SPL 25 - Mathematics

25.1 Bachelor programme

1.1. Introductory phase (STEP)

• 250010 VO Introduction into mathematical methodology
• 250052 UE Aid from the EDP
• 250015 VO Introduction to analysis
• 250017 UE Repetition course to "Introduction to Analysis"
• 250007 VO Introduction to linear algebra and geometry
• 250009 UE Tutorials "Introduction to linear algebra and geometry"
• 250008 UE Repetition course to linear algebra and geometry
• 250016 UE Tutorials "Introduction to analysis"

1.2. Compulsory courses for all students

• 250013 VO Linear algebra and geometry 2
• 250014 UE Tutorials to linear algebra and geometry 2
• 250028 VO Algebraic structures
• 250046 VO Higher analysis and elementary differential geometry
• 250047 UE Tutorial to "Higher analysis and elementary differential geometry"
• 250093 VO Modelling
• 250094 UE Tutorials "Modelling"
• 250024 VO Discrete mathematics
• 250025 UE Tutorials to " Discrete mathematics"
• 250029 UE Tutorials to "Algebraic structures"

Evening courses

• 250051 VO Analysis
• 250061 UE Tutorials to Analysis
• 250032 VO Linear Algebra and Geometry for SSTAP
• 250033 UE Tutorial: Linear Algebra and Geometry for SSTAP

1.3. Alternative group of compulsory modules "Mathematische Berufsvorbereitung"

• 250056 VO History of mathematics
• 250098 VO Basic Ideas of Mathematics

1.4. Alternative group of compulsory modules "Vorbereitung auf wissenschaftliche Arbeit"

• 250062 VO Partial differential equations
• 250063 UE Tutorials to "Partial differential equations"
• 250044 VO Functional analysis 1
• 250056 VO History of mathematics
• 250098 VO Basic Ideas of Mathematics
• 250045 UE Introductory Seminar to Functional analysis 1

25.2. Diploma Programme

First stage

2.1. Compulsory courses

• 250015 VO Introduction to analysis
• 250016 UE Tutorials "Introduction to analysis"
• 250007 VO Introduction to linear algebra and geometry
• 250009 UE Tutorials "Introduction to linear algebra and geometry"
• 250046 VO Higher analysis and elementary differential geometry
• 250047 UE Tutorial to "Higher analysis and elementary differential geometry"
• 250013 VO Linear algebra and geometry 2
• 250014 UE Tutorials to linear algebra and geometry 2
• 250028 VO Algebraic structures
• 250029 UE Tutorials to "Algebraic structures"
• 250024 VO Discrete mathematics
• 250025 UE Tutorials to " Discrete mathematics"

2.2 Elective Courses

• 250010 VO Introduction into mathematical methodology
• 250017 UE Repetition course to "Introduction to Analysis"
• 250008 UE Repetition course to linear algebra and geometry
• 250093 VO Modelling
• 250094 UE Tutorials "Modelling"

2.3. Evening courses

• 250051 VO Analysis
• 250061 UE Tutorials to Analysis
• 250032 VO Linear Algebra and Geometry for SSTAP
• 250033 UE Tutorial: Linear Algebra and Geometry for SSTAP

Second Stage

2.4. Lecture Courses, Tutorials, and Conversatoriums

• 250044 VO Functional analysis 1
• 250062 VO Partial differential equations
• 250063 UE Tutorials to "Partial differential equations"
• 250001 VO Commutative algebra
• 250110 VO Algebraic number theory
• 250111 PS Introductory Seminar to Algebraic number theory
• 250080 VO Algebraic geometry
• 250081 PS Introductory Seminar to Algebraic geometry
• 250089 VO [ en ] Mathematics of String Theory I - Lefschetz Pencils and Hodge Theory
• 250057 VO Lie groups
• 250058 PS Introductory Seminar to Lie groups
• 250012 VO Selcted topics in graph theory - "Graphs and groups"
• 250064 VO Selected topics in topological and lie groups
• 250076 VO Ordinary differential equations 2
• 250077 UE Introductory seminar to ordinary differential equations 2
• 250019 VO Measure and integration theory
• 250020 PS Introductory seminar to measure and integration theory
• 250078 VO Theory of approximation
• 250002 VO [ en ] Selected topics in differential equations
• 250003 PS [ en ] Introductory seminar to selected topics in differential equations
• 250127 VO [ en ] Introduction to inverse scattering theory with applications
• 250128 PS [ en ] Introductory Seminar for Introduction to inverse scattering theory with applications
• 250043 VO Selected topics in harmonic analysis
• 250074 VO Selected topics in functional analysis: Locally convex vector spaces
• 250040 VO Selected topics in differential geometry and partial differential equations - (Exterior Differential Systems)
• 250066 VO Selected topics in differential geometry and partial differential equations - Geodätengleichungen auf Differmorphismengruppen
• 250100 VO Numerical mathematics and modelling 2
• 250101 PS Introductory Seminar to Numerical mathematics and modelling 2
• 250067 VO Optimization and variational calculus
• 250068 PS Introductory seminar to optimization and variational calculus
• 050169 VU WA.ASC.NM.VU Numerical Methods for Differential Equations
• 250034 VO Biomathematics
• 250035 PS Introductory Seminar to Biomathematics
• 250070 VO Selected topics in applied mathematics - (Internal points procedures)
• 250104 VO Selected topics in applied mathematics (Lie algebras and quantum mechanics)
• 250108 VO Stochastic Processes
• 250083 VO Evolutionary Game Theory
• 250049 VO Probability theory 2
• 250060 VO Differential geometry 2
• 250072 VO Discrete Geometry
• 250121 VO Introduction to Mathematical Logic
• 250122 PS Introductory Seminar to Introduction to Mathematical Logic
• 250123 VO Introduction to Theoretical Informatic
• 250125 VO Selected topics in Mathematical Logic
• 250045 UE Introductory Seminar to Functional analysis 1
• 250129 VO [ en ] Stochastic Calculus for Finance

2.5. Mathematical Colloquium and Seminars

• 250107 KO Mathematical colloquium
• 250031 SE Seminar (the art of problem solving)
• 250091 SE Seminar (Combinatorics)
• 250023 SE Seminar (Number theory)
• 250082 SE Seminar (Algebraic Geometry)
• 250090 SE [ en ] Research Seminar in Homological Mirror Symmetry
• 250106 PJ+SE Project seminar (Algebra)
• 250112 PJ+SE Project seminar (Number theory)
• 250092 SE Seminar (Discrete mathematics)
• 250053 SE Seminar (Analysis) generalized functions
• 250059 SE Seminar (Analysis): Nonlinear Functional Analysis
• 250096 SE Seminar (Analysis) for SSTAP and Diploma
• 250079 SE Seminar (Scientific working)
• 250075 SE IK-Seminar (Analysis)
• 250065 SE WK Seminar (Differential Equations)
• 250004 SE [ en ] Seminar in (differential equations)
• 250097 SE Seminar (Selected topics in nonlinear partial differential equations
• 250048 SE Seminar (Complex Analysis)
• 250117 SE Seminar (Nonstandard-Analysis)
• 250105 PJ+SE Project seminar (Analysis)
• 250069 SE Seminar (Optimization)
• 250018 PJ+SE Project seminar (applied mathematics)
• 250103 PJ+SE Project seminar applied mathematics (data analysis)
• 250102 SE Privatissimum (Applied mathematics)
• 250036 SE [ en ] Seminar (Biomathematics)
• 250037 SE [ en ] Seminar (Mathematical population genetics)
• 250084 SE Seminar (Evolutionary Game Theory)
• 250038 PJ+SE IK-Project Seminar (Differential geometry)
• 250039 SE IK- Seminar (Lie groups)
• 250050 SE Seminar (Probability theory)
• 250109 SE Seminar (Dynamical Systems)
• 250124 SE Seminar in Mathematical Logic
• 250126 SE Reserch Seminar: Mathematical Logic
• 250130 SE Seminar (Transport Theory)

2.6. Elective Courses (2nd stage)

• 250098 VO Basic Ideas of Mathematics

25.3. Teacher training programme

First stage

3.1. Compulsory courses

• 250010 VO Introduction into mathematical methodology
• 250052 UE Aid from the EDP
• 250015 VO Introduction to analysis
• 250007 VO Introduction to linear algebra and geometry
• 250009 UE Tutorials "Introduction to linear algebra and geometry"
• 250021 VO Real analysis into several and complex analysis into variable for SSTAP
• 250022 UE Tutorial: Real analysis into several and complex analysis into variable for SSTAP
• 250032 VO Linear Algebra and Geometry for SSTAP
• 250033 UE Tutorial: Linear Algebra and Geometry for SSTAP
• 250005 VO School mathematics 1 (Arithmetic and Algebra)
• 250113 VO School mathematics 4 (Vector calculus)
• 250114 UE Tutorial: School mathematics 4 (Vector calculus)
• 250006 UE Tutorial: School mathematics 1 (Arithmetic and Algebra)
• 250016 UE Tutorials "Introduction to analysis"
• 250087 VO School mathematics - Applied mathematics
• 250088 UE Tutorial: School mathematics - Applied mathematics

3.2. Elective courses

• 250017 UE Repetition course to "Introduction to Analysis"
• 250008 UE Repetition course to linear algebra and geometry

