IIT JAM Exam Centre Change

The Mathematics (MA) syllabus for IIT JAM 2025 includes the following topics:
Real Analysis
Real analysis covers fundamental concepts such as sequences and series of real numbers, including convergence, bounded and monotone sequences, and Cauchy sequences. The syllabus includes the Bolzano-Weierstrass theorem, absolute convergence, and various tests of convergence such as the comparison test, ratio test, and root test. Additionally, power series, their radius and interval of convergence, and term-wise differentiation and integration are important topics. Functions of one real variable, including limits, continuity, the intermediate value property, differentiation, Rolle’s Theorem, the mean value theorem, and Taylor’s theorem, are also significant. The section concludes with Riemann integration, definite integrals, their properties, and the fundamental theorem of calculus.
Multivariable Calculus and Differential Equations
This section deals with functions of two or three real variables, including limits, continuity, and partial derivatives. Candidates must also understand total derivatives, maxima and minima of functions, and Lagrange multipliers. Integral calculus focuses on double and triple integrals, changing the order of integration, and calculating surface areas and volumes. The differential equations section includes Bernoulli’s equation, exact differential equations, integrating factors, and orthogonal trajectories. Candidates must also be familiar with the method of separation of variables, linear differential equations of second order with constant coefficients, the method of variation of parameters, and Cauchy-Euler equations.
Linear Algebra and Algebra
Linear algebra topics include matrices, systems of linear equations, rank, nullity, inverse, determinants, eigenvalues, and eigenvectors. Candidates should also understand the rank-nullity theorem and its implications. The section on finite-dimensional vector spaces covers linear independence, basis, dimension, linear transformations, matrix representation, range space, and null space. The algebra portion introduces groups, including cyclic groups, abelian and non-abelian groups, and permutation groups. Other key topics include normal subgroups, quotient groups, Lagrange’s theorem for finite groups, and group homomorphisms.
Understanding the complete syllabus allows candidates to prioritize key topics and create an effective study plan.