MATVSEMM7  Seminar (Mathematical Specialisation)  3.0 LP 

P  MATSEMM7  Seminar (Mathematics)  3.0 LP 
Section Subsidiary Topic (Minor)
Modules for courses with mainly mathematical content are not permitted here if they substantially overlap with other modules of the Bachelor's or Master's examination, or if the examination board states that they do not have a sufficiently advanced character.
Biology
In this subsidiary topic (minor), elective compulsory modules to a total of 18  21 CP from the following list or other advanced modules from the study programmes offered by the Department of Biology (or at least equivalent achievements) must be selected:
 
WP  BIOGM13M2 
Grundmodul 13: Mikrobiologie
This module can only be chosen if it has not already been part (as compulsory elective module) of the Bachelor examination in Mathematics.
 6.0 LP 

WP  MATBIOG11M2 
Biochemistry (for Mathematics Students)
This module can only be chosen if it has not already been part (as compulsory elective module) of the Bachelor examination in Mathematics.
 6.0 LP 
WP  BIOGM10M2  Grundmodul 10: Tierphysiologie  10.0 LP 
WP  MATBIOGM10M2  Animal Physiology (for Mathematics Students)  6.0 LP 
WP  BIOGM16M2  Grundmodul 16: Molekulare Biotechnologie  6.0 LP 
WP  BIOGM14M2  Grundmodul 14: Neuro/Entwicklungsbiologie  6.0 LP 
Chemistry
In this subsidiary topic (minor), elective compulsory modules to a total of 18  21 CP from the following list or other advanced modules from the study programmes offered by the Department of Chemistry (or at least equivalent achievements) must be selected:
 
WP  CHEBaCh10M1  Grundmodul: Organische Chemie II  6.0 LP 
WP  CHEBaCh16M1  Grundmodul: Physikalische Chemie III  5.0 LP 
WP  CHEBaCh17M1  Grundmodul: Theoretische Chemie  5.0 LP 
WP  CHEBaCh191M1  Grundmodul: Biochemie I  5.0 LP 
WP  CHEBaCh192M1  Grundmodul: Biochemie II  3.0 LP 
WP  CHEMMCh_BC_GMM5  Biochemie (Mastergrundmodul)  5.0 LP 
WP  CHEMMCh_OC_GMM5  Organische Chemie (Mastergrundmodul)  5.0 LP 
WP  CHEMMCh_PC_GMM5  Physikalische Chemie (Mastergrundmodul)  5.0 LP 
Electrical Engineering
In this subsidiary topic (minor), elective compulsory modules to a total of 18  21 CP must be chosen from one or two of the advanced study areas
of the bachelor's degree course [EIT82.781SG#2019] Electrical and Computer Engineering (EIT), whereby in each of the selected areas at least 6 CP are to be completed on modules from the corresponding section "MajorSpecific Advanced Subjects" of the bachelor's degree course or the master's degree course [EIT88.781SG#2010] Electrical and Computer Engineering (EIT) or at least equivalent achievements. The module [EITLRS504M3] Linear Control can be selected in each of the areas.  
WP  EITLRS504M3  Linear Control  5.0 LP 
Computer Science
In this subsidiary topic (minor), elective compulsory modules to a total of 18  21 CP must be chosen from one or two of the research and study areas
of the Department of Computer Science. In each of the chosen areas, modules associated to lectures or lectures with exercise classes or project modules from the section Computer Science Specialisation of the Bachelor's programme [INF82.79SG] Computer Science or from the Master's programme [INF88.79SG] Computer Science or at least equivalent achievements are admissible. In particular, the modules or module catalogues listed can be selected.  
WP  INFVIS_Ba_VMPOOL4  Specialization Bachelor TA Visualization and Scientific Computing  [4.0  8.0] LP 
WP  INF1453M6 
High Performance Computing (Introduction)
If a specialised module with a total of 12 LP is selected, this module can be taken as [INF1453_MATM6] Introduction to HPC (for Mathematics Students).
 5.0 LP 
WP  INF1454M6  High Performance Computing with GPUs  6.0 LP 
WP  INF1045M4  Visualization and Scientific Computing (Project)  8.0 LP 
WP  INF1457M6  Algorithmic Differentiation  5.0 LP 
WP  INFINSY_Ba_VMPOOL4  Specialization Bachelor TA Information Systems  [8.0] LP 
WP  INF2045M4  Information Systems (Project)  8.0 LP 
WP  INFSE_Ba_VMPOOL4  Specialization Bachelor TA Software Engineering  [4.0  8.0] LP 
WP  INF3045M4  Software Engineering (BachelorProject)  8.0 LP 
WP  INFVVS_Ba_VMPOOL4  Specialization Bachelor TA Distributed and Networked Systems  [4.0] LP 
WP  INF4045M4  Distributed and networked systems (Project)  8.0 LP 
WP  INF5651M6  Concurrency Theory  8.0 LP 
WP  INF5652M6  Advanced Automata Theory  8.0 LP 
WP  INF5653M5  Complexity Theory  8.0 LP 
WP  INF5045M4  Algorithms and Deduction (Project)  8.0 LP 
WP  INFES_Ba_VMPOOL4  Specialization Bachelor TA Embedded Systems and Robotics  [4.0  8.0] LP 
WP  INF6045M4  Embedded Systems (Project)  8.0 LP 
WP  INFKI_Ba_VMPOOL4  Specialization Bachelor TA Intelligent Systems  [4.0  8.0] LP 
WP  INF7551M6  Machine Learning II  Statistical ML  8.0 LP 
WP  INF7045M4  Intelligent Systems (Project)  8.0 LP 
Mechanical Engineering
In this subsidiary topic (minor), elective compulsory modules to a total of 18  21 CP must be chosen from one or two of the areas of expertise (KF)
of the bachelor's programme [MV82.103SG] Mechanical Engineering. In each of the selected areas at least 6 CP have to be completed on modules from the corresponding section of the bachelor's degree course or one of the master's programmes of the Department Mechanical and Process Engineering (MV) or at least equivalent achievements. Instead of a second area of expertise the module [MVMTS23M4] Measurement and control Theory can be selected, too.  
WP  MVMTS23M4  Measurement and control Theory  8.0 LP 
Physics
In this subsidiary topic (minor), elective compulsory modules to a total of 18  21 CP from the following list or other advanced modules (resp. module parts) from the study programmes offered by the Department of Physics (or at least equivalent achievements) must be selected:
 
