Our PhD Program in Mathematics combines advanced coursework, qualifying requirements, and guided research to prepare students for independent work in mathematics. This page describes the structure and expectations of the program.

Operational guidelines for the first year of Ph.D. Coursework

1) Core Courses (Mandatory): Every Ph.D. scholar must take at least two core courses from the prescribed Ph.D. core category.

This requirement is mandatory and strictly followed for all scholars.

2) Elective / Advanced Courses: In addition to the core courses, Ph.D. scholars may take advanced elective courses, which may include suitably advanced M.Sc. level courses. In such courses, the evaluation is expected at the Ph.D. level.

3) Undergraduate Course Restriction: A Ph.D. scholar may take at most two undergraduate courses as part of the coursework. Both courses must be Level 4 or higher, and this limit cannot be exceeded under any circumstance.

4) Ordinarily, a Ph.D. scholar may register for only one course under a given faculty member per semester. Any exception must be justified in writing and approved by the Department Research Committee (DRC).

5) Study in advanced topics / Research Project: If suitable coursework is not available as a structured course in the Institute bulletin, the scholar may register under heads such as Study in advanced topics / Research Project:

BITS G529 Research Project I
BITS G539 Research Project II
BITS G511 Advanced Project
BITS G513 Study in Advanced Topics

Ph.D. Qualifying Areas

Upon completing the coursework requirements, PhD students must qualify in two thrust areas of their choice. For each area, students are required to pass a minimum of two examinations.

Algebra	Commutative Rings, Non-commutative Rings, Groups and their Representations, Field Theory, Module Theory, Homological Algebra, Number Theory and Algebraic Geometry.
Analysis	Real Analysis, Complex Analysis, Functional Analysis, Nonlinear Analysis, Differential Geometry.
Differential Equations and Applications	Ordinary & Partial Differential Equations, Mathematical Biology, Mathematical Modeling, Fluid Dynamics, Applied Functional Analysis, Image Processing, Dynamical Systems, Control Theory.
Discrete Mathematics	Boolean and Fuzzy Logic, Graph Theory, Combinatorial Mathematics, Cryptography, Discrete Mathematical Structures, Design and Analysis of Algorithms, Lattice Theory, Coding Theory.
Applied Statistics	Statistical Inference, Regression Analysis, Statistical Quality Control, Demography, Design of Experiments & Analysis of Variance, Financial Mathematics, Stochastic Processes.
Operations Research	Queuing Theory, Inventory Systems, Reliability Theory, Data Envelopment Analysis, Linear and Nonlinear Programming.
Numerical Methods and Applications	Numerical Methods for Ordinary, Partial and Integro-Differential Equations and Applications to Fluid Dynamics and Fracture Mechanics.
Cosmology and Relativity	General Theory of Relativity, Alternative Theory of Relativity, Tensor Calculus.