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    Branch programme/details

    Computational Mathematics (0541TA170011)

    Faculty: Faculty of Mathematics and Physics
    Study programme: Computational Mathematics (N0541A170011)
    Form of study: full-time
    Type of study: Master's (post-Bachelor)
    Language of instruction: English
    Standard length of study: 2 years
    Application type: Online, Paper
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      Application submission date: 30.04.2023
      Note on date: Programme without specializations.
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      The programme Computational Mathematics is devoted to the development, analysis, algorithmization, and implementation of methods for computer processing of mathematical models. It represents a transition from theoretical mathematics to practically useful results. An emphasis is placed on the creative use of information technology and production of programming applications. An integral part of the programme is the verification of employed methods. The study is a natural continuation of the bachelor's programme General Mathematics, branch Numerical Analysis and Mathematical Modelling at the Faculty of Mathematics and Physics of the Charles University. The programme Computational Mathematics is designed in such a way that it enables to admit also students who finished a bachelor's study of Mathematics of another branch or at another university, requiring that they complete the missing knowledge.

      The students will first obtain knowledge of the modern theory of partial differential equations, linear and nonlinear functional analysis, finite element method, basics of numerical software, and methods for matrix calculations. Later the students will choose elective courses, in particular according to the topic of their master’s thesis.
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      **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: ( 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 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
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      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):
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      The graduate of the master's programme Computational Mathematics has obtained a knowledge in basic fields of numerical mathematics and computational techniques as well as of the theory of partial differential equations and he/she is able to apply them to the numerical solution of problems in applications, including an efficient computer implementation. For a given problem, he/she is able to design or choose a suitable numerical method, carry out its numerical analysis, implement the computer realization including the analysis of computational error and assess how much the computational results approach the reality. He/she has a sufficient qualification for both a doctoral study at a Czech or foreign university and a career in the practice, in particular, in industry, basic and applied research or in public administration.
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      Tuition [EUR] / per period: 5700 EUR / year
      Note on tuition [EUR]: The tuition fee for students from the EU is 3400 EUR per academic year.