Detail programu/oboru

This master's programme 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, theory of boolean functions, 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 geometry of computer vision and robotics, computer graphics and image processing, optimization methods, and relevant applications numerical linear algebra.

**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, Mathematics or Physics Master's programmes 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 academic background in the relevant fields;
• 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 programme 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/en/students/general-rules/assessment-of-university-degrees-and-studies-for-applicants-to-master-s-and-doctoral-studies). The officially authorized documents must be physically sent to the Study Office of the Faculty of Mathematics and Physics preferably by June 30, 2023, and by September 30, 2023 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 programme for which you are applying, you also must

• 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 programme, your study, and possibly also research interests and future career plans;

• letters of recommendation from professors and employers who can comment on your recent professional accomplishments and your qualifications for pursuing a master’s degree in mathematics, computer science or physics. You should arrange for letters of recommendation to be sent directly by your referees to the email address admission@mff.cuni.cz by May 31, 2023 at latest.

Please ask your referees to state “Recommendation letter for [your name], CS/Math/Physics programme” in the Subject of the email.

**Academic background**

In this paragraph we summarize the minimum knowledge required for applicants in the various study programmes and study branches offered at our faculty.

**Master’s Degree in Mathematics**

You must 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.

**Common requirements:** a sound background in linear algebra, real and complex analysis, measure theory, and probability theory.

Study programme **Mathematical Structures:** common requirements + group theory, mathematical logic.

Study programme **Mathematical Analysis:** common requirements + general topology, functional analysis, ordinary and partial differential equations.

Study programme **Computational Mathematics:** common requirements + numerical mathematics, functional analysis, ordinary and partial differential equations.

Study programme **Mathematical Modelling in Physics and Technology:** common requirements + classical mechanics, functional analysis, ordinary and partial differential equations.

Study programme **Probability, Mathematical Statistics and Econometrics:** common requirements + mathematical statistics, Markov chains.

Study programme **Financial and Insurance Mathematics:** common requirements + mathematical statistics, Markov chains, financial mathematics.

Study programme **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 other 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 on an English-taught programme 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, India, Ireland, Malta, New Zealand, UK, Republic of South Africa or 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 iBT: 85
TOEFL Essentials 9: Pass
TOEIC Listening and Reading: 750
The International English Language Testing System (IELTS): 6.5
Cambridge B2 First (formerly FCE): 180 (Grade A)
Cambridge C1 Advanced (formerly CAE): Pass
Cambridge C2 Proficiency (formerly CPE): Pass
The European Language Certificates (TELC) English C1: Pass
UNIcert English for Mathematicians Level C1: Pass
Duolingo: 105
Michigan English Test (MET): 64
Examination for the Certificate of Proficiency in English (ECPE): Pass
General State Language Examination in English in the Czech Republic: Pass

Podmínkou přijetí ke studiu v magisterském studijním programu je dosažení středního vzdělání s maturitní zkouškou. Podmínkou přijetí ke studiu v magisterském studijním programu, který navazuje na bakalářský studijní program, je rovněž řádné ukončení studia v kterémkoliv typu studijního programu.

Způsob ověření:	jiná forma
Datum ověření (přijímací zkoušky) od:		Do:
Náhradní termín (přijímací zkoušky):

Graduates have a broad knowledge of advanced algebra, geometry, logic, and their applications in IT, and can use it to solve advanced problems of mathematical information security and computer geometry. Graduates specializing in Mathematics for Information Security are well-acquainted with both present and prospective systems of data security and encryption. Graduates specializing in Computer Geometry have a deep knowledge of algebra and geometry, subjects that are applied in information technologies processing geometric information and data. The graduates are well-prepared for various jobs in information technologies where understanding and processing new knowledge and big data is needed. They are also prepared for an academic career.