Branch programme/details

The study program Mathematical analysis provides to the students advanced knowledge in several branches of mathematics which are traditionally considered to belong to mathematical analysis (theory of real functions, complex analysis, functional analysis, theory of both ordinary and partial differential equations). It is characterized by a deep insight to these branches and focus on their mutual connections. Advanced level of basic knowledge in these branches is reached by attending mandatory courses. In elective courses students deepen their knowledge in more narrow areas, chosen namely with respect to the topic of their master thesis. Thanks to the seminars the students may be in touch with current problems of mathematical research.
Mathematical analysis is a wide well-established area with narrow connections to other parts of mathematics. Methods of mathematical analysis are used, among others, in the probability theory, in numerial mathematics and for creating and examining mathematical models (in physics or other sciences). Students may encounter these connections in some of the elective courses. Aims of the program include preparation for a PhD study of matematical analysis or related areas at the Charles university or at another university. Students encounter applications of mathematical theories, theorems and methods for solving concrete problems. Therefore their future employment is not limited to academic positions.

** 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 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 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/recognition-of-foreign-university-degrees-and-studies. The officially authorized documents must be physically sent to the Study Office of the Faculty of Mathematics and Physics preferebly by June 30, 2020, and by September 30,2020 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:

- **Mathematics programmes:** - 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 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**

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**

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

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

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, Ireland, 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 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

Admission to Master's studies is conditioned by completed secondary education confirmed by a school-leaving certificate. Admission to Post-Bachelor studies (Master's programme) is likewise conditioned by completed education in any type of study programme.

Verification method:	other form
Confirmation date (of entrance exam) from:		Until:
Alternative date (of entrance exam):

A graduate of the study program Mathematical analysis has advaced knowledge in basic areas of mathematical analysis (theory of real functions, complex analysis, functional analysis, theory of ordinary and partial differential equations) and understands their mutual connections, including connections to other areas of mathematics. He or she is able to apply advanced theoretical methods to solving concrete problems. He or she is prepared for a PhD study, but the acquired knowledge and ability can be succesfully used in other areas (economics, technics, finance, natural sciences) as well.