# Master programs Technical Mathematics

Study Codes |
E 066 394 - Technical Mathematics E 066 395 - Statistics and Mathematics in Economics E 066 405 - Financial and Actuarial Mathematics |

Duration of Study | 4 Semesters |

Credits | 120 ECTS |

Degree |
Diplom-Ingenieur Master of Science |

Academic Program |
Technical Mathematics Statistics and Mathematics in Economics Financial and Actuarial Mathematics |

Curriculum Document |
Technical Mathematics Statistics and Mathematics in Economics Financial and Actuarial Mathematics |

# General information on the master's programme in Technical Mathematics

### General information on the master's programme in Technical Mathematics

Mathematical teaching and research at TU Wien has a strong international orientation. This offers students the opportunity to spend semesters abroad and to complete double diplomas. A number of mathematicians at the University of Technology have received prestigious awards. Both the math.space in Vienna's museum quarter and the Kurt-Gödel-Gesellschaft are led by University of Technology mathematicians.

### Career prospects in mathematics

Mathematical methods are increasingly in demand due to modern developments in industry and technology. For this reason, the job market for Mathematics graduates is generally very promising.

Your ability to analyse complex structures will open doors to diverse fields of employment, such as industry research and development departments, software companies, banks and insurance agencies, company consultancy firms, research institutions, government agencies and of course universities.

### Further information and contacts

- Faculty of Mathematics and Geoinformation

www.math.tuwien.ac.at - Student Council of Technical Mathematics

fsmat.at - Institute of Analysis and Scientific Computing

Wiedner Hauptstr. 8–10, 1040 Vienna

asc.tuwien.ac.at - Institute of Discrete Mathematics and Geometry

Wiedner Hauptstr. 8–10, 1040 Vienna

www.dmg.tuwien.ac.at - Institute of Mathematical Methods in Economics

Argentinierstr. 8 and Wiedner Hauptstr. 8–10, 1040 Vienna

iwm.tuwien.ac.at - Institute of Statistics and Probability Theory

Wiedner Hauptstr. 8–10, 1040 Vienna

www.statistik.tuwien.ac.at

# Master's programme in Technical Mathematics

### Master's degree structure (4 semesters)

**Analysis**

- Functional analysis
- Complex analysis
- Stochastic processes
- Calculus of variations

**Discrete mathematics**

- Algebra
- Analysis of algorithms
- Discrete methods
- Logic and principles of mathematics

**Geometry**

- Geometric data processing
- Differential geometry
- Geometric analysis
- Topology

**Modelling and numerical simulation**

- Modelling with partial differential equations
- Numerics of partial differential equations
- Finite element methods

**Related elective modulesFree electives and soft skillsThesis **

### Examination of the functional principles of the body's circulatory system

With the aid of mathematical models, medically relevant information such as stroke volume, elasticity and pulse waveform in the aorta can be calculated from the easily measured pulse and pressure curves.

### Electro-stimulation with neuroprestheses

In order to provide better help in the future to patients with nerve damage, models using partial and general differential equations are being developed and analysed. The simulation results thus obtained will provide the basis of medical improvements (e.g. design of hearing prostheses).

Simulation of sound wave distribution

Sounds waves spread through the sea across large distances, almost without attenuation. By comparing the simulated and experimentally measured wave field, it is possible to determine the density and speed of sound in water and on the sea bed, in order to pinpoint the location of oil reserves or shoals of fish.

### Modelling and simulation of semiconductors

Computer components are becoming ever smaller and doing more and more work. The current flow heats the tiny components to such an extent that they can get as hot as a light bulb. Numeric simulations can discover the source of the heat in order to channel it away.

Calculations for material science

For some years it has been possible to calculate the properties of materials using computational methods alone. The basis for this is the density functional theory, for which Walter Kohn from Vienna was awarded the Nobel Prize in Chemistry in 1998. Calculations in material science make it possible to develop ideal new technical materials or medicines.

### Symbolic and numeric calculation, computer algebra

Modern computer algebra systems contain techniques, embedded into the software, for solving mathematical problems at a precise symbolic level. However, natural limitations are quickly reached here, particularly in the field of applied analysis. Numerical simulation is based on structural implementation of mathematical models, the solution for which cannot be determined precisely using finite complexity. Complexity of calculation can thus be balanced against precision.

