Discrete Mathematics Sets and relations, elementary counting techniques, pigeon hole principle, partial orders,

Elementary probability theory

Automata Theory Regular expressions, non deterministic and deterministic finite automata, subset construction, regular languages, non regularity (pumping lemma), context free grammars, basic ideas about computable and non computable functions.

Algorithms O notation, recurrence relations, time complexity of algorithms, sorting and searching (bubble sort, quick sort, merge sort, heap sort).

Data structures Lists, queues, stacks, binary search trees, heaps.

Graphs Basic definitions, trees, bipartite graphs, matching's in bipartite graphs, breadth first search, depth first search, minimum spanning trees, shortest paths.

Algorithmic techniques Dynamic programming, divide and conquer, greedy.

Logic Boolean logic, truth tables, Boolean circuits - AND, OR, NOT and, NAND gates.

Fees and Scholarships

Research Scholars get a stipend of Rs 25000 per month for the first two years and Rs 28000 per month for the next three years, along with an annual book grant of Rs 10000. Scholars who do not stay in the hostel are eligible for a house rent allowance of 30% of stipend per month. The scholarship amounts are revised periodically, and are on par with the premier research institutes in India.

At the discretion of the Admissions Committee, students with a B.Sc. degree and those switching subjects may be admitted as Pre-Ph.D. students. For the first two years, Pre-Ph.D. students will be enrolled as a regular M.Sc. students in the corresponding subject. Till they complete their M.Sc. coursework or pass the Ph.D. qualifying examination, PrePh.D. students will receive a reduced scholarship, but will be eligible for other benefits similar to regular Ph.D. students.