Directorate of Studies 25 - Mathematics

Bachelor Mathematics (621 [4] - Version 2021)

Group of Compulsory Modules "Core" (90 ECTS)

StEOP: Introduction to the Mathematical Method (16 ECTS)

• 250001 KO Tutorials for 1st and 2nd semester
• 250003 UE [ en de ] STEOP: Exercises on Introduction to mathematical methodology
• 250026 VO STEOP: Introduction to mathematical methodology
• 250169 OL ( OV ) Infoveranstaltung für Erstsemestrige

IT Basics (2 ECTS)

• 250007 PR IT Basics

Introduction to Higher Mathematics (12 ECTS)

Alternative Compulsory Module: Mathematical Programming (2 ECTS)

• 250008 VU Mathematical programming

Alternative Compulsory Module: Exercise for Advanced Students (2 ECTS)

Analysis 2 (10 ECTS)

• 250027 VO Analysis 2
• 250028 PS [ de en ] Analysis 2
• 250055 KU Exercise Analysis for Advanced students

Linear Algebra 2 (10 ECTS)

• 250056 KU Exercise Linear Algebra for Advanced students
• 250082 VO Linear Algebra 2
• 250083 PS [ de en ] Linear Algebra 2

Discrete Mathematics and Computer Science (10 ECTS)

• 250050 VO Discrete Mathematics and Computer Science
• 250051 PS [ de en ] Discrete Mathematics and Computer Science

Algebra (10 ECTS)

Numerical Mathematics (10 ECTS)

Integration and Stochastics (10 ECTS)

Group of Elective Modules "Foundation" (50 ECTS)

Complex and Harmonic Analysis (10 ECTS)

Topology and Functional Analysis (10 ECTS)

Analysis 3 (10 ECTS)

• 250029 VO Analysis 3
• 250033 PS [ en ] Analysis 3

Probability Theory (10 ECTS)

• 250040 VO Probability theory and basic statistics
• 250041 PS [ en de ] Probability theory and basic statistics

Algebra 2 (10 ECTS)

• 250048 VO Algebra 2
• 250052 PS Algebra 2

Optimisation and Modelling (10 ECTS)

• 250054 VO Optimization and Modeling
• 250061 PS Optimisation and Modelling

Differential Equations and Modelling (10 ECTS)

Group of Electives Modules "Specialisation" (30 ECTS)

Gender Aspects in Mathematics (5 ECTS)

• 250064 VU Gender Aspects in Mathematics

Mathematical Logic (10 ECTS)

Geometry and Topology (10 ECTS)

Discrete Mathematics (5 ECTS)

Image and Signalprocessing (5 ECTS)

Variational Calculus (5 ECTS)

Partial Differential Equations (10 ECTS)

• 250004 VO Partial Differential Equations
• 250005 PS [ en ] Partial Differential Equations

Numerical Methods for Ordinary and Partial Differential Equations (10 ECTS)

Number Theory (5 ECTS)

Cryptography (5 ECTS)

• 250013 VU Cryptography

Commutative Algebra and Algebraic Geometry (5 ECTS)

Statistics and Data Science (10 ECTS)

• 250009 VO Statistics and Data Science
• 250011 PS Statistics and Data Science

Financial Mathematics (10 ECTS)

Biomathematics and Game Theory (5 ECTS)

• 250110 VO Biomathematics and Game Theory

Machine Learning (10 ECTS)

Dynamical Systems (5 ECTS)

Selected Topics from Probability Theory (10 ECTS)

Current Developments and Applications 1 (10 ECTS)

• 250112 VU Mathematical modelling

Current Developments and Applications 2 (5 ECTS)

• 250037 VU The art of problem solving

Compulsory Module Bachelor's Seminar (10 ECTS)

• 250032 SE Bachelorseminar

Bachelor Teacher Training Programme: Mathematics (193 057, 198 420)

UFMA01 Introductory and Orientation Period ( 7 ECTS)

• 250001 KO Tutorials for 1st and 2nd semester
• 250019 KO Tutorials for introductary phase
• 250169 OL ( OV ) Infoveranstaltung für Erstsemestrige

UFMA02 Aspects of Mathematics (3 ECTS)

UFMA03 Geometry (16 ECTS)

• 250159 VO Geometry and linear algebra for secondary school teacher accreditation programme
• 250163 UE ( KPH Krems PH-WIEN ) Geometry and linear algebra for secondary school teacher accreditation programme

UFMA04 Analysis (16 ECTS)

• 250166 VO Analysis in one variable for secondary school teacher accreditation programme
• 250167 UE ( PH-NÖ ) Analysis in one variable for secondary school teacher accreditation programme

UFMA05 Stochastics (14 ECTS)

• 250171 VO School mathematics stochastics
• 250172 UE ( PH-NÖ PH-WIEN ) School mathematics stochastics

UFMA06 Applied mathematics (12 ECTS)

• 250173 VO Applied mathematics for secondary school teacher accreditation programme
• 250174 VO ( PH-NÖ ) Mathematics in everyday life and in science applications
• 250175 UE ( PH-WIEN ) Applied mathematics for secondary school teacher accreditation programm

