Mathematics

The Master’s program in Mathematics leads students to achieve a deep and solid understanding of higher mathematics. It is designed to encourage analytical thinking, creativity and comprehensive understanding combined with ability to apply mathematical methods to real-life problems. 

It offers degrees in several study branches ranging from pure abstract mathematics to applications in various fields:

• Mathematical Structures
  provide deep knowledge of advanced algebra, geometry, logic, and combinatorics.
• Mathematical Analysis
  focuses on advanced real function theory, complex analysis, functional analysis, ordinary and partial differential equations.
• Numerical and Computational Mathematics
  deals with design, analysis, algorithmization, and implementation of methods for computer processing of mathematical models.
• Mathematical Modeling in Physics and Technology
  is an interdisciplinary field connecting mathematical analysis, numerical mathematics, and physics to develop and apply mathematical models of natural phenomena.
• Probability, Mathematical Statistics and Econometrics
  offers advanced courses in probability theory, optimization, statistical modeling, and random processes, and applies the methods to solve problems from economics, technology, natural sciences, and informatics.
• Financial and Insurance Mathematics
  focuses on mathematical methods for finance, life and non-life insurance, and financial management.

The graduates find employment not only at universities and research institutes, but also in banks, financial and insurance companies, pharmaceutical industry, software industry, marketing, or telecommunication companies.

• 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 2017 in Prague that is organized by the Faculty of Mathematics and Physics, 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 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).
• 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.

Academic background

Common requirements for all study branches: A sound background in linear algebra, real and complex analysis, measure theory and probability theory.
Study branch Mathematical Structures: Common requirements + group theory, mathematical logic.
Study branch Mathematics for Information Technologies: Common requirements + commutative and computer algebra, theoretical and applied cryptography.
Study branch Mathematical Analysis: Common requirements + general topology, functional analysis, ordinary and partial differential equations.
Study branch Numerical and Computational Mathematics: Common requirements + numerical mathematics, functional analysis, ordinary and partial differential equations.
Study branch Mathematical Modelling in Physics and Technology: Common requirements + classical mechanics, functional analysis, ordinary and partial differential equations.
Study branch Probability, Mathematical Statistics and Econometrics: Common requirements + mathematical statistics, Markov chains.
Study branch Financial and Insurance Mathematics: Common requirements + mathematical statistics, Markov chains, financial mathematics.

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.

Entrance examination – Master’s programme
Applicants who will not sufficiently demonstrate the necessary background listed above by May 9, 2017, 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 (the links provide a more detailed description of the topics for the entrance examination in pdf):

Master of Mathematics
Study branch Financial and Insurance Mathematics: Mathematics (2 problems), Probability and Statistics (1 problem), Financial Mathematics (1 problem). You might wish to look at sample tests: the 2013 test (pdf) and it’s solution (pdf), or the 2014 test (pdf) and it’s solution (pdf), or the 2016 test (pdf) and it’s solution (pdf).

All other study branches: Mathematics (4 problems). You might wish to look at sample tests: the 2013 test (pdf) and it’s solution (pdf), or the 2014 test (pdf) and it’s solution (pdf), or the 2016 test (pdf) and it’s solution (pdf). See here: http://www.mff.cuni.cz/admission/admission/