Second stage

3.3 Mathematics

• 250041 VO Applied mathematics for SSTAP
• 250042 UE Tutorial: Applied mathematics for SSTAP
• 250054 VO Differential equations for SSTAP
• 250055 UE Tutorial: Differential equations for SSTAP
• 250071 PS Computer course for SSTAP
• 250056 VO History of mathematics
• 250072 VO Discrete Geometry
• 250098 VO Basic Ideas of Mathematics
• 250030 SE Seminar Secondary School Teacher Accreditation Programme (Algebra)
• 250026 SE Seminar for Secondary School Teacher Accreditation Programme (Applied mathematics)
• 250096 SE Seminar (Analysis) for SSTAP and Diploma
• 250085 SE Seminar for SSTAP (Stochastics)

3.4. Didactics of mathematics

• 250120 VO Indroduction to didactics of mathematics
• 250115 SE Seminar to the school practical training
• 250011 SE Seminar for planning teaching units
• 250086 SE Seminar for planning teaching units
• 250116 SE Seminar on mathematics education
• 250118 SE Seminar on mathematics education
• 250005 VO School mathematics 1 (Arithmetic and Algebra)
• 250006 UE Tutorial: School mathematics 1 (Arithmetic and Algebra)
• 250087 VO School mathematics - Applied mathematics
• 250088 UE Tutorial: School mathematics - Applied mathematics
• 250113 VO School mathematics 4 (Vector calculus)
• 250027 VO Problems in teaching mathematics
• 250114 UE Tutorial: School mathematics 4 (Vector calculus)

3.5. Elective courses (second stage)

• 250024 VO Discrete mathematics
• 250025 UE Tutorials to " Discrete mathematics"
• 250093 VO Modelling
• 250094 UE Tutorials "Modelling"
• 250119 VO Selected topics in mathematics education

25.4. Master Programme

• 250107 KO Mathematical colloquium
• 250031 SE Seminar (the art of problem solving)

4.1. Specialization "Algebra, number theory and dicrete mathematics"

Basic courses, specialization "Algebra"

• 250110 VO Algebraic number theory
• 250111 PS Introductory Seminar to Algebraic number theory
• 250091 SE Seminar (Combinatorics)
• 250082 SE Seminar (Algebraic Geometry)
• 250090 SE [ en ] Research Seminar in Homological Mirror Symmetry
• 250023 SE Seminar (Number theory)
• 250039 SE IK- Seminar (Lie groups)
• 250106 PJ+SE Project seminar (Algebra)
• 250112 PJ+SE Project seminar (Number theory)
• 250092 SE Seminar (Discrete mathematics)

Advanced courses, specialization "Algebra"

• 250001 VO Commutative algebra
• 250080 VO Algebraic geometry
• 250081 PS Introductory Seminar to Algebraic geometry
• 250057 VO Lie groups
• 250089 VO [ en ] Mathematics of String Theory I - Lefschetz Pencils and Hodge Theory
• 250012 VO Selcted topics in graph theory - "Graphs and groups"
• 250064 VO Selected topics in topological and lie groups

4.2. Specialization "Analysis"

Basic courses, specialization "Analysis"

• 250075 SE IK-Seminar (Analysis)
• 250053 SE Seminar (Analysis) generalized functions
• 250059 SE Seminar (Analysis): Nonlinear Functional Analysis
• 250096 SE Seminar (Analysis) for SSTAP and Diploma
• 250065 SE WK Seminar (Differential Equations)
• 250004 SE [ en ] Seminar in (differential equations)
• 250097 SE Seminar (Selected topics in nonlinear partial differential equations
• 250048 SE Seminar (Complex Analysis)
• 250079 SE Seminar (Scientific working)
• 250105 PJ+SE Project seminar (Analysis)
• 250117 SE Seminar (Nonstandard-Analysis)

Advanced courses, specialization "Analysis"

• 250076 VO Ordinary differential equations 2
• 250077 UE Introductory seminar to ordinary differential equations 2
• 250078 VO Theory of approximation
• 250002 VO [ en ] Selected topics in differential equations
• 250003 PS [ en ] Introductory seminar to selected topics in differential equations
• 250074 VO Selected topics in functional analysis: Locally convex vector spaces
• 250043 VO Selected topics in harmonic analysis
• 250040 VO Selected topics in differential geometry and partial differential equations - (Exterior Differential Systems)
• 250066 VO Selected topics in differential geometry and partial differential equations - Geodätengleichungen auf Differmorphismengruppen
• 250127 VO [ en ] Introduction to inverse scattering theory with applications
• 250128 PS [ en ] Introductory Seminar for Introduction to inverse scattering theory with applications