UFMA07 Teaching Methodology (10 ECTS)

• 250018 VU Advanced topics in mathematics education
• 250022 PR Methodology of using ICT in teaching mathematics
• 250176 PR Practicum on using ICT in teaching mathematics
• 250178 SE ( PH-NÖ PH-WIEN ) Seminar on lesson planning

UFMA08 Arithmetic and algebra for secondary schools (4 ECTS)

UFMA09 Electives Teacher Training Programme (0-10 ECTS)

• 250002 SE ( PH-NÖ ) Room geometry and CAD
• 250080 PLV ( PH-NÖ ) Summer school mathematic
• 250180 SE ( KPH Krems ) Assessment and grading of students in high-school mathematics
• 250181 SE ( PH-WIEN ) Meine Schüler/innen verstehen mich nicht - Sprachsensibler Mathematikunterricht

UFMA10 Subject-based Practicum - Mathematics (7 ECTS)

• 250184 SE ( PH-NÖ PH-WIEN ) Seminar for Subject-based Praticum - Mathematics

UFMA11 Bachelormodul (8 ECTS)

• 250032 SE Bachelorseminar

Non curricula lectures

Bachelor Teacher Training Programme Descriptive Geometry (193 044, 198 405)

Master Mathematics (821 [2] - Version 2016)

Orientation Course

Elective Modules (75 ECTS)

Specialization "Algebra, number theory and dicrete mathematics" (51 ECTS)

Basic courses, specialization "Algebra"

• 250039 SE [ en ] Algebra and Number Theory
• 250044 SE [ en ] Algebra
• 250045 SE [ en ] AG Discrete Mathematics
• 250046 SE [ en ] Geometry and Topology
• 250057 VO [ en ] Group theory
• 250058 PS [ en ] Introductory Seminar on group theory
• 510002 SE [ en ] Project Seminar Algebra (VSM)

Advanced courses, specialization "Algebra"

• 250021 VO [ en ] Selected Topics in Algebraic Number Theory
• 250025 PS [ en ] Selected Topics in Algebraic Number Theory
• 250042 VO [ en ] Analytic Number Theory
• 250059 VO [ en ] Diophantine Approximation
• 250062 VO [ en ] Topics in Combinatorics
• 250065 VO Topics in Algebraic Geometry 2
• 250066 VO [ en ] Introduction to p-adic Analysis
• 250067 PS [ en ] Introduction to p-adic Analysis

Specialization "Analysis" (51 ECTS)

• 250076 VO [ en ] Approximation Theory

Basic courses, specialization "Analysis"

• 250010 PS [ en ] Introductory Seminar on Dynamical System and Nonlinear Differential Equations
• 250034 SE [ en ] Topics in Analysis and Geometry
• 250072 SE [ en ] Complex Analysis Seminar
• 250081 VO [ en ] Real analysis
• 250085 SE [ en ] Seminar Analysis
• 250099 VO [ en ] Advanced functional analysis
• 250115 VO [ en ] Dynamical Systems and Nonlinear Differential Equations
• 250121 PS [ en ] Introductory seminar on Advanced functional analysis
• 250162 SE [ en ] MCMP Seminar
• 510003 SE [ en ] PDE Afternoon Seminar (VSM)
• 510004 SE [ en ] Harmonic Analysis (VSM)
• 510005 SE [ en ] Seminar on Calculus of Variations (VMS)

Advanced courses, specialization "Analysis"

• 250063 VO [ en ] Topics in the Calculus of Variations
• 250066 VO [ en ] Introduction to p-adic Analysis
• 250067 PS [ en ] Introduction to p-adic Analysis
• 250074 VO [ en ] Topics in Real Analysis
• 250075 VO Geometric Analysis of First Order Linear PDEs
• 250094 VO [ en ] Numerics of Partial Differential Equations
• 250095 VU [ en ] Mathematics of Machine Learning
• 250103 VU [ en ] Introduction to Mathematical Methods in Continuum Mechanics
• 250133 VO [ en ] Introduction to Geometric Measure Theory

Specialization "Applied mathematics and scientific computing" (51 ECTS)

Basic courses, specialization "AMaSciCo"

• 250035 SE [ en ] Seminar Optimization
• 250070 SE [ en ] Seminar Applied Mathematics
• 250071 PS [ en ] Introductory seminar on Advanced numerical analysis
• 250078 VO [ en ] Advanced numerical analysis
• 250084 SE [ en ] Mathematical/Computational Astro/Quantum Physics
• 250090 SE [ en ] Applied Machine Learning
• 250120 SE [ en ] ( REMOTE ) Joint Seminar with Fudan University and RICAM
• 250122 SE [ en ] Tomography 2
• 510003 SE [ en ] PDE Afternoon Seminar (VSM)
• 510004 SE [ en ] Harmonic Analysis (VSM)
• 510005 SE [ en ] Seminar on Calculus of Variations (VMS)

Advanced courses, specialization "AMaSciCo"

