Subject Guidelines and Procedures

Mathematics (Framed under Article 2 of the Rules of the Deemed University)

The TIFR graduate programme in Mathematics will follow the basic guidelines and procedures set out in this document prepared by the Mathematics Subject Board.

Degrees, Programmes and Eligibility

Integrated Ph.D. Programme: Currently offered at the School of Mathematics, Mumbai and CAM, Bengaluru.

M.Sc. Programme: The M.Sc. degree is offered only as part of the Ph.D. programme. See below for details. There is no separate M.Sc. programme in Mathematics.

Ph.D. Programme: Currently offered at the School of Mathematics, Mumbai and CAM, Bengaluru. A new Ph.D. programme is also being planned at ICTS, Bengaluru.

The Ph.D. and Integrated Ph.D. (I-Ph.D.) Programmes in the School of Mathematics, TIFR, Mumbai, will lead to a Doctor of Philosophy (Ph.D.) degree in Mathematics. Students who are without a Master's degree will generally be admitted to the Integrated Ph.D. Programme. Subject to completion of the necessary requirements, they will obtain an M.Sc. degree in Mathematics, the study for which is to be completed within the first two years of their Ph.D. programme.

The Graduate School of the Institute (see the links menu) has more information and forms for downloading.

Eligibility: The eligibility criterion for admission to the Ph.D. programmme is a Master's degree in any of Mathematics, Statistics, Science or Technology (M.A. / M.Sc. / M.Math. / M.Stat. / M.E./ M.Tech.) and the eligibility criterion for admission to the Integrated Ph.D. programme is a Bachelor's degree in any of Mathematics, Statistics, Science or Technology (B.A. / B.Sc. / B.Math. / B.Stat. / B.E. / B.Tech.). Students with a four-year Bachelor's degree may be considered for admission to the Ph.D. programme.

Admission Procedure

Ph.D. and I-Ph.D. Programme: There will be a yearly Entrance Examination for admission to these programs. The eligible candidates will have to first appear for a written screening test. Candidates who pass the screening test will be called to appear for an interview, which is the main part of the examination.

In exceptional cases, a Special Entrance Examination may be administered at any time of the year to an especially promising candidate at the discretion of the Subject Board.

Provision for Foreign Students: The above provision for a Special Entrance Examination will also apply to especially promising candidates from abroad.

Description of Programmes

The study plan is formulated in terms of units termed as Year 0, Year 1 and Year 2, described below.

Integrated Ph.D. Programme: The selected candidates for the I-Ph.D. programme (who are without a Master's degree) will begin their programme with the Year 0. After successfully completing the Year 0 and the relevant examinations, these students will proceed to take the Year 1 courses. After successful completion of Year 0 and Year 1 and the relevant examinations, the students will be eligible for the degree of M.Sc. in Mathematics, subject to enrollment and registration requirements of the TIFR Deemed University.

Ph.D. Programme: Selected candidates for the Ph.D. programme who already have a Master's degree will directly join the programme in Year 1. After successfully completing the Year 1 and the relevant examination, these students will proceed to Year 2. Students are expected to identify a topic and an advisor and begin research work for their Ph.D. Thesis within six months of completing the second year course requirements. The Ph.D. Thesis is expected to be completed within 3 to 4 years after completing the second year course requirements. The programme culminates in the submission of the Ph.D. Thesis for a Thesis Examination. The successful candidates are awarded the Ph.D. degree of TIFR in Mathematics.

The course of study during the Years 0, 1, and 2 is as follows. The syllabus for these courses is available with the Mathematics Subject Board.

Year 0: During this year, there will usually be four one-semester courses on topics which are necessary background for graduate study and are normally covered in a good Master's programme in Universities. These courses may be either lecture courses or supervised self-study courses, depending on the number of such students. Each of the 4 courses will be worth 6 Credit Points, making a total of 24 Credit Points for Year 0.

Year 1: There will normally be three courses, in Algebra, Analysis, and Topology, each running for two semesters. Each of the 3 courses will be worth 8 Credit Points, making a total of 24 Credit Points for Year 1.

