This master's program focuses on deeper knowledge of various mathematical disciplines and their algorithmic aspects. The student can specialize either in Mathematics for Information Security or in Computer Geometry.
Mathematics for Information Security focuses on deepening theoretical knowledge of number theory, probability theory, the theory of error-correcting codes, complexity theory, theory of elliptic curves, and computer algebra applied to some of these subjects. Attention is also given to practical aspects such as internet security, standards in cryptography, and legal aspects of data security.
Computer Geometry deepens theoretical knowledge in various algebraic and geometric subjects together with their applications in the geometry of computer vision and robotics, computer graphics and image processing, optimization methods, and numerical linear algebra.
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
- Melab 77
- 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)
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|Alternative date (of entrance exam)
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Graduates are well acquainted with both the present and prospective systems of data security and encryption, including their mathematical principles, practical applications, and standards. The mathematical knowledge covers the theoretical background of cryptography in full breadth (number theory, self-correcting codes, the complexity of algorithms, elliptic curves, one-way functions). Graduates also understand the structure of cryptographic protocols and are aware of the basic legal aspects of data security. The graduates are well prepared for jobs concerning data security, encryption, and authorization, where some knowledge of applied mathematical principles is needed.
Program taught in: