DOCTORAL PROGRAM

Doctoral (PhD) Program Structure and Graduation Requirements 

Short Description of the Doctoral (PhD) Program

Our PhD program comprises coursework, research and dissertation components. Its duration is 3-6 academic years. Normally, doctoral (PhD) students have to reside in Budapest at least during the first 3 years. The ideal situation is when a PhD student accomplishes the whole coursework and completes her/his dissertation within 3 years from the date of enrollment. The (maximum) 6-year period, between the date of enrollment and the date of dissertation submission, allows enough flexibility for our students.  In their first year, called Probationary Period, students have the status of Probationary Doctoral (PhD) Candidates. During this period they earn most of the course credits, write a dissertation proposal, and take the Comprehensive Exam covering the three mandatory courses, as well as the Candidacy Exam covering three elective courses in subjects related to the disertation proposal (see below). After students pass these exams they have the status of Doctoral (PhD) Candidates and focus mainly on research towards the PhD dissertation, under close supervision. More details are provided below.

The department offers courses in various parts of mathematics and its applications. The regular courses are delivered during the two main terms, Fall and Winter Term, that start the second half of September and early January, respectively (and each of them has a duration of 12 weeks). We also schedule special courses and invited lecture series beyond these two terms, especially during the Spring Term.

PhD students have to earn at least 30 credits in mandatory and elective courses, and take 6 credits for audit (no credit earned), usually on the supervisor’s recommendation. Note that 1 credit = 12 x 50 minutes = 600 teaching minutes. Normally one takes at least 24 course credits in the first year, including all mandatory courses. The remainder of the required course credits is normally taken in the second year. Students are also required to earn 18 research credits.

Probationary Period

Starts on the date of enrollment and terminates when the Candidacy Exam is successfully passed, normally by the end of the first year. Probationary Doctoral (PhD) Candidates have to reside in Budapest for the duration of the academic year.

First Year Coursework

In the first year, a PhD student has to normally earn at least 24 course credits, including 3 mandatory courses: Topics in Algebra, Topics in Combinatorics, and Applied Functional Analysis. Each regular course has 3 credits. Among the required course credits, each student has to earn at least 9 credits in elective courses (see Chapter Courses below) in a specific area which is supposed to be the framework of her/his forthcoming PhD dissertation.

Instructors provide students with syllabi, which include in particular the dates and forms of examination (quizzes, midterm and final exam, classroom presentations, etc.) as well as the formula which gives the final grade. The minimum passing grade for any course is C+ (worth 2.33 out of 4.00). Note that our university uses the US credit system. For further details, please visit http://www.ceu.hu/node/5360/572, Section Student Rights, Rules and Academic Regulations.

Departmental Seminar

Probationary PhD Candidates have to attend regularly the Departmental Seminar sessions which take place weekly during the Fall and Winter Term. This is worth 2 credits per academic year (1 credit per term) for a Pass/Fail qualification. This seminar aims to offer our mathematical community (students, faculty members and visitors) a proper framework for discussions on various topics in mathematics and its applications. Our students are encouraged to participate actively, by giving talks on topics that are close to their specific areas of interest, including their own findings. In particular, the seminar offers the most adequate framework for PhD dissertation defenses which are considered as its special sessions. Sometimes, public lectures given by our faculty members or visitors are scheduled.

Dissertation Proposal

Soon after enrollment, every probationary PhD candidate is assigned an advisor (or early supervisor) by the Mathematics Doctoral Program Committee (DPC). The advisor’s role is primarily to help the student in choosing an adequate research topic and preparing a Dissertation Proposal. The proposal should be 3-5 pages long and should contain:
- title of research work
- name of student
- name of advisor
- general presentation of the subject
- research problem(s) and intended results
- short description of previous work related to the problem(s)
- reference list.
The proposal is normally submitted (with the supervisor’s consent) to the Math DPC by the end of April. If there are objections and/or recommendations, the student has the right to re-submit an improved version of her/his proposal only once, in two weeks. Once it is approved by the Math DPC, the student receives 4 credits.

Credits to be earned in the first year:

The Grade Point Average (GPA) is calculated from the grades earned for coursework. A student with GPA < 3.00 cannot go to the Comprehensive Examination (see below). In order to qualify for the Comprehensive Exam, a probationary PhD student has to earn at least 24 course credits, plus 2 research credits for participation in the Departmental Seminar, and have a 3.00 or higher GPA. Otherwise, her/his student status is terminated.

