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)

• EXAM ON-SITE COMM Introduction to mathematical methodology
• 250001 KO Tutorials for 1st and 2nd semester
• 250003 UE [ de en ] 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 Linear Algebra 2

Discrete Mathematics and Computer Science (10 ECTS)

• 250050 VO Discrete Mathematics and Computer Science
• 250051 PS 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 Analysis 3

Probability Theory (10 ECTS)

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

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)

• 250067 VO Image and Signalprocessing

Variational Calculus (5 ECTS)

Partial Differential Equations (10 ECTS)

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

Number Theory (5 ECTS)

Cryptography (5 ECTS)

• 250072 VO Cryptography

Commutative Algebra and Algebraic Geometry (5 ECTS)

Statistics and Data Science (10 ECTS)

Financial Mathematics (10 ECTS)

Biomathematics and Game Theory (5 ECTS)

• 250066 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)

Current Developments and Applications 2 (5 ECTS)

Compulsory Module Bachelor's Seminar (10 ECTS)

• 250032 SE Bachelorseminar

Bachelor Mathematics (621 [3] - Version 2014)

GHM Introductory and Orientation Period (15 ECTS)

EHM Introduction to university level mathematics (18 ECTS)

ANA Analysis (11 ECTS)

LAG Linear algebra and analytical geometry (12 ECTS)

ZTH Number theory (5 ECTS)

PRO Programming (5 ECTS)

HAN Advanced analysis (10 ECTS)

NUM Numerical analysis (10 ECTS)

KAN Complex analysis (5 ECTS)

PTS Probability and statistics (10 ECTS)

DMA Discrete mathematics (5 ECTS)

DGL Differential equations (14 ECTS)

ALG Algebra (14 ECTS)

MIK Mathematics in the sciences and society (3 ECTS)

• 250157 KO The art of problem solving

TFA Topology and functional analysis (12 ECTS)

• 250075 UE [ en de ] Tutorials on functional analysis
• 250090 VO Functional analysis

BAS Bachelor seminar with thesis (10 ECTS)

• 250032 SE Bachelorseminar

WLO Mathematical logic (optional module) (7 ECTS)

WFM Applied mathematics: finance (optional module) (7 ECTS)

WST Stochastics (optional module) (7 ECTS)

WAS Applied mathematics: statistics (optional module) (7 ECTS)

WGO Applied mathematics: graph theory and discrete optimization (optional module) (7 ECTS)

WBS Applied mathematics: biomathematics and game theory (optional module) (7 ECTS)

• 250066 VO Biomathematics and Game Theory
• 250074 UE Tutorials on biomathematics and game theory

WDG Classical differential geometry (optional module) (7 ECTS)

WCG Applied mathematics: algorithmic geometry (optional module) (7 ECTS)

WOP Applied mathematics: optimization (optional module) (7 ECTS)

WKR Applied mathematics: cryptography (optional module) (7 ECTS)

• 250072 VO Cryptography
• 250106 UE UE Übung zu Kryptographie

WMO Applied mathematics: modelling (optional module) (7 ECTS)

• 250062 VU Mathematical modeling

WND Applied mathematics: numerical methods for differential equations (optional module) (7 ECTS)

Additional Optional module (7 ECTS)

• 250067 VO Image and Signalprocessing
• 250076 UE Tutorials on image and signal processing
• 250141 VO Applied machine learning
• 250144 UE Applied machine learning

Non curricula lecture

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

UFMA01 Introductory and Orientation Period ( 7 ECTS)

• EXAM COMM STEOP: Introduction to mathematics
• 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-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 [ de en ] ( PH-WIEN ) Applied mathematics for secondary school teacher accreditation programm

UFMA07 Teaching Methodology (10 ECTS)

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

UFMA08 Arithmetic and algebra for secondary schools (4 ECTS)

UFMA09 Electives Teacher Training Programme (0-10 ECTS)

• 250017 SE ( MIXED PH-NÖ ) Lernvideos für einen motivierenden Mathematikunterricht in der Sekundarstufe
• 250080 PLV ( PH-NÖ ) Summer school mathematic
• 250139 SE Seminar: Enrichment in Secondary School Mathematics Bachelor
• 250180 SE ( KPH Krems ) Assessment and grading of students in high-school mathematics
• 250181 SE ( PH-NÖ ) Meine Schüler/innen verstehen mich nicht - Sprachsensibler Mathematikunterricht

UFMA10 Subject-based Practicum - Mathematics (7 ECTS)

• 250183 SE ( PH-NÖ ON-SITE ) Seminar for Subject-based Praticum - Mathematics
• 250184 SE ( 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)