WP  PHYG3M2  Fundamentals of quantum physics  18.0 LP 
WP  PHYE1M3  Physics of condensed matter and statistical physics  20.0 LP 
WP  PHYE2M3  atomic physics  5.0 LP 
Economics and Business Sciences
In this subsidiary topic (minor), elective compulsory modules to a total of 18  21 CP must be chosen from one or two of the research and study areas
of the Master's programme [WIW88.21SG] Business Studies or at least equivalent achievements. In each of the selected areas, modules to a total of at least 6 LP must be completed. In particular, the modules associated to lectures or lectures with exercise classes of the module catalogues listed below can be selected:  
WP  WIWWINMPOOL7  Field of Specialization: Business Information Systems & OR  [4.0  6.0] LP 
WP  WIWCONMPOOL7  Field of Specialization: Management Accounting  [4.0  9.0] LP 
WP  WIWETMPOOL7  Field of Specialization: Economic Theory  [4.0  4.5] LP 
WP  WIWEPSMPOOL7  Field of Specialization: Entrepreneurship  [3.0  6.0] LP 
WP  WIWFEMPOOL7  Field of Specialization: Financial Economics  [4.0  6.0] LP 
WP  WIWFUBMPOOL7  Field of Specialization: Finance and Banking Management  [4.0  4.5] LP 
WP  WIWHRMOBMPOOL7  Field of Specialization: Human Resource Management and Organizational Behavior  [4.0  9.0] LP 
WP  WIWIOEMPOOL7  Field of Specialization: Industrial Economics  [4.0  4.5] LP 
WP  WIWLOGMPOOL7  Field of Specialization: Logistics  [4.0  9.0] LP 
WP  WIWMKTMPOOL7  Field of Specialization: Marketing  [3.0  6.0] LP 
WP  WIWPOMMPOOL7  Field of Specialization: Produktionsmanagement  [4.0  9.0] LP 
WP  WIWREMPOOL7  Field of Specialization: Environment, Resources, Energy: Economics and Policy  [4.0  4.5] LP 
WP  WIWSWPMPOOL7  Field of Specialization: Taxation and Auditing  [4.0  6.0] LP 
WP  WIWSICMPOOL7  Field of Specialization: Strategy, Innovation and Cooperation  [4.0  9.0] LP 
WP  WIWSMGMPOOL7  Field of Specialization: Sustainability Management  [4.0  9.0] LP 
The choice of the modules is limited by the chosen mathematical specialisation: