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".
 in WiSe  EN  9.0 CP 

WP  MAT4014M4  Cryptography  in SuSe  EN  9.0 CP 
WP  MAT4028M4 
Plane Algebraic Curves
Not possible if the chosen specialisation is "Algebraic Geometry and Computer Algebra".
 in SuSe  EN  4.5 CP 
WP  MAT6011M4 
Probability Theory
Not possible if the chosen specialisation is "Financial Mathematics", "Statistics" or "Stochastic Analysis".
 in WiSe  EN  9.0 CP 
WP  MAT7011M4 
Functional Analysis
Not possible if the chosen specialisation is "Stochastic Analysis".
 in SuSe  EN  9.0 CP 
WP  MAT8011BM4 
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  MAT4024M4 
padic Numbers
Not possible if the chosen specialisation is "Algebra and Number Theory".
 irreg. SuSe  EN  4.5 CP 
WP  MAT4025M4 
Character Theory of Finite Groups
Not possible if the chosen specialisation is "Algebra and Number Theory".
 irreg. SuSe  EN  4.5 CP 
WP  MAT4029M4 
Quadratic Number Fields
Not possible if the chosen specialisation is "Algebra and Number Theory".
 irreg. SuSe  EN  4.5 CP 
WP  MAT4016M6  Algebraic Topology  irreg.  EN  9.0 CP 
WP  MAT4019M6  Elliptic Functions and Elliptic Curves  irreg.  EN  3.0 CP 
WP  MAT4020M6  Multilinear Algebra  irreg.  EN  3.0 CP 
WP  MAT4021M6  Manifolds  irreg.  EN  9.0 CP 
WP  MAT4026M6  Riemannian Surfaces  irreg.  EN  3.0 CP 
WP  MAT4027M6  Elliptic Curves in Positive Characteristics  irreg.  EN  3.0 CP 
WP  MAT4911M6  Categories  irreg.  EN  3.0 CP 
WP  MAT4915M6  Introduction to Tensor Categories  irreg.  EN  3.0 CP 
WP  MATRMMPOOL7  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  MAT4014M4  Cryptography  in SuSe  EN  9.0 CP 

WP  MAT5011M4 
Integer Programming: Polyhedral Theory and Algorithms
Not possible if the chosen specialisation is "Optimisation".
 in WiSe  EN  9.0 CP 
WP  MAT5012M4 
Nonlinear Optimization
Not possible if the chosen specialisation is "Optimisation".
 in SuSe  EN  9.0 CP 
WP  MAT6011M4 
Probability Theory
Not possible if the chosen specialisation is "Financial Mathematics", "Statistics" or "Stochastic Analysis".
 in WiSe  EN  9.0 CP 
WP  MAT6012M4 
Regression and Time Series Analysis
Not possible if the chosen specialisation is "Financial Mathematics" or "Statistics".
 in SuSe  EN  9.0 CP 
WP  MAT6014M6 
Monte Carlo Algorithms
Not possible if the chosen specialisation is "Financial Mathematics" or "Statistics".
 irreg. SuSe  EN  9.0 CP 
WP  MAT6015M4 
Foundations in Financial Mathematics
Not possible if the chosen specialisation is "Financial Mathematics" or "Statistics".
 in SuSe  DE  3.0 CP 
WP  MAT7011M4 
Functional Analysis
Not possible if the chosen specialisation is "Stochastic Analysis".
 in SuSe  EN  9.0 CP 
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".
 in WiSe  EN  9.0 CP 
WP  MAT8011AM4 
Numerics of ODE
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  MAT8011BM4 
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  MAT8012AM4 
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  MAT5914M6  Mathematics of Quantum Computing  irreg.  EN  4.5 CP 
WP  MAT6510M4 
Foundations in Mathematical Image Processing
Not possible if the chosen specialisation is "Image Processing and Data Analysis".
 irreg.  EN  9.0 CP 
WP  MAT8017M6 
Dynamical Systems
Not possible if the chosen specialisation is "Modelling and Scientific Computing".
 irreg. SuSe  EN  4.5 CP 
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".
 irreg. SuSe  EN  9.0 CP 
WP  MAT8123M4 
DifferentialAlgebraic Equations
Not possible if the chosen specialisation is "Modelling and Scientific Computing".
 irreg. SuSe  EN  4.5 CP 
WP  INF1456M6  Optimization in Fluid Mechanics  irreg. SuSe  EN  4.5 CP 
WP  INF1455M6  Topology Optimization  irreg. SuSe  DE/EN  4.5 CP 
WP  MAT7010M6  Spline Functions  irreg.  EN  3.0 CP 
WP  MAT8013AM4 
Introduction to Neural Networks
Not possible if the chosen specialisation is "Modelling and Scientific Computing" or "Systems and Control Theory".
 irreg.  EN  4.5 CP 
WP  MAT8012M6 
Systems and Control Theory
Not possible if the chosen specialisation is "Modelling and Scientific Computing" or "Systems and Control Theory".
 2 Sem. from irreg.  EN  9.0 CP 
WP  MATAMMPOOL7  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 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] CP  

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

P  MATSEMM7  Seminar (Mathematics)  in WiSe/SuSe  DE/EN  3.0 CP 
Section Master Thesis
P  MATMAMATM7  Master Thesis (Mathematics, M.Sc.)  in WiSe/SuSe  DE/EN  30.0 CP 

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.
 in SuSe  DE  6.0 CP 

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.
 in WiSe  DE  6.0 CP 
WP  BIOGM10M2  Grundmodul 10: Tierphysiologie  in WiSe  DE  10.0 CP 
WP  MATBIOGM10M2  Animal Physiology (for Mathematics Students)  in WiSe  DE  6.0 CP 
WP  BIOGM16M2  Grundmodul 16: Molekulare Biotechnologie  in SuSe  DE  6.0 CP 
WP  BIOGM14M2  Grundmodul 14: Neuro/Entwicklungsbiologie  in SuSe  DE  6.0 CP 
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  in WiSe  DE  6.0 CP 
WP  CHEBaCh16M1  Grundmodul: Physikalische Chemie III  in WiSe  DE  5.0 CP 
WP  CHEBaCh17M1  Grundmodul: Theoretische Chemie  in SuSe  DE  5.0 CP 
WP  CHEBaCh191M1  Grundmodul: Biochemie I  in WiSe  DE  5.0 CP 
WP  CHEBaCh192M1  Grundmodul: Biochemie II  in SuSe  DE  3.0 CP 
WP  CHEMMCh_BC_GMM5  Biochemie (Mastergrundmodul)  in WiSe/SuSe  DE  5.0 CP 
WP  CHEMMCh_OC_GMM5  Organische Chemie (Mastergrundmodul)  in WiSe  DE  5.0 CP 
WP  CHEMMCh_PC_GMM5  Physikalische Chemie (Mastergrundmodul)  in SuSe  DE  5.0 CP 
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  in WiSe  DE  5.0 CP 
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] CP  
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).
 in SuSe  DE/EN  5.0 CP 
WP  INF1454M6  High Performance Computing with GPUs  in WiSe  DE/EN  6.0 CP 
WP  INF1045M4  Visualization and Scientific Computing (Project)  in WiSe/SuSe  DE/EN  8.0 CP 
WP  INF1457M6  Algorithmic Differentiation  in WiSe  EN  5.0 CP 
WP  INFINSY_Ba_VMPOOL4  Specialization Bachelor TA Information Systems  [8.0] CP  
WP  INF2045M4  Information Systems (Project)  in WiSe/SuSe  DE/EN  8.0 CP 
WP  INFSE_Ba_VMPOOL4  Specialization Bachelor TA Software Engineering  [4.0  8.0] CP  
WP  INF3045M4  Software Engineering (BachelorProject)  in WiSe/SuSe  DE  8.0 CP 
WP  INFVVS_Ba_VMPOOL4  Specialization Bachelor TA Distributed and Networked Systems  [4.0] CP  
WP  INF4045M4  Distributed and networked systems (Project)  in WiSe/SuSe  DE  8.0 CP 
WP  INF5651M6  Concurrency Theory  in WiSe  EN  8.0 CP 
WP  INF5652M6  Advanced Automata Theory  in SuSe  EN  8.0 CP 
WP  INF5653M5  Complexity Theory  in WiSe  EN  8.0 CP 
WP  INF5045M4  Algorithms and Deduction (Project)  in WiSe/SuSe  DE  8.0 CP 
WP  INFES_Ba_VMPOOL4  Specialization Bachelor TA Embedded Systems and Robotics  [4.0  8.0] CP  
WP  INF6045M4  Embedded Systems (Project)  in WiSe/SuSe  DE/EN  8.0 CP 
WP  INFKI_Ba_VMPOOL4  Specialization Bachelor TA Intelligent Systems  [4.0  8.0] CP  
WP  INF7551M6  Machine Learning II  Statistical ML  in WiSe  EN  8.0 CP 
WP  INF7045M4  Intelligent Systems (Project)  in WiSe/SuSe  DE/EN  8.0 CP 
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  in WiSe  DE  8.0 CP 
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  in WiSe  DE  18.0 CP 
WP  PHYE1M3  Physics of condensed matter and statistical physics  in SuSe  DE  20.0 CP 
WP  PHYE2M3  atomic physics  in WiSe  DE  5.0 CP 
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] CP  
WP  WIWCONMPOOL7  Field of Specialization: Management Accounting  [4.0  9.0] CP  
WP  WIWETMPOOL7  Field of Specialization: Economic Theory  [4.0  4.5] CP  
WP  WIWEPSMPOOL7  Field of Specialization: Entrepreneurship  [3.0  6.0] CP  
WP  WIWFEMPOOL7  Field of Specialization: Financial Economics  [4.0  6.0] CP  
WP  WIWFUBMPOOL7  Field of Specialization: Finance and Banking Management  [4.0  4.5] CP  
WP  WIWHRMOBMPOOL7  Field of Specialization: Human Resource Management and Organizational Behavior  [4.0  9.0] CP  
WP  WIWIOEMPOOL7  Field of Specialization: Industrial Economics  [4.0  4.5] CP  
WP  WIWLOGMPOOL7  Field of Specialization: Logistics  [4.0  4.5] CP  
WP  WIWMKTMPOOL7  Field of Specialization: Marketing  [3.0  6.0] CP  
WP  WIWPOMMPOOL7  Field of Specialization: Produktionsmanagement  [4.0  9.0] CP  
WP  WIWREMPOOL7  Field of Specialization: Environment, Resources, Energy: Economics and Policy  [4.0  4.5] CP  
WP  WIWSWPMPOOL7  Field of Specialization: Taxation and Auditing  [4.0  6.0] CP  
WP  WIWSICMPOOL7  Field of Specialization: Strategy, Innovation and Cooperation  [4.0  9.0] CP  
WP  WIWSMGMPOOL7  Field of Specialization: Sustainability Management  [4.0  9.0] CP 
The choice of the modules is limited by the chosen mathematical specialisation: