Detail programu/oboru

The master level program "Mathematical structures" is aimed at broadening student's general mathematical background in algebra, geometry, combinatorics and mathematical logic, and at acquiring a deeper knowledge in selected parts of these areas. The aim is to offer a fairly general overview of modern structural mathematics as well as leading the student towards an independent creative work. The emphasis is on areas in which we have lecturers that are on top of their fields.

**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 for 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 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 Act 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 confirming completion of higher education which will be assessed by the faculty itself (no fee is being charged).

Detailed information on how the condition of obtaining a 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":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 Department of Student Affairs of the Faculty of Mathematics and Physics preferably by June 30, 2025, and by September 30, 2025, at the latest. If you do not deliver the document concerning your 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 Computer science, Mathematics 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, 2025 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.

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 must 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, Republic of South Africa, UK or USA are exempt from this requirement. Applicants who provide us with comparable qualifications demonstrating proficiency in English (i.e., CEFR level C1) also meet our requirements.

Students who have completed our Bachelor programme in English are also exempt from this requirement.

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 180 (Grade A)
Cambridge C1 Advanced Pass
Cambridge C2 Proficiency 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):

A graduate of the programme has advanced knowledge of algebra, geometry, combinatorics and mathematical logic. These enable him or her to understand and to contribute to recent research. The abstract nature of the field, the depth and the difficulty of the study, lead to a development of the graduate's ability to analyse, structure and solve various problems of complex and abstract nature. Besides academia the graduate will function well in various positions where it is required to understand and to be able to use
new advances and large systems.