Study

Here we present only an informal study guide that should help you to understand the philosophy of our study programmes, and that discusses issues that are specific for mathematical modelling. If you want to know more about studying at the Faculty of Mathematics and Physics, please see the faculty webpages.

For extensive formal description of the study programmes see either web pages of Faculty of Mathematics and Physics or web pages of the “supervisor” of mathematical study programmes (in Czech only).

Contacts

If you have any questions concerning the study of mathematical modelling, please contact us at the following email addresses:

If you are not sure who you want to talk to, please contact Vít Průša (prusv@karlin.mff.cuni.cz).

Master study programmes

Since 2013 there exist two master study programmes. One of them, namely the study programme Mathematical Modelling in Physics and Technology (Matematické modelování ve fyzice a technice) is designed for students of mathematics, and the other one, namely the study programme Matematical and Computational Modelling in Physics (Matematické a počítačové modelování ve fyzice), is designed for students of physics.

These two programmes share the same philosophy, but they differ in emphasis on particular topics, see below. These two study programmes are substantially redesigned versions of the older study programmes running before 2013. The study programme Mathematical Modelling in Physics and Technology (the programme for students of mathematics) is running according to the new curriculum since the academic year 2013/2014, the programme Matematical and Computational Modelling in Physics designed for students of physics was oficially approved in 2014 and is running since the academic year 2015/2016. Prior to 2015/2016 the programmes were taught according the old curriculum.

If you want to know what you will learn when studying mathematical modelling at the Faculty of Mathematics and Physics, Charles University, see the general overview. For a detailed list of courses, see the curriculum below.

Admission

Concerning the general overview of the admission procedure, please see the webpages of the Faculty of Mathematics and Physics. Concerning the required academic background, the requirements differ according to the study programme:

If you are not yet familiar with advanced subjects such as functional analysis but you are still strongly motivated to study mathematical modelling, please contact us, and we will try to recommend you textbooks and other material for self-study.

Note also, that if you have a sufficiently strong academic record, you can apply for the exemption from the entrance examination.

Curriculum

The curriculum is, in both study programmes focused on mathematical analysis (applied functional analysis, theory of partial differential equations) and numerical mathematics (numerical solution of partial differential equations, high performance computing). The mathematicaly oriented courses are then supplemented by courses focused on physics. Concerning the physics the students can choose to focus on:

  • continuum mechanics (mechanics and thermodynamics of Newtonian and non-Newtonian fluids, mechanics and thermodynamics of solids),
  • molecular dynamics (molecular dynamics simulations including large biomolecules or plasma, statistical physics),
  • quantum systems (atomic processes with applications in non-relativistic astrophysics and chemical physics, scattering theory),
  • general relativity (astrophysics, cosmology, numerical methods for solving Einstein equations),
  • particle physics (properties of elementary particles, simulations of particle collisions, statistical methods in evaluation of data acquired in modern detectors).

We think that combining high level knowledge from various fields is essential in successful description of natural phenomena, therefore the courses are taught by the specialists actively working in the respective fields. For example, the courses in high performance computing and matrix analysis are taught by specialists from the Institute of Computer Science of the Academy of Sciences of the Czech Republic, courses on functional analysis are taught by specialists from the Department of Mathematical Analysis and so forth. This makes our study programmes unique and very challenging.

The expected length of the study is two years. You are expected to choose the topic of your thesis during the first year of your study. There are three sets of courses: compulsory, compulsory elective and optional.

Concerning the compulsory courses you must complete all of them. The strange term compulsory elective means that you must complete some of these courses. (The term “some” means that you need certain number of credits from these subjects, see faculty webpages for details.) The choice is yours, but it should reflect the topic of your thesis. Talk to your thesis supervisor if you want to check which courses are suitable for you! The choice of the optional courses is completely up to you. Ask your thesis supervisor, classmates or the people responsible for the study programme, see contacts, for a hint.

For a detailed curriculum please see the following links:

Thesis topics

See the Study Information System for a list of thesis topics. You can also directly contact members of the Division of Mathematical Modelling or scientists from the other institutions participating on the study programme, and ask them to propose a new thesis topic.

State exam

After two years the study is completed by the state exam that has two parts — thesis defense and oral part. The oral part of state exam consists of answering several question concerning the topics specific for the given study programme. In principle you should expect questions on the level of the compulsory courses listed in the curriculum above.

For a detailed list of the topics please see the following links

Doctoral study programmes

Details concerning doctoral study programmes can be found at the faculty web page.