IIT Joint Admission test MSC Mathematics

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Books on Real Analysis
A Course in Calculus and Real Analysis by Sudhir R. Ghorpade and Balmohan V. Limaye
A course of Mathematical Analysis by Shanti Narayan
A first course in Mathematical Analysis by Somasundaram, Choudhari
Elementary analysis: the theory of calculus by K. A. Ross
Fundamentals of Real Analysis by V.K Krishnan
Introduction to Real Analysis by R. G. Bartle and D. R. Sherbert
Mathematical Analysis by Apostol T.M
Mathematical Analysis by Binmore K.G
Methods of Real Analysis by Richard.R Goldberg
Principles of Mathematical Analysis by Rudin .W
Real Analysis by H.L. Royden

Books on Probability and Statistics
A Brief Course in Mathematical Statistics by Hogg, R.V. and Tanis, E.A
A text Book of Statistics by C.E Weatherban
An Introduction to Probability and Statistics by Rohatgi, V. K. and Saleh, A. K
An Outline of Statistical Theory by Goon, A.M., Gupta, M.K. and Dasgupta, B
Fundamentals of Mathematical Statistics by Gupta, S.C. and Kapoor, V.K
Introduction to Probability Models by Ross, S. M
Introduction to the Theory of Statistics by Mood, A.M., Graybill, F.A. and Boes, D
Mathematical Statistics by Ray & Sharma
Statistics by Murray & Spiegel

Books on Differential Equations
Advanced Engineering Mathematics by Sastri S.S
Advanced Engineering Mathematics by Wylie, C.R. and Burrett, L.C
Differential and integral equations by Collins, P.J
Differential equations and the calculus of variations by Yankosky
Differential equations and their applications by Ahsan,Z
Differential Equations by G.F.Simmons
Partial differential equations – methods and applications by Mcowan, R.C

Books on Differential Calculus
Differential calculus by Balachanda Rao and C.K Santha
Differential Calculus by Gorakh Prasad

Books on Algebra
Abstract Algebra by Bhattacharya, Jain & Nagpal
Complex numbers from A to Z, by T.Andreescu, D.Andrica
Elementary Linear Algebra by Chatles W.Curtis
Elementary Linear Algebra by H.Anton
Fundamental structure in Modern Algebra by R.S. Mishra and N.N.Bhattacharya
Linear Algebra and its Applications by David C. Lay

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The Joint Admission test for Masters (JAM) is an admission test to M.Sc. and other post-B.Sc. programs at the Indian Institutes of Technology (IITs).

IIT JAM 2015 will be administered by IIT Guwahati. On the basis of performance in IIT JAM 2015, candidates shall be admitted to postgraduate programs of the following IITs:

Indian Institute of Technology Bombay (IITB)
Indian Institute of Technology Delhi (IITD)
Indian Institute of Technology Guwahati (IITG)
Indian Institute of Technology Kanpur (IITK)
Indian Institute of Technology Kharagpur (IITKgp)
Indian Institute of Technology Madras (IITM)
Indian Institute of Technology Roorkee (IITR)
Indian Institute of Technology Bhubhaneswar (IITBBS)
Indian Institute of Technology Gandhinagar (IITGN)
Indian Institute of Technology Hyderabad (IITH)
Indian Institute of Technology Indore (IITI)
IIT Ropar

JAM 2015 Important Dates

Commencement of Online Registration and Application Process: 03rd Sept 2014

Last Date for Payment of Fee through Challan: 30th Sept 2014

Closure of Online Application Procedure: 09th October 2014

JAM 2015 Examination: 08th February 2015

Announcement of JAM 2015 Results: 19th March 2015

IIT JAM 2015 application fee

Payment of fee can be made through challan or through net banking.

For one test paper

Female candidates (all categories): Rs. 750
Male candidates (general & OBC): Rs. 1500
Male candidates (SC/ ST/ PD): Rs. 750

For two test papers

Female candidates (all categories): Rs. 1050
Male candidates (general & OBC): Rs. 2100
Male candidates (SC/ ST/ PD): Rs. 1050

IIT JAM Mathematics Syllabus

Sequences and Series of real numbers: Sequences and series of real numbers. Convergent and divergent sequences, bounded and monotone sequences, Convergence criteria for sequences of real numbers, Cauchy sequences, absolute and conditional convergence; Tests of convergence for series of positive terms - comparison test, ratio test, root test, Leibnitz test for convergence of alternating series.

Functions of one variable: limit, continuity, differentiation, Rolle's Theorem, Mean value theorem. Taylor's theorem. Maxima and minima.

Functions of two real variables: limit, continuity, partial derivatives, differentiability, maxima and minima. Method of Lagrange multipliers, Homogeneous functions including Euler's theorem.

Integral Calculus: Integration as the inverse process of differentiation, definite integrals and their properties, Fundamental theorem of integral calculus. Double and triple integrals, change of order of integration. Calculating surface areas and volumes using double integrals and applications. Calculating volumes using triple integrals and applications.

Vector Calculus: Scalar and vector fields, gradient, divergence, curl and Laplacian. Scalar line integrals and vector line integrals, scalar surface integrals and vector surface integrals, Green's, Stokes and Gauss theorems and their applications.

Differential Equations: Ordinary differential equations of the first order of the form y'=f(x,y). Bernoulli's equation, exact differential equations, integrating factor, Orthogonal trajectories, Homogeneous differential equations-separable solutions, Linear differential equations of second and higher order with constant coefficients, method of variation of parameters. Cauchy- Euler equation.

Real Analysis: Interior points, limit points, open sets, closed sets, bounded sets, connected sets, compact sets; completeness of R, Power series (of real variable) including Taylor's and Maclaurin's, domain of convergence, term-wise differentiation and integration of power series.

Linear Algebra: Vector spaces, Linear dependence of vectors, basis, dimension, linear transformations, matrix representation with respect to an ordered basis, Range space and null space, rank-nullity theorem; Rank and inverse of a matrix, determinant, solutions of systems of linear equations, consistency conditions. Eigenvalues and eigenvectors. Cayley-Hamilton theorem. Symmetric, skewsymmetric, hermitian, skew-hermitian, orthogonal and unitary matrices.

Group Theory: Groups, subgroups, Abelian groups, non-abelian groups, cyclic groups, permutation groups; Normal subgroups, Lagrange's Theorem for finite groups, group homomorphisms and basic concepts of quotient groups (only group theory).

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