• 250043 VU [ en ] Kinetic Theory Applied to Biology
• 250049 VO [ en ] Spectral Graph Theory
• 250063 VO [ en ] Topics in the Calculus of Variations
• 250068 VO [ en ] Entanglement in quantum many-body systems: Mathematical results
• 250094 VO [ en ] Numerics of Partial Differential Equations
• 250095 VU [ en ] Mathematics of Machine Learning
• 250100 VO [ en ] Convex Optimization
• 250103 VU [ en ] Introduction to Mathematical Methods in Continuum Mechanics
• 250104 VO [ en ] Global Optimization

Specialization "Biomathematics" (51 ECTS)

Basic courses, specialization "Biomathematics"

• 250097 SE [ en ] Seminar (Mathematical Population Genetics)
• 250106 VO [ en ] Mathematical population genetics
• 250108 PS [ en ] Introductory seminar on mathematical population genetics
• 250115 VO [ en ] Dynamical Systems and Nonlinear Differential Equations
• 250128 SE [ en ] Seminar (AG Biomathematik)

Advanced courses, specialization "Biomathematics"

• 250010 PS [ en ] Introductory Seminar on Dynamical System and Nonlinear Differential Equations
• 250043 VU [ en ] Kinetic Theory Applied to Biology

Specialization "Geometry and Topology" (51 ECTS)

Basic courses, specialization "Geometry"

• 250034 SE [ en ] Topics in Analysis and Geometry
• 250046 SE [ en ] Geometry and Topology
• 250096 VO [ en ] Analysis on Manifolds
• 250150 VO [ en ] Low dimensional topology
• 250158 PS [ en ] Introductory seminar on Analysis on manifolds
• 250162 SE [ en ] MCMP Seminar

Advanced courses, specialization "Geometry"

• 250065 VO Topics in Algebraic Geometry 2
• 250105 SE [ en ] Seminar Geometry
• 250130 VO [ en ] Metric Geometry
• 250133 VO [ en ] Introduction to Geometric Measure Theory
• 250150 VO [ en ] Low dimensional topology

Specialization "Mathematical logic and theoretical informatics" (51 ECTS)

Basic courses, specialization "Logic"

• 250089 SE [ en ] Logic Colloquium
• 250102 SE [ en ] Research Seminar in Set Theory
• 250153 VO [ en ] Introduction to theoretical computer science
• 510010 SE [ en ] Seminar mathematics (doctoral programm) 2/4

Advanced courses, specialization "Logic"

• 250136 VO [ en ] Topics in Model Theory
• 250137 VO [ en ] Topics in Set Theory
• 250138 VO [ en ] Dynamics of Polish Groups

Specialization "Stochastics and dynamical systems" (51 ECTS)

Basic courses, speicialization "Stochastics"

• 250010 PS [ en ] Introductory Seminar on Dynamical System and Nonlinear Differential Equations
• 250092 SE [ en ] AG Ergodic Theory
• 250107 SE [ en ] Seminar Stochastics and Dynamics
• 250115 VO [ en ] Dynamical Systems and Nonlinear Differential Equations
• 250185 PS [ en ] Introductory Seminar on Advanced Probability Theory
• 250189 VO [ en ] Advanced Probability Theory
• 510006 SE [ en ] Vienna Seminar in Mathematical Finance and Probability (VSM)
• 510007 SE [ en ] Vienna Probability Seminar (VSM)

Advanced courses, specialization "Stochastics"

• 250016 VO [ en ] Mathematical Finance (Continuous Time)
• 250095 VU [ en ] Mathematics of Machine Learning
• 250101 PS [ en ] Mathematical Finance (Continuous Time)
• 250109 VO [ en ] Ergodic Theory
• 250133 VO [ en ] Introduction to Geometric Measure Theory
• 250138 VO [ en ] Dynamics of Polish Groups

Further Electives (15 ECTS)

• 250036 VO [ en ] Topics from Habilitations
• 250147 OL [ en ] Information for beginning master students

Master Teacher Training Programme: Mathematics (196 057, 199 520)

UFMAMA01 Mathematics in Rn (12 ECTS)

UFMAMA02 Advanced mathematics (3 ECTS)

• 250020 VO Number theory for pre-service teachers

UFMAMA03 Application-orientation for mathematic class (4 ECTS)

• 250191 VO Schulmathematik Angewandte Mathematik
• 250192 UE ( PH-NÖ PH-WIEN ) School mathematics: applied mathematics

UFMAMA04 Optional Courses Teaching Methodology (3 ECTS)

• 250017 SE ( PH-NÖ ) Lernvideos für einen motivierenden Mathematikunterricht in der Sekundarstufe
• 250114 KO Mathematik macht Freude
• 250143 KO Colloquium of mathematics didactics
• 250146 SE Seminar Subject-specific didactics

UFMAMA05 Practice Module (Didactic Supervision) (4 ECTS)

• 250193 SE ( KPH Krems PH-NÖ PH-WIEN ) Seminar for teaching practice

Master Teacher Training Programme: Descriptive Geometry (196 505)