Mathematical modelling is an interdisciplinary field connecting mathematical analysis, numerical mathematics, and physics. The curriculum is designed to provide excellent basic knowledge in all these disciplines and to allow a flexible widening of knowledge by studying specialized literature when the need arises. All students take compulsory courses in continuum mechanics, partial differential equations, and numerical mathematics. The students will acquire ability to design mathematical models of natural phenomena (especially related to continuum mechanics and thermodynamics), analyze them, and conduct numerical simulations. After passing the compulsory classes, the students get more closely involved with physical aspects of mathematical modelling (model design), with mathematical analysis of partial differential equations, or with methods for computing mathematical models. The grasp of all levels of mathematical modelling (model, analysis, simulations) allows the students to use modern results from all relevant fields to address problems in physics, technology, biology, and medicine that surpass the scope of the individual fields. Graduates can pursue academic or commercial careers in applied mathematics, physics and technology.
Entrance examination – Master's programme
Applicants who will not sufficiently demonstrate the necessary background listed above by 9 May 2016, or with their application, will be invited to take the entrance examination in Prague.
The entrance examination for a Master's programme at the Faculty of Mathematics and Physics at Charles University consists of four problems, each worth 25 points. In case of an incomplete solution a proportional number of points will be given. The maximum total score is 100. The minimum score for admission is 40 points out of 100. Depending on the study programme and study branch, the examination has the following structure:
- Mathematics (4 problems)
Master’s Entry Requirements
The goal of the admissions review process is to select from the pool of applicants those individuals who have shown the best capability and diligence expected of Charles University students. To apply for our Mathematics or Computer Science Master's programmes delivered in English you must
- hold or be working towards a Bachelor’s or Master’s diploma and provide a certified copy thereof; in cases required by law, a certification of equivalence of education must accompany the application,
- have sufficient academic background in the relevant fields (see below for details); this can be demonstrated by passing the specialized entrance examination in June 2016 in Prague that is organized by the Faculty of Mathematics and Physics, Charles University, or by providing transcripts (academic records) of your previous education accompanied by syllabi of the completed courses; promising students who do not have this background may be admitted with the provision that they complete the missing knowledge from Bachelor's courses,
- have sufficient command of the English language; this can be demonstrated by providing your results in one of the standardized English tests that we recognize (see below for details).
You are also welcome to accompany your application by
- a statement of purpose in which you describe your reasons for applying to the proposed programme, your study and possibly also research interests and future career plans,
- letters of recommendation as recent as possible from professors and employers who can comment on your recent professional accomplishments and your qualifications for pursuing a Master's degree in mathematics or computer science.
English Language Proficiency
All applicants must have an adequate command of English in order to enrol at Charles University. An applicant’s proficiency level in English may be demonstrated by various language tests; any language test results should not be older than two years. The only exemption from this requirement is for students who have completed at least two years of their previous education with English as the sole language of instruction in one of the following countries: Australia, Canada, Ireland, New Zealand, UK, or USA.
The table below summarizes the minimum requirements in the various tests of English that we recognize; you must meet the minimum score for at least one of the tests listed here, or provide us comparable results for other recognized qualifications (if in doubt please contact us to obtain specific required scores for other internationally recognized English Language qualifications).
Test Minimum score
- TOEFL Paper / Computer / Internet based - 550 / 213 / 80
- SAT Critical Reading and Writing - 550 in each part
- ACT English and Reading - 24
- International Baccalaureate English - 6
- The International English Language Testing System (IELTS) - 6.5
- Cambridge ESOL FCE A level
- Cambridge ESOL CPE, or Cambridge ESOL CAE - Passed
- City&Guilds International ESOL, or City&Guilds International Spoken ESOL - Expert level
- The European Language Certificates - Level TELC English C1
- UNIcert English for Mathematicians - Level C1
- Melab - 77
- Examination for the Certificate of Proficiency in English (ECPE) - Pass
- Test of English for International Communication (TOEIC) - 605
- Vancouver English Centre (VEC) level / online score - 13-14 / 74
- General State Language Examination in English in the Czech Republic - Pass
Conditions for admission without entrance examination
In this paragraph we summarize the minimum knowledge required for applicants in the various study programmes and study branches offered at our faculty.
Master of Mathematics
Common requirements: A sound background in linear algebra, real and complex analysis, measure theory and probability theory.
Study branch Mathematical Modelling in Physics and Technology: + classical mechanics, functional analysis, ordinary and partial differential equations.
Academic records demonstrating the necessary background must show the dates of enrolment and the subjects or courses taken, together with the units of credit or time allotted to each subject. The records must also include a complete description of the institution's grading scale or other standard of evaluation. Unless academic records and diplomas are routinely issued in English by the institution, the official records in their original language must be submitted with an authorized, complete, and exact English translation.
Information on the exercise of graduates
The graduate has mastered methods and results in continuum mechanics and thermodynamics, mathematical analysis of partial differential equations, and numerical mathematics and is ready to widen his/her knowledge by studying specialized literature. He/she can formulate questions regarding the physical substance of natural phenomena, especially those related to the behaviour of fluids and solid matter in the framework of classical physics, with applications to technology, medicine, biology, geophysics, and meteorology. He/she can choose appropriate mathematical models for such phenomena, perform its mathematical analysis, and conduct numerical simulations with suitable methods. He/she can critically analyze, evaluate, and tie in the whole modelling process. In simpler cases, he/she is able to assess the errors in the modelling process and predict the agreement between the numerical results and the physical process. The graduate is ready to work in interdisciplinary teams. He/she can pose interesting questions in a format ready for mathematical investigation and use abstract mathematical results for addressing applied problems.
This school offers programs in:
Last updated November 20, 2016