The program in Mathematical Analysis offers students advanced knowledge of traditional fields of mathematical analysis (real function theory, complex analysis, functional analysis, ordinary and partial differential equations). It is characterized by a depth of insight into individual topics and an emphasis on their mutual interconnections. Basic knowledge of these topics at an advanced level is provided by the set of compulsory courses. Elective courses deepen the knowledge of selected fields, especially those related to the topic of the diploma thesis. Seminars provide contact with contemporary mathematical research. Mathematical analysis has close relationships with other mathematical disciplines, such as probability theory, numerical analysis, and mathematical modeling. Students become familiar with these relationships in some of the elective courses.
The program prepares students for doctoral studies in mathematical analysis and related subjects. Applications of mathematical theory, theorems, and methods to applied problems broaden the qualification to employment in a non-research environment.
Description of verification and evaluation criteria
Conditions for Admission
The goal of the admissions review process is to select from the pool of applicants those individuals who have shown the capability and diligence expected of Charles University students. To apply for our Computer Science or Mathematics Master's programs given in English you must:
hold or be working towards a Bachelor’s or Master’s diploma and provide a certified copy thereof;
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).
Bachelor’s or Master’s Diploma
Each applicant into a Master’s program must deliver an officially authorized copy of a Bachelor’s or Master’s diploma, or a confirmation of a faculty or university concerning a successful completion of Bachelor’s or Master’s studies. This requirement does not apply to students and graduates of Bachelor’s or Master’s studies at the Faculty of Mathematics and Physics of the Charles University.
The applicants who graduated from a higher education institution abroad, must deliver one of the following documents in order to prove their previous education: a document about a general recognition of foreign higher education in the Czech Republic obtained according to § 89 and 90 of the higher education law of the Czech Republic (so-called "nostrification"), or a foreign document about a foreign higher education if it is automatically recognized in the Czech Republic, according to its international agreements, without further official processing (diploma and diploma supplements from Slovakia, Poland, Hungary, Slovenia), or a foreign document about completing higher education which will be assessed by the faculty itself (no fee is being charged). Detailed information on how the condition of obtaining previous Bachelor’s or Master’s degree should be proven by the alumni of foreign higher education institutions, as well as additional information, may be found on faculty webpages, here: https://www.mff.cuni.cz/studium/bcmgr/os/nostrifikace.htm . The officially authorized documents must be physically sent to the Study Office of the Faculty of Mathematics and Physics by June 30, 2019, at the latest. If you do not deliver the document about a completed education, you will be neither accepted nor enrolled for Master’s studies.
In addition to this, depending on the program for which you are applying, you also must
Computer Science program: have sufficient academic background in the relevant fields (see below for details); this can be demonstrated by solving a given take-home assignment correctly and on time, and by providing transcripts (academic records) of your previous education accompanied by syllabi of the completed courses (i.e., you must submit both the assignment and the transcript). For the take-home assignment, you may consult your notes, textbooks, Internet resources, friends etc. but the submitted solution must be your own work. To correctly solve the take-home assignment means to obtain at least 70 percent of the maximum score.
Mathematics program: have sufficient academic background in the relevant fields (see below for details); this can be demonstrated by providing transcripts (academic records) of your previous education accompanied by syllabi of the completed courses.
You are also welcome to accompany your application by:
a statement of purpose in which you describe your reasons for applying to the proposed program, 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.
In this paragraph, we summarize the minimum knowledge required for applicants in the various study programs and study branches offered at our faculty.
Master’s Degree in Computer Science
Study branches Theoretical Computer Science, Computational Linguistics, Discrete Models and Algorithms, Computer Graphics and Game Development, Software and Data Engineering, Software Systems, Artificial Intelligence: background in calculus, linear algebra, discrete mathematics, probability, logic, computer programming, algorithms and data structures, computer organization, and the theory of automata and formal grammars.
Master’s Degree in Mathematics
Common requirements: 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 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.
Study branch Mathematics for Information Technologies: common requirements + commutative and computer algebra, theoretical and applied cryptography.
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. These records must also include a complete description of the institution’s grading scale or another standard of evaluation. Unless academic records and diplomas are routinely issued in English by the institution concerned, the official records in their original language must be submitted with an authorized, complete, and exact English translation.
English Language Proficiency
An applicant must have an adequate command of English in order to enroll in an English-taught program at Charles University. Proficiency in English may be demonstrated by one of the standard language tests listed below; any language test results should not be older than two years. Students who have completed at least two years of their previous education with English as the sole language of instruction in Australia, Canada, Ireland, New Zealand, UK, Republic of South Africa or the USA are exempt from this requirement. Applicants who provide us with comparable qualifications demonstrating proficiency in English also meet our requirements.
The table below lists the various tests of English that we recognize, and gives the minimum score that should be obtained.
Test Minimum Score
TOEFL Paper/Computer/Internet-based 550/213/80
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
Examination for the Certificate of Proficiency in English (ECPE) Pass
Test of English for International Communication (TOEIC) 605
General State Language Examination in English in the Czech Republic Pass
Conditions for admission
Admission to Master's studies is conditioned by completed secondary education confirmed by a school-leaving certificate. Admission to Post-Bachelor studies (Master's program) is likewise conditioned by completed education in any type of study program.
Confirmation date (of entrance exam)
from: __ until: __
Alternative date (of entrance exam)
from: __ until: __
Graduates have received a good knowledge of important branches of mathematics. (Theory of real and complex functions, measure theory and integration, functional analysis, differential equations, potential theory etc.) Graduates are well prepared for jobs in research as well as in firms and institutions where an active and creative approach to the solution of problems of various kinds is required.