# IIT JAM Mathematics Syllabus 2023

The IIT JAM mathematics syllabus 2023 consists of topics like algebra, calculus, variables etc. The candidates who want to do their master in science in Mathematics should take a look at the JAM mathematics syllabus, provided by the exam conducting authorities.

Listed below are the topics included in IIT JAM mathematics syllabus 2023.

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.

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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).

## IIT JAM Mathematics exam pattern

Below is the exam pattern for IIT JAM mathematics 2023.

 Events Details Duration of the Exam 3 hrs Number of Questions 60 Questions Total Sections 3 (Section A, B and C) Types of Questions Multiple Choice Questions (MCQs)Multiple Select Questions (MSQs) Numerical Answerable Type Questions (NAT) Negative Marking Only for Section A Total Marks 100

## IIT JAM mathematics syllabus 2023- Weightage

Below listed are the topics of IIT JAM mathematics syllabus with thier weightage.

 Topic Weightage Real Analysis 21% Calculus of Single Variable 18% Linear Algebra 14% Calculus of Two Variables 14% Vector Calculus 12% Differential Equation 11% Abstract Algebra 10%

## IIT JAM Mathematics books for preparation

Listed below are books for IIT JAM mathematics preparation.

 Topic Author Integral Calculus F. Ayres (Schaumâ€™s), Gorakh Prasad Principles of Real Analysis S. C. Malik. Real Analysis H. L. Royden. Vector Calculus Murray R. Spiegel (Schaumâ€™s), A.R.Vasishtha Linear Algebra Seymour Lipschitz (Schaumâ€™s), H. Anton, A.R.Vasishtha. Modern Algebra A. R. Vasishtha 8. University Algebra: N. S. Gopalakrishan. Ordinary Differential Equation Peter J. Collins, G.F. Simmons, M.D. Raisinghania.