Mathematics (Framed under Article 2 of the Rules of the Deemed University)
The graduate programme by the School of Mathematics at TIFR (Mumbai) will follow the basic guidelines and procedures set out in this document prepared by the Subject Board for Mathematics.
For procedural instructions for registration, synopsis submission, and thesis submission please refer to this page.
Degrees, Programmes and Eligibility
Integrated Ph.D. Programme: Currently offered at the School of Mathematics, Mumbai.
M.Sc. Programme: The M.Sc. degree is offered only as part of the Integrated 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.
The Ph.D. and Integrated Ph.D. (I-Ph.D.) Programmes in the School of Mathematics, TIFR, Mumbai, will lead to a Ph.D./I-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, the students will obtain an M.Sc. degree in Mathematics, the study for which is to be completed within the first two years of their I-Ph.D. programme.
Eligibility: The eligibility criterion to be considered for admission to the Ph.D. programme 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 to be considered 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.). The candidates 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 two stage written examination (see this link ).
In exceptional cases, a Special Entrance Examination may be administered 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
Each year the School of Mathematics runs three pairs of courses, in Algebra, Analysis, and Topology, each course running for a semester. Each of the courses will be worth 8 Credit Points, making a total of 48 Credits.
I-Ph.D. Programme: The student enrolled in the I-Ph.D. programme (the selected candidate who does not have a Master's degree) is expected to finish his/her I-Ph.D. in six years.
The student is to complete 10 courses within first two years of the programme. The first six courses should cover the above mentioned courses in Algebra, Analysis and Topology.
Out of the remaining 4 courses, one course is the M.Sc. term paper. The term paper is one of the requirements for the M.Sc. degree and this requirement includes within its scope an introduction to research methodology. This should feature an expository article by the student on a theorem or a topic which is sufficiently important and non-trivial. The student should have a designated advisor for the term paper.
Each of the remaining three courses should be a semester long advanced course, and is to be completed within second year of the programme. This advanced course can be a lecture/reading course.
The 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 I-Ph.D. in the topic of one of these courses.
Each course is worth 8 Credit Points.
After successfully performing in the relevant first year and second year examinations, the student will be eligible for the degree of M.Sc. in Mathematics (subject to enrollment and the registration requirements of the TIFR Deemed University).
The student is expected to identify a topic and an advisor and begin research work towards her/his I-Ph.D. thesis within two and half years of the start of the programme. The I-Ph.D. thesis is expected to be completed within 4 to 5 years after completing the second year course requirements. The programme culminates in the submission of the I-Ph.D. thesis for a thesis examination. The successful candidates are awarded an I-Ph.D. degree of TIFR in Mathematics.
Ph.D. Programme: The student enrolled in the Ph.D. programme (the selected candidate who already has a Master's degree) is expected to finish her/his Ph.D. in five years.
The student is to complete 9 courses within first two years of the programme, one of which includes within its scope an introduction to research methodology.
In the first year the student should cover all the six above mentioned courses in Algebra, Analysis and Topology.
After successfully completing the Year 1 and the relevant examination, the student will proceed to Year 2. The rest of the three courses should consist of 3 semester long advanced (lecture/reading) courses in Year 2, one of which includes within its scope an introduction to research methodology. The 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 course is worth 8 Credit Points.
The student is expected to identify a topic and an advisor and begin research work towards her/his Ph.D. thesis within two years of the start of the programme. 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 a Ph.D. degree of TIFR in Mathematics.
Course titles and codes (as they will appear on the transcripts)
| Algebra 1 | MTH-101.1 |
| Analysis 1 | MTH-102.1 |
| Topology 1 | MTH-103.1 |
| Algebra 2 | MTH-104.1 |
| Analysis 2 | MTH-105.1 |
| Topology 2 | MTH-106.1 |
| Advanced course 1 | MTH-201.1 |
| Advanced course 2 | MTH-202.1 |
| Advanced course 3 | MTH-203.1 |
| Advanced course (RM) | MTH-204.1 |
| MSc Term Paper (RM) | MTH-205.1 |
In the above list, RM indicates that the course includes within its scope an introduction to Research Methodology. The courses with codes MTH-10x.1 are common to both the Ph.D. and the I-Ph.D. programmes. Course codes MTH-201.1, MTH-202.1 and MTH-204.1 are meant for Ph.D. students, while course codes MTH-201.1, MTH-202.1, MTH-203.1 and MTH-205.1 are meant for I-Ph.D. students.
Students may credit courses offered at other centres of TIFR (in consultation with the Subject Board).
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
Each semester, of the first year of the programme, there will be evaluation for the courses.
At the end of the first year there will be a final examination (normally by the end of April).
The I-Ph.D. student will be given marks for the performance on a scale of 100, and the requirement for passing will be 50% in each course. 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.
The Ph.D. student will be given an overall grade in terms of Pass or Fail, for all three subjects combined.
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 after evaluation.
In exceptional circumstances, the School of Mathematics may, considering various factors such as the background of a student and her/his performance in earlier courses, decide to sanction some extra time as deemed appropriate but not exceeding one year for the completion of the course requirements. 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. (I-Ph.D.) Thesis: The students, after satisfying the second year course requirements, can seek registration for Ph.D. (I-Ph.D.). For this, they shall apply to the Subject Board within the completion of two (two and half) years 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.
Thesis Monitoring Committee: At the time of registration of PhD/IPhD thesis, a Thesis Monitoring Committee consisting of
- the thesis advisor and the co-advisor (if one exists),
- one member of the Subject Board other than the thesis advisor and co-advisor, and
- one other regular faculty member in the School of Mathematics close to the proposed subject of the thesis or from the Subject Board
will be constituted. The Thesis Monitoring Committee will monitor the student's progress and make an annual recommendation on the continuation of the fellowship of the student to the Dean through the Subject Board. The Thesis Monitoring Committee for a registered student may be modified at a later date (adhering to the rules of its composition stated above) by the student and the thesis advisor in consultation with the Subject Board.
Approval of Submission of Ph.D. (I-Ph.D.) synopsis and Ph.D. (I-Ph.D.) Thesis: After the student completes her/his Ph.D. (I-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.