Year 2: Each student has to take 3 semester long lecture/reading course during the Year 2. A student has to inform the Subject Board about his/her preferences for courses at the beginning of each semester, and finalise the choice in consultation with the Board. It is expected that the student will later pursue research for Ph.D. in the topic of one of these courses. Each of the 3 courses will be worth 8 Credit Points, making a total of 24 Credit Points for Year 2.

Assignment of Research Programmes and Advisors for Ph.D. Thesis: It will be the responsibility of the student to find a research programme and an advisor, suitable to the student's aptitude and interests. There is no formal procedure for assignment of research programmes and advisors. Students are expected to develop serious interest in a broad area of specialisation by the end of their second year, and they are welcome to consult other members of the School for suggestions about the course of action to be pursued.

Qualifying and Evaluation Procedures

Year 0 Examination: There will be written examinations (of 3 hour duration each) for the four courses in Year 0. To pass the Year 0 Examination, which will be a precondition for being allowed to proceed to Year 1, a student has to obtain 50% marks in each of the courses. The students who pass will be accorded the grades Distinction, I st class, or II nd class, the requirements for which will be a minimum of 75%, 60% and 50% marks respectively, on average.

Year 1 Examination: This will generally be an oral examination for all three subjects at the end of the course (normally in the month of April). The M.Sc. candidates will be given marks for the performance in convenient multiples of 5 or 10, on a scale of 100, and the requirement for passing will be 50% in each course (see below with regard to grades). The Ph.D. candidates who are not M.Sc. candidates will be given an overall grade in terms of Pass or Fail, for all three subjects combined. A student has to pass in all the courses in order to proceed to Year 2.

M.Sc. Examination: The Year 0 and Year 1 examinations will together constitute the M.Sc. Examination. This is worth a total 48 Credit points. A student has to pass in all the courses in order to be declared successful. The overall percentage of marks will be calculated as the weighted average of marks in all the courses (of both the years), with weightage proportional to the Credit Points. The grades Distinction, I st class and II nd class will be given, for which the requirement will be 75%, 60% and 50%, in overall percentage, respectively.

The Board may also organise a qualifying exam for a student at a later stage upon request, provided it is formally supported by a member of the School undertaking to be the thesis advisor for the student. Approval of such a request will be subject to its being consistent with the general conditions set forth by the Academic Council. Such an exam will be held only once for any particular student.

In meritorious cases the course requirements may be waived.

An extra year may be sanctioned for completion of second year course requirements and registration in exceptional circumstances or for students with different backgrounds. A residency period of at least two years after registration will be a requirement for the award of a Ph.D. degree.

Registration for Ph.D. Thesis: Students who pass the second year can seek registration for Ph.D. For this, they shall apply to the subject board within 6 months of completing the second year course requirements and seek formal approval of the Board for registration. The application should contain the name of the proposed thesis advisor and a broad description of the topic of research intended to be pursued, endorsed by the proposed thesis advisor.

Eligiblity for Advisors: Any regular Academic member of the School of Mathematics with at least two years of postdoctoral experience is eligible to be a thesis advisor.

Approval of Submission of Ph.D. synopsis and Ph.D. Thesis: After a student completes his Ph.D. research project, with the permission of the Thesis Advisor the student will forward a synopsis of the thesis to the Subject Board to obtain prior approval for submission of the synopsis to the Deemed University Office. The same procedure will once again be followed to obtain prior approval for submission of the corresponding Thesis. The Subject Board will in general give its decisions in about a week.

Once the Subject Board approves the submission of a synopsis/thesis, the rest of the process of submission and evaluation of the synopsis/thesis will follow the general guidelines prescribed by the Academic Council, as given in the document Deemed University: Rules and Procedures.

Visiting Students' Research Programme

Every year the Mathematics Subject Board will run a programme mostly for students at M.Sc. level, which will enable them to visit the School of Mathematics for a month for a course of supervised study. Exceptionally well-prepared students at an earlier stage may be considered.

For more information check the VSRP link.