Comprehensive Examination

This is a written exam which is normally taken on May 15 or before,  and consists in a couple of theoretical questions and/or problems related to the material of the mandatory courses (i.e., Topics in Algebra, Topics in Combinatorics, and Applied Functional Analysis), as specified in the syllabi of these courses. The minimum passing grade for the comprehensive exam is B+ (worth 3.33). Students may retake it only once, before the candidacy examination (see below). Failure to pass the comprehensive exam automatically terminates the student’s participation in the program.

Candidacy Examination

If a student successfully passes the comprehensive exam and earns 4 (research) credits for the Dissertation Proposal (see above), then s/he is entitled to take the Candidacy Exam. This is a Pass/Fail oral exam which is normally taken on June 10 or before, after passing the comprehensive. It is given in the area in which the student has chosen to write the PhD dissertation. More precisely, the exam covers the material of at least 3 courses (9 credits) taken in the area of the dissertation subject, as specified above (see Section First Year Coursework). The list of these courses must not include any of the three mandatory courses (i.e., Topics in Algebra, Topics in Combinatorics,  and Applied Functional Analysis). Good general knowledge of the specific area is also expected. In particular the student should be able to answer questions related to her/his Dissertation Proposal. On this examination the student should demonstrate depth and breadth of knowledge as well as maturity and real mastery of basic material and the ability to apply it to specific problems. The student should meet with her/his advisor (early supervisor) well in advance to prepare a written list of topics to be covered on the Candidacy Exam. This list is sent to the Math DPC for approval and then distributed to the examiners. A copy of the Dissertation Proposal is also sent to the examiners before the exam. The Math DPC should select at least three examiners, including the student’s advisor. The head of this committee will be one of the examiners, other than the student’s advisor. After a student passes the Candidacy Exam, s/he has the status of Doctoral (PhD) Candidate. Failure to pass this exam automatically terminates the student’s participation in the program.

Candidacy Period

of a student starts when s/he passes the Candidacy Exam. Therefore, normally, this period starts from the second year of studies. Doctoral Candidates are required to reside in Budapest during their candidacy period and participate in the academic life of the department, in particular by attending seminars, workshops, etc. However, with a prior approval of the Math DPC, a Doctoral Candidate may spend specified periods of time away from Budapest, if this helps the student progress toward the PhD. The permission may be given for maximum one year at a time, subject to the prior supervisor’s agreement. Even students who no longer receive stipend need permission to spend time elsewhere.

Credits to be earned during the Second and Third Year

During the Second Year, Doctoral Candidates are required to complete their course work by earning additional course credits, until they reach a total of 30 course credits and also by taking some additional courses for audit (worth 6 credits in total, but no credit earned). Of course, every student is allowed to take more elective courses in the first year, including courses for audit only, so that the coursework load is diminished accordingly in the second year. To summarize, 30 course credits, plus 6 credits in courses for audit, are required for each student to complete her/his coursework. Students are encouraged to take some courses offered by other departments which may be useful in preparing the dissertation. They are also allowed to take some elective MS courses, if recommended by their supervisors, either for audit or for credit, getting the same number of credits. All these credits are taken into account for the required coursework. Even more, they are allowed to take (for audit only, no credit earned) any of the MS mandatory courses, if they wish to refresh their knowledge, but these courses are not counted for the required coursework.

It is worth mentioning that in the Second and the Third Year, students should primarily do research, under close supervision, towards the PhD dissertation. In particular, they are required to attend the Departmental Seminar sessions (worth 2 research credits/AY for a Pass/Fail qualification) and meet regularly with their supervisors for consultation (for which each student earns 4 research credits/AY for a Pass/Fail qualification). For these credits, the supervisor may ask the student to attend certain research seminars and give talks. Participation in workshops and conferences is also taken into account.

Summarizing, each Doctoral Candidate has to earn 2(2 + 4) = 12 research credits during the second and the third academic year.

Upon completion of all the above requirements except the dissertation the Math DPC will recommend the candidate to be awarded the M. Phil. Degree in Mathematics and its Applications.

Dissertation Writing and Defense

Normally a Doctoral Candidate writes her/his PhD dissertation within 3 years from the date of enrollment. However, the duration of PhD studies may be extended up to 6 years (or even more in exceptional cases). The Candidacy Period terminates when the dissertation is successfully defended. For details see Dissertation.