Elective Modules (75 ECTS)

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

Basic courses, specialization "Algebra"

• 250057 VO [ en ] Group theory
• 250058 PS [ en ] Introductory seminar on group theory
• 250059 VO [ en ] Combinatorics
• 250060 PS [ en ] Introductory seminar on Combinatorics
• 250065 SE [ en ] Seminar Discrete Mathematics
• 250142 SE [ en ] Seminar Combinatorics
• 510001 SE [ en ] Algebra and Number Theory (VSM)
• 510002 SE [ en ] Project Seminar Algebra (VSM)

Advanced courses, specialization "Algebra"

• 250030 VO [ en ] Random Walks on Groups
• 250111 VO [ en ] Diophantine Approximation
• 250112 VO [ en ] Commutative Algebra
• 250113 VO [ en ] Topics in Number Theory
• 250116 VO [ en ] Graded Rings and Projective Geometry
• 250117 VO [ en ] Representation Theory of Groups
• 250145 VO [ en ] Algebraic Geometry III
• 250161 PS [ en ] Topics in Number Theory

Specialization "Analysis" (51 ECTS)

Basic courses, specialization "Analysis"

• 250010 PS [ en ] Introductory Seminar on Dynamical System and Nonlinear Differential Equations
• 250034 SE [ en ] ( MIXED ) Topics in Analysis and Geometry
• 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"

• 250095 PS [ en ] Schramm-Loewner Evolution
• 250118 VO [ en ] Topics in Real Analysis
• 250119 VO Dispersive Wave Equations
• 250125 VO [ en ] Interval Analysis
• 250140 VO [ en ] Schramm-Loewner Evolution

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 Advanced numerical analysis
• 250078 VO [ en ] Advanced numerical analysis
• 250084 SE [ en ] Mathematical/Computational Astro/Quantum Physics
• 250120 SE [ en ] 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"

• 250042 VU [ en ] Mathematics of Machine Learning
• 250043 VU [ en ] Kinetic Theory Applied to Biology
• 250079 VO [ en ] Topics in Finite Elements
• 250123 VU [ en ] Image Processing
• 250124 VO [ en ] Graph Algorithms and Machine Learning
• 250125 VO [ en ] Interval Analysis
• 250148 VO [ en ] Mathematical Aspects of Tensor Networks in Many-Body Physics
• 260061 VO [ en ] Tensor network methods in many-body physics

Specialization "Biomathematics" (51 ECTS)

Basic courses, specialization "Biomathematics"

• 250094 SE [ en ] Seminar (Mathematical Population Genetics)
• 250115 VO [ en ] Dynamical Systems and Nonlinear Differential Equations
• 250126 VO [ en ] Mathematical ecology and pattern formation
• 250127 PS [ en ] Introductory Seminar on Mathematical Ecology
• 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
• 250105 SE [ en ] Complex Network Analysis Project
• 550001 VO+SE [ en ] Molecular Population Genetics: making sense of sequence data

Specialization "Geometry and Topology" (51 ECTS)

Basic courses, specialization "Geometry"

• 250034 SE [ en ] ( MIXED ) Topics in Analysis and Geometry
• 250096 VO [ en ] Analysis on Manifolds
• 250129 VO [ en ] Algebraic Topology
• 250131 PS [ en ] Algebraic Topology
• 250132 SE [ en ] Seminar Geometry and Topology
• 250158 PS [ en ] Introductory seminar on Analysis on manifolds
• 250162 SE [ en ] MCMP Seminar

Advanced courses, specialization "Geometry"

• 250133 VO [ en ] ( MIXED ) Lorentzian Geometry
• 250145 VO [ en ] Algebraic Geometry III

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
• 250134 VO [ en ] Introduction to Mathematical logic
• 250135 PS [ en ] Introductory Seminar on Mathematical Logic
• 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

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 Dynamical Systems
• 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 PS [ en ] Schramm-Loewner Evolution
• 250101 PS [ en ] Mathematical Finance (Continuous Time)
• 250138 VO [ en ] Ergodic Theory
• 250140 VO [ en ] Schramm-Loewner Evolution

Further Electives (15 ECTS)

• 250036 VO [ en ] Topics from Habilitations
• 250147 OL [ en ] ( OV ) 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)

UFMAMA03 Application-orientation for mathematic class (4 ECTS)

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

UFMAMA04 Optional Courses Teaching Methodology (3 ECTS)

• 250025 SE Seminar: Enrichment in Secondary School Mathematics Master
• 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)