### Cryptography, information and coding theory

The modern information society places ever higher demands on the transfer, security and reliability of data. In information theory, the terms entropy (uncertainty), information and redundancy in information systems are analysed and questions regarding the relationship between transmission speed and reliability as well as the optimal compression of data are dealt with. Coding theory is concerned with the issue of error recognition and correction. Neither CDs nor satellite transmissions would be possible without it. Cryptography today is far removed from any espionage clichés and represents an indispensable foundation of electronic payments and all forms of e-commerce and e-government.

### Algorithms for graphs and data structures

Special graphic models are used, for example, to model the growth of the internet, the spread of infections or social networking structures.

The mathematical analysis of the structure of such graphs, but also of other objects (e.g. data structures), is important to the performance analysis of various algorithms and for designing more efficient algorithms, amongst other things.

# Master's programme in Statistics and Mathematics in Economics

### Master's degree structure (4 semesters)

**Mathematics specialism**

- Functional analysis
- Stochastic processes
- Time series analysis
- Numerics of differential equations

**Statistics and Probability Theory specialism**

- Advanced probability theory
- Mathematical statistics
- Bayes statistics
- Multivariate statistics

**or Mathematics in Economics specialism**

- Game theory modelling
- Non-linear optimisation
- Applied operational research
- Dynamic macro-economics

**Mathematical principles**

- Non-linear optimisation
- Differential equations 2
- Functional analysis 1

**Additional subjectsFree electives and soft skillsThesis **

### Econometrics

Econometrics is defined as the field of economic sciences which is concerned with the application of mathematical statistics and the tools of statistical inference to problems of empirical measurement with regard to relationships postulated by economic theory. Since the foundation of the Econometric Society by Ragnar Frisch in 1933, the unification of the three disciplines of statistics, economic theory and mathematics has been called econometrics.

### Economics

The research group ECON is concerned with that area of exploration for which the other research groups are developing methods: economics. Teaching includes overview modules as well as some more in-depth subjects on which we are also conducting research. Our main focus subjects are macroeconomics, evolutionary economics, economic policy simulation, monetary economics, political economics and European integration.

### Operational Research (OR)

OR is concerned with the interdisciplinary solution (support for decision-making) of planning problems in economics, technology, informatics, medicine etc. by exploiting modern developments in mathematics, statistics and informatics.

# Financial and Actuarial Mathematics

### Master's degree structure (4 semesters)

**Financial mathematics**

- Financial mathematics, time-continuous model
- Functional analysis
- Stochastic analysis

**Actuarial mathematics**

- Risk and ruin theory
- Private business law
- Advanced mathematical life insurance
- Stochastic control theory

** Related elective modulesFree electives and additional qualifications (soft skills)Thesis**

Some of the typical themes that are covered by the compulsory and elective courses in this programme are introduced below.

### Mathematics and financial markets

Did you know that mathematicians are much sought after in Wall Street and other financial markets? In the last 20 years, mathematics has become a key technology in the financial sector. Sophisticated mathematical models are used in the management of financial risk.

### Financial mathematics

The classic model for a stock market price is based on a model from molecular physics. This describes the movement of a particle as a result of random collisions with other particles.

Share price development is influenced in the same way by the constant flow of buy and sell orders. Each one of these orders nudges the share price up or down slightly. In 1973, F Black and M Scholes used this model to derive a formula for valuing stock options. In 1997, this formula was awarded the Nobel prize for economics. Modern research is working intensively to develop this model further.

### Risk management

Insurance and banking live on risk. They have to assess the probability of losses, which must be actively budgeted for. Today, highly complex mathematical models are used for the management of financial risks. Mathematics is at the core of probability theory. It allows one to bring order to chaos.

### Actuarial mathematics

For a long time, insurance companies have been using probability theory to determine premiums and to calculate the financial reserves that are required to meet their insurance obligations.

In recent years, the management of investment risk has also become increasingly important. Mathematicians who are qualified in these fields receive attractive and lucrative job offers in the insurance industry.

# Further information

### Dean of Studies

Ao.Univ.Prof. Dr.phil. Günther Karigl

T +43-1-58801-10453

E g.karigl@tuwien.ac.at

### Chairman of Curriculum Commission

Ao.Univ.Prof. Dipl.-Ing. Dr.techn. Martin Goldstern

T +43-1-58801-11822

E martin.goldstern@tuwien.ac.at

### Student association

Fachschaft Technische Mathematik

T +43-1-58801-49544

E strv@fsmat.at

http://fsmat.at

Freihaus

Wiedner Haupstraße 8 –10 | 1040 Wien

Raum DA01G2 | Bereich rot | Stock 1