Master's Programmes in Technical Mathematics

Course ID

UE 066 393 - Master's Programme Mathematical Modelling in Engineering: Theory, Numerics, Applications
UE 066 394 - Master's Programme Technical Mathematics
UE 066 395 - Master's Programme Statistics and Mathematical Methods in Economics
UE 066 405 - Master's Programme Financial and Actuarial Mathematics

Duration of course

4 semesters

Credits

120 ECTS

Certificate received upon completion

Diplom-Ingenieur
Master of Science

Course programmes

General information on the Master's Programme 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 TU Wien 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
    dmg.tuwien.ac.at
  • Institute of Stochastics and Mathematical Methods in Economics
    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 Mathematical Modelling in Engineering: Theory, Numerics, Applications

Master's programme structure (4 Semester)

Analysis Basics (at Uni L'Aquila)

  • Functional Analysis
  • Dynamic Systems
  • Partial Differential Equations
  • Control Systems

Numerics Basics (at TU Wien)

  • Programming
  • Numerics of Differential Equations

Focus on Modelling and Numerics (at TU Wien)

  • Modelling
  • Scientific Computing

Focus on Mathematics in Social Sciences (at Uni L‘Aquila)

  • Analysis 
  • Modelling of Collective Behavior
  • Mathematical Fluid Mechanics

Foreing Languages (Italian, German)

Bound elective subjects

Free elective subjects and Soft Skills

Thesis

This course is offered in cooperation between the University of L'Aquila, Italy (1st semester) and the Vienna University of Technology (2nd semester); The 3rd and 4th semester can be completed at one of the two universities, depending on the chosen focus. The program is offered in English.

Mathematical modelling refers to the use of modern analytical and numerical techniques to describe or simplify real physical, industrial or socio-scientific problems, so that a "good" solution can be identified within a reasonable time - mostly through numerical simulations. This requires a sense of application as well as sound knowledge of mathematics and computer science. This master's programme is therefore interdisciplinary between mathematics, computer science and engineering.

The design of aircraft wings today is not carried out in the wind tunnel, but by numerical simulations on the computer. First, the air flow (with or without friction) is modeled by a partial differential equation from fluid mechanics. The finite element method provides the numerical-mathematical tool for their exact solution. Due to the complex geometry, real problems can only be implemented on parallel high-performance computers.

While in physics and mechanics many equations of motion have been known in their basic features for some centuries, the collective behavior of large clusters of people or flocks of animals is a new field of research. At first one tries to fathom from experiments the typical movement behavior of individuals. Averaging over a large number of participants often leads to a partial differential equation for group dynamics. Corresponding numerical simulations are e.g. essential for the planning of emergency exits in public buildings or major events.

Master's Programme Technical Mathematics

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 modules
Free electives and soft skills
Thesis

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.

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).

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.

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.

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.

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.

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.

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 Proramme Statistics and Mathematics in Economics

Master's programme 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
  • Bayesian 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 subjects
Free electives and soft skills
Thesis

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.

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.

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.

Master’s Programme Financial and Actuarial Mathematics

Master's programme 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 modules
  • Free 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.

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.

The classic model for a stock market price is based on a model from molecular physics. It 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.

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.

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.

Dean of Studies

Gernot Tragler

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

Vice Dean of Studies

Robert Weber

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

More Information and Contact

Dekanat der Fakultät für Mathematik und Geoinformationen
Wiedner Hauptstraße 8
1040 Wien

T +43-1-58801-10003
E dekmug@mail.tuwien.ac.at

Website of the Dean's office

Student Association

Student Association Technical Mathematics

Wiedner Hauptstraße 8-10
Raum DA01G2, 1. Stock
1040 Wien

T +43-1-58801-49544
strv@fsmat.at 
fsmat.at