This master's programme is aimed at all students who wish to concentrate on a core academic area of mathematics.
Preparatory bachelor's degree (6 semesters)
The four-semester master's programme in Mathematics can be taken upon successful completion of any six-semester Mathematics bachelor's programme offered in Austria. Four such bachelor's degrees are offered at Vienna University of Technology:

• Mathematics in Science and Technology,
• Mathematics in Computer Sciences,
• Statistics and Mathematics in Economics and
• Financial and Actuarial Mathematics.

Core fields common to all these programmes are analysis, linear algebra, probability theory and statistics as well as numerical mathematics. The master's degree in Mathematics follows on from these programmes.

Master's degree structure (4 semesters)

• Algebra
• Functional Analysis
• Topology
• Theory of Stochastic Processes
• Complex Analysis
• Elective modules in Analysis and Stochastics
• Elective modules in Discrete Mathematics
• Related elective modules
• Free electives and additional qualifications ("soft skills")
• Thesis

Career prospects
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 programme universities.
In many branches of research-oriented mathematics, a broad knowledge of various different core mathematical subject areas is required. Imparting this knowledge is the most important objective of the master's degree in Mathematics. For students who do not want to specialise so much in their master's programme (as in other master's programmes at Vienna University of Technology), but would rather receive broader training, the master's degree in Mathematics is ideal. The same applies to students with ambitious academic goals who want to follow their master's degree with a doctorate, and for whom as many options as possible should remain open with regard to their specialisation.

The master's degree in Statistics accommodates the increasing significance of and need for mathematical methods for non-deterministic (stochastic) processes and statistical analysis thereof. These methods are of fundamental importance, for example, in technometry (risk analysis of technical systems), in various different branches of industry (forecasting, quality assurance), in the natural sciences, for example in biometry and chemometry (dose-effect relationships, duration analyses).
On the basis of the bachelor's degree in Statistics and Mathematics in Economics or another relevant bachelor's degree such as the bachelor's degree in Data Engineering & Statistics, the master's degree in Statistics teaches more in-depth mathematical and statistical methods for developing new knowledge and decision-making principles. The programme also gives corresponding consideration to the application of stochastic models.

Master's degree structure (4 semesters)

• Functional Analysis
• General Regression Models
• Bayes Statistics
• Mathematical Statistics
• Statistics seminar
• Statistical Simulation and Computer-Intensive Methods
• Classification and Discriminant Analysis
• Non-Parametric Methods in Statistics
• Theory of Stochastic Processes
• Related elective modules
• Free electives and additional qualifications ("soft skills")
• Thesis

Career prospects
Statistical methods are used in technology, medicine, biology, environmental sciences and in economic and social sciences In general, graduates can work in all fields in which data is collected and analysed. For example:

• in quality assurance in institutes and companies
• in insurance agencies and banks
• in market and opinion research
• in statistical institutions and offices
• in biometry (investigation of living creatures using statistical methods)
• in social research
• in international organisations

Master's degree structure (4 semesters)

• Mathematical Finance
   – Stochastic Analysis
   – Mathematical Finance: Contemporary Models
   – Functional Analysis
• Mathematical Insurance
   – 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

Current research themes
Some characteristic themes currently being worked on as part of the programme, in compulsory or optional modules, are listed below.

Mathematics and financial markets
Did you know that mathematicians are highly sought-after on Wall Street and in 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 risks.

Mathematical Finance
The classic stock exchange rate model 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 purchase and sales orders. Each of these orders increases or decreases the share price slightly. F. Black and M. Scholes used this model in 1973 to derive a formula for assessment of options. In 1997, this formula was awarded the Nobel prize for economics. Modern research is working intensively on the further development of these models.

Risk management
Insurance companies and banks make their living from 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 order to be brought to the randomness.

Mathematical insurance
Insurance companies have long been using probability theory to determine premiums, as well as to calculate the financial reserves required to fulfil insurance services.
In recent years, the handling of assessment risk has also taken on increasing importance. Mathematicians who are qualified in these fields will receive attractive and lucrative job offers in the insurance industry.

Career prospects Mathematical methods are becoming increasingly more important thanks to modern developments in industry and technology. As a result, the job market for mathematics graduates — particularly in the finance and insurance sectors — is very promising. Your ability to analyse complex structures will open doors to diverse fields of employment, such as banks and insurance agencies, consultancy firms, industry research and development departments, software companies, research institutions, government agencies and of programme universities (see also: fam.tuwien.ac.at/jobs/). Students can gain a first look into the relationship between theory and practice by working with the Christian Doppler Laboratory for Portfolio Risk Management, which is run by the research group, together with partners from industry.