## Mathematical modelling

Mathematical modelling is a unique and very **challenging interdisciplinary bachelor, master and postgraduate study programme** running at Faculty of Mathematics and Physics, Charles University in Prague. The master study programmes combine profound education in mathematics, in particular in

**mathematical analysis**(theory of partial differential equations);**numerical mathematics**(numerical solution of partial differential equations, high performance computing);

with a specialized education in a branch of physics such as

**continuum mechanics**(mechanics of Newtonian and non-Newtonian fluids, solid mechanics);**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, numerical simulations of particle collisions, statistical methods in evaluation of data acquired in modern detectors).

The objective of the master study programmes is to provide students top level education in mathematics, and to teach them how to use such knowledge in practice, namely in physics and engineering and also in other scientific fields. The same holds for the doctoral study programme as well as for the bachelor study programme.

Despite the breadth of the these fields we conduct, together with our renowned external collaborators, **excellent research** in all the fields named above. (See our research profile for more details.) This enables us to keep our students in touch with the state-of-the-art methods and techniques (master study) and give them a chance to participate in the top level scientific research (postgraduate study).

## What you will learn

In the course of the study you will learn how to formulate questions concerning natural phenomena and **develop physically consistent mathematical models** that can be utilized to answer these questions. You will learn how to **study qualitative mathematical properties of these models** and how to **develop and implement appropriate numerical schemes** that can be used in numerical simulations of the given phenomena. You will master the skill to distinguish between essential and nonessential characteristics of the given phenomena. Knowing the details concerning physics, mathematical and numerical analysis, you will be able to evaluate the strengths and weaknesses of the mathematical models, and the utility of the results obtained using such models.

In particular you will be given high quality education in **foundations of the theory of partial differential equations, functional analysis, numerical analysis and numerical software**. Once you master the foundation of these fields, you will **specialize** (usually by the choice of the topic of your thesis) in one of these fields and **in a particular branch o physics**. In most cases the theses are concerned with topics that are related to the applications of mathematical methods to a solution of relevant problems in physics and engineering, but you can also write theoretically oriented thesis focused solely on mathematical and numerical analysis.

You will have a chance to **participate in the research** conducted in the department and in the research institutions such as Nečas Center for Mathematical Modeling. You will also have access to our research infrastructure such as the computational cluster Sněhurka. It is common that our students spent some time on an internship at out research partners that are, amongst others, Ruprecht-Karls-Universität Heidelberg (joint postgraduate research programme), University of Oxford or Texas A&M University.

Our students are founding members of Charles University in Prague Chapter of SIAM, which is a local student-lead branch of renowned Society for Industrial and Applied Mathematics (SIAM). The purpose of a chapter is to “generate interest in applied mathematics and computational science by providing students opportunities to share ideas and enthusiasm with fellow students and faculty from any relevant department on campus, explore career opportunities, make contacts that will last a lifetime, and develop leadership skills”.

Our graduates are well prepared to work both in academic and commercial sector not only because of **excellent knowledge basis**, but also because of their **independence**, **flexibility**, and the ability to **simultaneously communicate with various specialists** such as mathematicians, physicists, engineers and programmers. (See our study page for details concerning curriculum, admission procedure and so forth.)

Do you want to know more? Check out our research profile, study site, and meet the people involved in the teaching and research activities.

## History

The study programme was founded in 1987 by Jindřich Nečas (1929-2002, prominent mathematical analyst), Jan Kratochvíl (1934-2019, solid mechanics) and Ivo Marek (1933-2017, numerical mathematics). Currently the study programme is managed by Josef Málek.