The Institute offers Teaching Assistantships requiring eight hours of work per week. Students can also be supported by scholarships / fellowships of other organizations such as National Board for Higher Mathematics, Council of Scientific & Industrial Research, University Grants Commission, Department of Science & Technology. For the current round of admissions, RA category seats are not available. Admissions take place twice a year in June and in December. The candidates should have obtained first class at the Masters degree in Mathematics/Statistics/Computer Science and must have a valid GATE score or an award of NBHM/CSIR/UGC Research Fellowship.

A special welcome to all who wish to pursue a career in Mathematics and Statistics research. The Department of Mathematics, IITB offers Ph.D. program in the areas of Mathematics and Statistics. Admission to the PhD program is based on a written test and interview. There are separate written tests and interviews for students in Mathematics and Statistics. The syllabus is given below. Students are required to choose one option specifying either Mathematics or Statistics.

To know more about the research interests of faculty members, please visit the page here. The program leading to the Ph.D. degree involves a course credit requirement, clearing of qualifier examinations and a research project leading to thesis submission. For more details, follow one of the links below

Syllabus for Mathematics Entrance Exam

Students in the PhD program have to fulfill the Qualifying Examination requirement within 3 semesters of joining. Please read further for details.

Qualifying Examinations are conducted in the following seven subjects twice every year: (1) Algebra, (2) Analysis, (3) Geometry and Topology, (4) Differential Equations, (5) Probability, (6) Statistics and (7) Combinatorics and Theoretical Computer Science. Typically these exams are conducted during 1-15 July and 15-31 December each year and the results are declared by 21st July and 7th January, respectively. Each exam is out of 100 and the pass mark is 60.

The student may attempt Qualifying Examinations in subjects of his/her choice. In order to fulfill the Qualifying Examination requirement the student has to pass in any two Qualifying Examinations within 3 semesters of joining the PhD program.

In case a student fails to complete the Qualifying Examination requirement at the end of his/her third semester, then he/she has the option of transferring to M.Phil. program, by continuing for about a semester, so as to complete the requirements for an M.Phil.degree.

The student may register with a Ph.D. thesis supervisor after the successful fulfillment of the coursework and Qualifying Examination requirement. Until that time the Faculty Advisor shall be the guide for all official purposes.

** Syllabus for qualifying examinations can be found** **here.**

All Ph.D students having M.Sc. or equivalent qualification shall acquire a minimum of 34 credits within the first three semesters of joining the Ph.D. program. The students shall also maintain a minimum CPI of 6.0 CPI in each of these semesters. These requirements are to be satisfied subject to the following conditions:

(a) Each student must credit at least 3 core Ph.D courses.

(b) Credits acquired through Ph.D courses (core/elective) shall be 24 or more.

(c) Students may earn upto a maximum of 8 credits through seminar courses (MAS801/MAS802).

(d) Students may credit up to two 500-level M.Sc. courses (for example, those that are relevant for the topic of qualifiers) to partially satisfy the credit requirement.

Ph.D. students have to compulsorily take the course MA899 (Communication Skills). Normally they should pass this course within one year of joining. This course is offered once every year, typically in the Autumn semester and has 0 credits. Students having a qualifying degree from an IIT and who have cleared the ‘Communication Skills’ course during their M.Tech. Program are not required to take the Communication Skills course.

The following core courses are offered in each of the corresponding semesters.

Course Code | Name of the Course | L | T | P | C |
---|---|---|---|---|---|

MA 811 | Algebra I | 3 | 0 | 0 | 6 |

MA 813 | Measure Theory | 3 | 0 | 0 | 6 |

MA 815 | Differential Topology | 3 | 0 | 0 | 6 |

MA 817 | Partial Differential Equations I | 3 | 0 | 0 | 6 |

MA 833 | Weak Convergence and Martingale Theory | 3 | 0 | 0 | 6 |

MA 861 | Combinatorics-I | 3 | 0 | 0 | 6 |

MA 863 | Theoretical Statistics I | 3 | 0 | 0 | 6 |

Course Code | Name of the Course | L | T | P | C |
---|---|---|---|---|---|

MA 812 | Algebra II | 3 | 0 | 0 | 6 |

MA 814 | Complex Analysis | 3 | 0 | 0 | 6 |

MA 816 | Algebraic Topology | 3 | 0 | 0 | 6 |

MA 818 | Partial Differential Equations II | 3 | 0 | 0 | 6 |

MA 820 | Stochastic Processes | 3 | 0 | 0 | 6 |

MA 823 | Probability I | 3 | 0 | 0 | 6 |

MA 824 | Functional Analysis | 3 | 0 | 0 | 6 |

MA 862 | Combinatorics-II | 3 | 0 | 0 | 6 |

MA 867 | Statistical Modelling- I | 3 | 0 | 0 | 6 |

In addition to the above courses, some or all of the following courses may be offered subject to sufficient demand from the students and availability of faculty.

Course Code | Name of the Course | L | T | P | C |
---|---|---|---|---|---|

MA 839 | Advanced Commutative Algebra | 3 | 0 | 0 | 6 |

MA 841 | Topics in Algebra I | 3 | 0 | 0 | 6 |

MA 843 | Topics in Analysis I | 3 | 0 | 0 | 6 |

MA 845 | Topics in Combinatorics I | 3 | 0 | 0 | 6 |

MA 847 | Topics in Geometry I | 3 | 0 | 0 | 6 |

MA 849 | Topics in Topology I | 3 | 0 | 0 | 6 |

MA 851 | Topics in Number Theory I | 3 | 0 | 0 | 6 |

MA 853 | Topics in Differential Equations I | 3 | 0 | 0 | 6 |

MA 855 | Topics in Numerical Analysis I | 3 | 0 | 0 | 6 |

MA 857 | Topics in Probability I | 3 | 0 | 0 | 6 |

MA 859 | Topics in Statistics I | 3 | 0 | 0 | 6 |

MA 864 | Topics in Category Theory I | 3 | 0 | 0 | 6 |

MAS 801 | Seminar | 0 | 0 | 0 | 4 |

Course Code | Name of the Course | L | T | P | C |
---|---|---|---|---|---|

MA 842 | Topics in Algebra II | 3 | 0 | 0 | 6 |

MA 844 | Topics in Analysis II | 3 | 0 | 0 | 6 |

MA 846 | Topics in Combinatorics II | 3 | 0 | 0 | 6 |

MA 848 | Topics in Geometry II | 3 | 0 | 0 | 6 |

MA 850 | Topics in Topology II | 3 | 0 | 0 | 6 |

MA 852 | Topics in Number Theory II | 3 | 0 | 0 | 6 |

MA 854 | Topics in Differential Equations II | 3 | 0 | 0 | 6 |

MA 856 | Topics in Numerical Analysis II | 3 | 0 | 0 | 6 |

MA 858 | Topics in Probability II | 3 | 0 | 0 | 6 |

MA 860 | Topics in Statistics II | 3 | 0 | 0 | 6 |

MA 865 | Topics in Category Theory II | 3 | 0 | 0 | 6 |

MAS 802 | Seminar | 0 | 0 | 0 | 4 |

**Note:** *Each course is of 6 credits with the structure of 3-0-0-6. A prerequisite for an even numbered course is exposure to the preceding odd numbered course, except in the case of MA 824 for which exposure to MA 819 shall be the prerequisite.*