4.3. Specialization "Applied mathematics and scientific computing"

Basic courses, specialization "AMaSciCo"

• 250100 VO Numerical mathematics and modelling 2
• 250101 PS Introductory Seminar to Numerical mathematics and modelling 2
• 250067 VO Optimization and variational calculus
• 250068 PS Introductory seminar to optimization and variational calculus
• 250069 SE Seminar (Optimization)
• 250065 SE WK Seminar (Differential Equations)
• 250018 PJ+SE Project seminar (applied mathematics)
• 250103 PJ+SE Project seminar applied mathematics (data analysis)
• 250102 SE Privatissimum (Applied mathematics)
• 250130 SE Seminar (Transport Theory)

Advanced courses, specialization "AMaSciCo"

• 250078 VO Theory of approximation
• 050169 VU WA.ASC.NM.VU Numerical Methods for Differential Equations
• 250070 VO Selected topics in applied mathematics - (Internal points procedures)
• 250104 VO Selected topics in applied mathematics (Lie algebras and quantum mechanics)
• 250129 VO [ en ] Stochastic Calculus for Finance

4.4. Specialization "Biomathematics"

Basic courses, specialization "Biomathematics"

• 250108 VO Stochastic Processes
• 250034 VO Biomathematics
• 250035 PS Introductory Seminar to Biomathematics
• 250037 SE [ en ] Seminar (Mathematical population genetics)
• 250084 SE Seminar (Evolutionary Game Theory)
• 250036 SE [ en ] Seminar (Biomathematics)

Advanced courses, specialization "Biomathematics"

• 250083 VO Evolutionary Game Theory

4.5. Specialization "Geometry and Topology"

Basic courses, specialization "Geometry"

• 250057 VO Lie groups
• 250058 PS Introductory Seminar to Lie groups
• 250060 VO Differential geometry 2
• 250039 SE IK- Seminar (Lie groups)
• 250059 SE Seminar (Analysis): Nonlinear Functional Analysis
• 250082 SE Seminar (Algebraic Geometry)
• 250090 SE [ en ] Research Seminar in Homological Mirror Symmetry
• 250038 PJ+SE IK-Project Seminar (Differential geometry)

Advanced courses, specialization "Geometry"

• 250080 VO Algebraic geometry
• 250081 PS Introductory Seminar to Algebraic geometry
• 250089 VO [ en ] Mathematics of String Theory I - Lefschetz Pencils and Hodge Theory
• 250040 VO Selected topics in differential geometry and partial differential equations - (Exterior Differential Systems)
• 250066 VO Selected topics in differential geometry and partial differential equations - Geodätengleichungen auf Differmorphismengruppen
• 250064 VO Selected topics in topological and lie groups
• 250072 VO Discrete Geometry

4.6. Specialization "Mathematical logic and theoretical informatics"

Basic courses, specialization "Logic"

• 250121 VO Introduction to Mathematical Logic
• 250122 PS Introductory Seminar to Introduction to Mathematical Logic
• 250123 VO Introduction to Theoretical Informatic
• 250124 SE Seminar in Mathematical Logic
• 250126 SE Reserch Seminar: Mathematical Logic

Advancede courses, specialization "Logic"

• 250125 VO Selected topics in Mathematical Logic

4.7. Specialization "Stochastics and dynamical systems"

Basic courses, speicialization "Stochastics"

• 250108 VO Stochastic Processes
• 250019 VO Measure and integration theory
• 250020 PS Introductory seminar to measure and integration theory
• 250050 SE Seminar (Probability theory)
• 250109 SE Seminar (Dynamical Systems)
• 250130 SE Seminar (Transport Theory)

Advanced courses, specialization "Stochastics"

• 250049 VO Probability theory 2
• 250129 VO [ en ] Stochastic Calculus for Finance

25.5. Service teaching

5.1. Mathematics for Physics and related fields

• 260224 VO Analysis for Physicists I
• 260225 UE Problem session to Analysis for Physicists I
• 260226 VO Linear Algebra for Physicists
• 260227 UE Problem session to Linear Algebra for Physicists

5.2. Informatics

• 050101 VO Mathematics for Computer Science Ed. 1
• 050123 VO Unix System Administration 1
• 050102 UE Problem Session: Introduction to Unix System Administration 1
• 050164 VO Algorithms, Data Structures and Programming 2
• 050165 UE Problem Session: Algorithms, Data Structures and Programming 2
• 050169 VU WA.ASC.NM.VU Numerical Methods for Differential Equations
• 050166 VU Internet Applications
• 050071 PR Laboratory for Specialized Didactics
• 050140 VU Seminar with Bachelor Thesis
• 050122 UE Introductory Seminar Mathematics for Computer Science Ed. 1