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    Detail programu/oboru

    Mathematical Modelling in Physics and Technology (0541TA170019)

    Fakulta: Matematicko-fyzikální fakulta
    Studijní program: Mathematical Modelling in Physics and Technology (N0541A170019)
    Forma studia: prezenční
    Druh studia: navazující magisterské
    Jazyk výuky: angličtina
    Standardní doba studia: 2 roky
    Forma přihlášky: Elektronická, Listinná

    • Na tento program/obor nyní nelze podat elektronickou přihlášku.

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      Termín podání přihlášky: 30.04.2023
      Poznámka k termínu: Programme without specializations.
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      Mathematical modeling is an interdisciplinary study programme that combines mathematical analysis, numerical mathematics and physics. The programme is designed in such a way that the students acquire specialised as well as general knowledge in all mentioned fields, and they are ready, if required by the problem they are studying, to deepen their knowledge by studying highly specialized scientific works. All students are required to attend lectures on continuum mechanics, mathematical analysis of partial differential equations and numerical mathematics with the objective to acquire the ability to design mathematical models of natural phenomena (especially in the field of mechanics and continuum thermodynamics), and analyze and implement numerical methods for computer simulations of the given phenomenon. After completing the compulsory courses the students focus more closely on either the physical aspects of mathematical modeling (design of mathematical models), the mathematical analysis of partial differential equations, or methods for numerical solution of these equations. Extensive experience with all aspects of mathematical modeling (model design, analysis, simulation) enables students to use the state-of-the-art knowledge from all aforementioned fields in solving complex problems in physics, technology, biology and medicine that are beyond the scope of particular specialised fields. Graduates of the study programme are ready to work in the academic as well as commercial institutions that rely on mathematical modelling and simulations in their study of natural phenomena.
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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: (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
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      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):
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      The graduate has advanced theoretical knowledge of mathematical analytical and numerical methods applicable in the mathematical modeling of natural phenomena. In particular, he/she knows mathematical methods for the study of dynamical systems described by ordinary or partial differential equations, and he/she knows how to apply the methods in selected scientific disciplines. The graduate is able to design mathematical models for given natural/technical/social phenomena, analyse the basic mathematical properties of the proposed models, select the appropriate numerical method for their computer processing, and evaluate the benefits and limitations of the models in terms of their applicability in answering relevant practical questions.
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      Výše poplatků [EUR] / za období: 5700 EUR / rok
      Poznámka k poplatku [EUR] za studium v cizím jazyce: The tuition fee for students from the EU is 3400 EUR per academic year.