Master's programme in Mathematics and courses suggested for Master's students interested in biomathematics

The current curriculum for the Master of Science in Mathematics is divided in the following parts:

(1) The core modules are designed for students with prior knowledge from a typical Bachelor's programme in mathematics. Each core module provides students with standardized content, consisting of a core lecture (6 ECTS) and the corresponding core introductory seminar (4 ECTS). 

The core modules are meant to consolidate the foundations knowledge of the students and to broaden their mathematical perspectives; from the available modules, students have to choose 3 core modules, totaling 30 ECTS.

(2) The specialization courses build upon the core courses and dive deeper into a particular area; these courses offer students a broad range of choices, from advanced mathematical topics to highly application-oriented subjects. Students have to complete 30 ECTS from the specialization courses, and additional 8 ECTS from reading seminars. 

(3) 22 ECTS shall be obtained by elective courses that can also come from adjacent areas like physics, computer science, economy or biology, depending on the mathematical specialization chosen.

(4) The curriculum concludes with the Master work (27 ECTS) and the Master defense (3 ECTS).

For all students interested in biomathematics, we suggest taking the following courses in the order below.

First and/or second semester

From the list of core courses, we recommend taking the following courses:

• Stochastic Processes (VO + PS) - this core course covers discrete time Markov chains, long-term behaviour of stochastic processes, and martingale theory, and it is normally offered each winter semester.
• Advanced Partial Differential Equations (VO + PS) - this core course starts with a review of some basic aspects of linear PDEs, and it then focuses on discussing some methods and techniques for investigating certain types of nonlinear PDEs; depending on the academic years, this course takes place either in the winter or in the summer semester (please check updated information in the u:find website - see the next section).

From the list of specialization courses, we suggest following the next courses:

• Mathematical Ecology and Pattern Formation (VO + PS) - this course is normally offered each winter semester. The goal of this lecture is to give students a solid toolbox to derive and analyse models for population dynamics (ecology) and pattern formation. The modeled phenomena include population dynamics, both structured and unstructured (competition, symbiosis, etc.), disease dynamics, developmental biology, and pattern formation. The course focuses on deterministic mathematical modeling (ODEs, PDEs, dynamical systems) with modeling of cell biology as an application.
• Mathematical Population Genetics (VO + PS) - this course is normally offered each summer semester. This course provides an introduction to mathematical modeling in population genetics. The course focuses on stochastic modeling and it explores how evolutionary processes such as mutation, natural selection, recombination, and random genetic drift shape patterns of genetic variation in natural populations. 
• Introductory seminar AG Biomathematics (SE) - this course is offered each semester. The seminar provides a broad overview of topics in biomathematics on the basis of classical and new scientific literature. Each topic is briefly introduced by one of the instructors, followed by a student presentation of a paper. The seminar does not require any prior knowledge of biomathematics and it is therefore the recommended first seminar in biomathematics that you should choose.

Second and/or third semester

In the second and third semesters, students interested in biomathematics might take additional 1-2 courses in this area, depending on the exact offer. 

Courses offered more or less regularly (but not necessarily every year) in the previous years included, for example: Kinetic Theory Applied to Biology (VU), Dynamical systems and nonlinear differential equations (VO), Modelling Interacting Particle Systems in Science (VU), Exploring Random Genealogies (VO), Probabilistic Models in Biomathematics (VO), and Molecular Population Genetics: Making Sense of Sequence Data (VO + SE). In each semester there are normally 1 or 2 of these courses offered.

The exact offer of these courses and the exact topics covered varies depending on availability of the teachers. Depending on prerequisites, some of these courses might be more appropriate for the subsequent semesters.

In addition, students are encouraged to take core courses beyond biomathematics, in particular:

• Dynamical Systems (VO + PS) - this lecture provides an introduction to the theory of dynamical systems and dynamical chaos, including bifurcation theory; depending on the academic years, this course takes place either in the winter or in the summer semester (please check updated information in the u:find website - see the next section).

Third and/or fourth semester

• Modeling in Evolutionary Ecology and Epidemiology (VU) - this course is normally offered each winter semester, and it can serve as a preparation for a Master thesis. In this course, students develop the ability to formalize problems in mathematical biology, particularly in ecological, evolutionary, and epidemiological modeling. Students learn to construct mathematical models that describe the dynamics and interactions of processes in biological systems; participants also learn basic analytical tools used for analyzing a complex model, such as dimensional analysis, some foundations of stochastic processes, and the separation-of-time-scales technique.
• Mathematical Population Genetics (SE) - this course is normally offered in each winter semester. It is an advanced seminar in mathematical population genetics (also including topics from ecology and epidemiology) with presentation of new scientific literature and own ongoing research (primarily for students preparing for a Master thesis in biomathematics, and for PhD students).

We recommend taking also some of the advanced seminars offered by members of the Biomathematics Group; the offer of these advanced courses varies during the various semesters (see the examples listed above in the courses suggested for the second/third semester).

You can find all courses currently offered for the Master of Science in Mathematics in the u:find directory of the University of Vienna, by following this path:

u:find → Directorate of Studies 25 - Mathematics → Master Mathematics (821 [3] - Version 2025)

Back to the list of all courses offered by the Biomathematics Group.