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    Branch programme/details

    Algebra, number theory, and mathematical logic (0541VD170020)

    Faculty: Faculty of Mathematics and Physics
    Study programme: Algebra, number theory, and mathematical logic (P0541D170020)
    Form of study: full-time
    Type of study: doctoral
    Language of instruction: English
    Expected minimum number of accepted students Expected number of accepted students: 1
    Standard length of study: 4 years
    Application type: Online, Paper
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      Application submission date: 30.04.2025
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      Charge for an on-line application: 1500 CZK
      Charge for a paper application: 1500 CZK
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      Entrance examination to all programmes taught in English
      The entrance examination for all study programmes consists of two rounds.

      1st round
      Assessment of candidates on the basis of the attachments to the application form. The admissions committee evaluates attachments according to the following criteria:
      a) Results and quality of previous studies (grades, quality of the university, time since the graduation)
      b) Compatibility of the applicant’s Master’s degree with the scientific field of the doctoral programme
      c) Quality of a motivation letter
      d) Content of recommendation letters and their relevance
      e) Publications or other professional achievements, proving the candidate's qualifications for doctoral studies
      f) The level of English language proficiency

      The assessment of each criterion is on a scale of 0-5 points, i.e. a maximum of 30 points can be obtained in the evaluation. To qualify for the 2nd round of the entrance exam, the candidate must obtain at least 15 points. If the candidate obtains at least 24 points, the admission committee will initiate an online interview with the candidate in which the candidate may obtain additional 5 bonus points.

      The 2nd round of the entrance examination is then waived for all applicants who obtain at least 28 points (including the bonus points from the interview). These applicants will be admitted for doctoral studies at the faculty.

      The results of the 1st round will be communicated to candidates by May 15, 2025 at the latest.

      Invitation to 2nd round of the entrance examination
      The invitation to 2nd round of the entrance examination will be sent to those applicants, who
      • submitted a complete application together with its obligatory attachments before the deadline,
      • paid the application fee,
      • were not awarded the waiver of the 2nd round of the entrance examination before mid-May, 2025. The invitation to an entrance examination is delivered through the University Electronic Information System. In mid-May, 2025, all applicants without a waiver receive an invitation to take the 2nd round of the entrance examination from the Faculty of Mathematics and Physics. If the Faculty approves the waiver after sending out the invitation, the invitation ceases to apply.

      2nd round
      The second round of the entrance examination may be conducted online, by means of information and communication technologies. It consists of two parts, the first one of which is related to the suggested dissertation topic, the second part then concerns the foundations of the scientific field of the study programme. The examination committee will evaluate the accuracy and completeness of all answers for a given part on a scale of grades: Excellent, Very good, Good and Fail. The applicant will get the following amount of points for each grade: Excellent 20 points, Very good 14 points, Good 8 points and Fail 0 points. The candidate can therefore obtain a maximum of 40 points in the 2nd round. The committee assesses the answers in particular from the point of view of correctness, completeness, accuracy and a demonstrated knowledge of the field. The exam will be conducted in English.

      Points for the first and second rounds are added together (bonus points from the 1st round interview are not taken into account). In order to pass the entrance examination, the applicant must obtain at least 45 points from both rounds together. The applicants with lower total scores cannot be admitted to doctoral studies.

      Admission conditions after the 2nd round
      The point threshold for admission to individual study programs will be set by the dean of the faculty, taking into account the expected number of admissions and the capacity and financial constraints of the faculty. The dean must announce the admission thresholds for individual programmes before July 1st , 2025. Applicants who, in the sum of the points for both rounds of the subject entrance exam, have reached at least the point threshold for admission to the given study program, will be admitted to study. The estimated minimal number of people admitted to each doctoral study programme after the 2nd round of the entrance exam is one applicant.

      Demonstrating English language proficiency
      English language proficiency should be demonstrated by fulfilling at least one of the following conditions:
      A. The applicant spent at least two years of his/her previous education at secondary or university level with English as the sole language of instruction in one of the following countries: Australia, Canada, India, Ireland, Malta, New Zealand, Pakistan, South Africa, UK or USA.
      B. The applicant has passed one of the following exams (in some cases we recognize the exam only with a minimum score or level):
      • General State Language Examination in English in the Czech Republic
      • TOEFL Essentials – 10 points
      • TOEFL iBT – 95 points
      • TOEFL ITP – 627 points
      • IELTS – 7 points
      • C2 Proficiency (formerly known as CPE) - Pass
      • C1 Advanced (formerly known as CAE) - Pass
      • ESOL International (C1 – C2)
      • TELC (The European Language Certificates) – TELC English C1 - Pass
      • UNIcert English for Mathematicians: Level C1 – level C1
      • Melab – 85 points
      • Examination for the Certificate of Proficiency in English (ECPE) - Pass
      • Test of English for International Communication (TOEIC) – 785 points

      Based on the evaluation by the examination committee, the faculty may offer the applicant, through the university's electronic information system, a different form of study in the same doctoral study program than the one for which he applied for study. The faculty sets a period of at least seven days for the applicant to accept the offer. If the applicant accepts the offer, the faculty changes the form of study in the application and the dean issues a decision regarding admission to study in the new form of study. If the applicant does not accept this offer or does not reply to the offer within the specified period, the dean will issue a decision regarding admission to study in the form of study for which the applicant has applied.
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      Admission to Doctoral studies is conditioned by successful completion of a Master's study programme.

      Verification method: entrance exam
      Confirmation date (of entrance exam) from: 09.06.2025 Until: 20.06.2025
      Alternative date (of entrance exam): 23.06.2025 Until: 27.06.2025
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      Our graduates possess state-of-the-art knowledge in the field of Theoretical Computer Science and Artificial Intelligence and actively add new results to these areas. They have experience with algorithm and data structure design and analysis, with AI tasks that include problem solving, automated planning, decision making, optimization, machine learning, design of cognitive models and robotic systems. The graduates are familiar with the core principles of scientific work and are able to specify their own research goals to solve the problems. They have experience with the work in an international environment, with university teaching, and with team work, typically involving development of complex software projects/systems. They know how to present their results and justify them in international competition. After graduation, they can work mainly in research and development both in academic and commercial environments.
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      Tuition [CZK] / per period: 1000 CZK / year