Department Of Mathematics IIT Bombay

I want to do M.Sc. Mathematics Course in the Department of Mathematics, IIT Bombay so can you provide me the details of the program?

[shikha]

The Department of Mathematics, Indian Institute of Technology Bombay offers M.Sc. Mathematics Course of duration 2 years.

M.Sc. Mathematics Course

This 2 year Programme, offers an exciting opportunity to students who are interested in Mathematics and/or Statistics and who wish to pursue courses in teaching and research.

Admission Requirements

Bachelor's degree in Arts/Science/Statistics/Computer Science/Engineering with First Class/Division, with Mathematics or Statistics as one of the subjects for at least two years of the Bachelor's programme.

Final selection for admission will be based on the performance in the written entrance test to be conducted at the Institute.

Entrance Test-

The entrance test will be held in the last week of June/ first week of July at IIT, Bombay.

The test will consist of two papers, one in the morning and the other in the afternoon of the same day.

The following is the syllabus for the entrance examination.

Syllabi for Entrance Test for Both Applied Statistics & Informatics and Mathematics

PAPER I (100 marks, 3 hrs)

This paper is designed to test the basic understanding of various topics through straightforward questions, spread out more or less uniformly over the following seven headings:

There will be 15 objective type questions to be chosen from 20 such questions. Each correct answer will get 2 points while each incorrect answer will be given an appropriate nev gative credit.( If a question is not attempted, it will be given 0 points.) The candidates are advised to spend about one hour on these questions. In addition, there will be 7 questions, each carrying 10 points to be chosen from 14 questions, 2 on each of the 7 headings. In these questions the candidates will have to show their work.

PAPER II (50 marks, 2 hours)

This paper is designed to test certain qualities like mental alertness, logical thinking, aptitude for experimentation, pattern recognition, etc. This paper will have 5 moderately difficult questions of 10 points each to be chosen from 7 or 8 questions. When a candidate is unable to solve a given problem fully, he/she is advised to write down a possible approach to the solution, to solve it in some special case etc.

I. Sequences, Series and Differential Calculus:

Cauchy criterion, absolute and conditional convergence, tests of convergence, continuity and differentiability of functions of one variable, Rolle's theorem, Mean value theorem, Taylor's theorem

II. Integral Calculus and Differential Equations:

Riemann integral, Fundamental theorem of Calculus, improper integrals, double and triple integrals, areas and volumes, differential equations of 1st order and 1st degree, linear differential equations with constant coefficients.

III. Vector Algebra and Vector Calculus:

Dot, cross and triple products with applications to geometry, partial derivatives, gradients, divergence, curl, Laplacian, Green's, Stoke's and Gauss theorems (without proofs) and their applications.

IV. Set Theory and Algebra:

Functions, equivalence relations and partitions, permutations and combinations; unique factorisation of integers and polynomials, Euclid's algorithms for g.c.d, remainder theorem; groups, subgroups, Lagranges theorem, normal subgroups, quotient groups, permutation groups.

V. Linear Algebra and Numerical Methods:

Rn as a vector space, linear transformations, matrices and determinants, inverse of a matrix, rank, systems of linear equations. Divided differences, interpolation by polynomials, Gregory-Newton formula, Lagranges formula; solution of equations by bisection and Newton type methods.

VI. Probability:

Descriptive probability, random variables and their distribution functions, standard probability distribution, Independence, Central limit theorem and Bayes theorem (without proofs).

VII. Statistics:

Measures of location and dispersion, Correlation and regression analysis, Estimation and Testing Hypothesis.

Contact-

Department of Mathematics
IIT Bombay, Infinite Corridor, Academic Section, Powai, Mumbai, Maharashtra 400076