Mathematics

Indian Institute of Technology Kanpur

PhD Mathematics

Objective Of The Program

The Department offers PhD programs in Mathematics and Statistics with the twofold objective of preparing researchers capable of contributing to advanced fields and developing well-trained teaching faculty. The department fosters a vibrant academic environment supported by highly motivated faculty members. Faculty actively pursue research in recent and emerging areas and promote interdisciplinary collaboration. Approximately 290 research scholars have graduated from the department and currently serve as faculty at various institutes and universities in India and abroad. Several graduates have also pursued careers in industry.

Structure of The Program

Course work:

Students must complete at least 54 postgraduate course credits within the first two semesters. This includes successful completion of at least three courses from the Compulsory Course Basket, which consists of the following:

  1. Algebra (MTH 751)
  2. Analysis (MTH 753)
  3. Advanced ODE and PDE (MTH 756)
  4. Topology and Geometry (MTH 757)
  5. Numerical Analysis (MTH 758)

In addition, all students must register for:

  • A zero-credit postgraduate seminar course for at least two semesters, and
  • The course ``Introduction to Profession and Communication Skills’’ (MTH 888M).

The following additional points should be noted:

  1. The minimum credit requirement does not include the credits earned from the course MTH 888M.
  2. Beyond the minimum credit requirements, the Departmental Postgraduate Committee (DPGC) may advise a student to enroll in additional courses based on his/her academic background. Refer to Section 7.1 of the PG Manual for further details.
  3. According to Section 7.3 of the PG Manual, students may audit courses of interest. However, audited courses will not appear on the registration form or grade transcript.

Comprehensive examination:

All students must pass a comprehensive examination that evaluates overall comprehension in Mathematics. Eligibility to take the examination is granted only after completion of all course requirements and attainment of a minimum Cumulative Performance Index (CPI) of 6.5 out of 10. The comprehensive examination must be completed successfully within four months of fulfilling the minimum coursework credit requirements. A student enrolled in the PhD programme attains candidacy only upon successful completion of the comprehensive examination. This examination will have both written and oral components. The following regulations apply to the written part of the Comprehensive examination:

  1. Students admitted to the PhD in Mathematics programme in the 2025-26-II semester will undertake separate two-hour written examinations for each compulsory subject: Algebra (MTH 751), Mathematical Methods (MTH 752), and Analysis (MTH 753). The syllabi for these examinations will be based on the approved course content for each respective subject.
  2. Students admitted to the PhD in Mathematics programme in the 2026-27-I semester and subsequent semesters will be required to take separate written examinations in exactly three of the following subjects: Algebra (MTH 751), Analysis (MTH 753), Advanced ODE and PDE (MTH 756), Topology and Geometry (MTH 757), and Numerical Analysis (MTH 758). Each examination will have a duration of two hours. The syllabi for these examinations will be based on the approved course content for each respective subject. Students may attempt a subject examination even if they have not enrolled in the corresponding course at the Department of Mathematics, IITK.
  3. In both cases, the written examination will account for 50% of the final assessment.

The Oral Comprehensive Board is constituted in accordance with Section 8.4 of the PG Manual. Please refer to Section 8 of the PG Manual for more detailed information.

State of Art Seminar:

Every Ph.D. student admitted to the candidacy for the Ph.D. degree is required to deliver a general seminar covering the State of Art of the area of research. This seminar, viz., the State of Art Seminar must be delivered within six monthsof passing the comprehensive examination.

Open Seminar:

Before finalizing the thesis, every Ph.D. student must deliver an Open Seminar in which the research work will be presented to obtain comments and criticism, which are to be incorporated in the thesis. The maximum time duration for the submission of the thesis after the delivery of the open seminar is six months. The PhD Thesis Board consists of three members in addition to the thesis supervisor(s) approved by the Chairman, Senate. At least two members of the board (other than the supervisor(s)) must be from outside the Institute and at least one of these two must be from within the country. The thesis supervisor(s), in consultation with the Head, proposes a list of examiners consisting of at least three extra names over and above the required number of members for the thesis board. The Chairman, Senate in consultation with Chairperson, SPGC selects the members of the thesis board from this list. The names of members of the thesis board are kept confidential till successful completion of the oral examination.

Academic requirements for the program

  1. As prescribed by Section 7.1 and Annexure IX of the PG Manual, minimum and maximum duration for graduation are 5 semesters and 12 semesters respectively. In addition, a student must complete at least 54 credits (for students admitted after an M. Sc.) or 72 credits (for students admitted after a B.Tech./4-year B.S. degree) from coursework (this includes only postgraduate course credits and does not include credits earned through the course MTH 888M or any PG Seminar course) and 72 credits from research for graduation.
  2. As per Section 4.3 of the PG Manual, the normal semester load is defined as equivalent of 36 credits. Therefore, all students are required to register for at least 36 credits in every semester of their program, unless the student has been granted a semester leave by the competent authority.
  3. The minimum CPI requirement for continuing in the PhD program is 6.5.
  4. As per Section 7.7.3 of the PG Manual, a student will normally not be allowed to continue in the Ph.D. program if

i) his/her CPI is below 6.5, or

ii) he/she obtains two Fs or two Es or one F and one E in the same or different courses, or iii) he/she accumulates eight or more Xs towards thesis grades, or

iv) he/she accumulates six or more Xs towards thesis grades in two consecutive semesters, or

v) he/she secures Xs in all the thesis credits registered for in two consecutive semesters.