IIT JAM Mathematics Syllabus 2025

The IIT JAM Mathematics syllabus covers a wide range of topics, testing both theoretical understanding and problem-solving abilities. Below is a detailed breakdown of the key areas:
Real Analysis
Sequences and Series: Convergence of sequences, bounded and monotone sequences, Cauchy sequences, Bolzano-Weierstrass theorem.
Series Convergence Tests: Absolute convergence, comparison test, ratio test, root test.
Power Series: Radius and interval of convergence, term-wise differentiation and integration.
Functions of One Real Variable: Limits, continuity, intermediate value property, differentiation, Rolle’s Theorem, mean value theorem, L’Hospital’s rule, Taylor’s theorem and series, maxima and minima.
Riemann Integration: Definite integrals, properties, and the fundamental theorem of calculus.
The real analysis section is crucial in understanding the fundamental concepts of calculus and mathematical reasoning. Many competitive exams, including IIT JAM, heavily emphasize these topics. Candidates should focus on problem-solving and proof-based questions to strengthen their understanding of these concepts.
Multivariable Calculus and Differential Equations
Functions of Two or Three Variables: Limits, continuity, partial derivatives, total derivative, maxima and minima.
Integral Calculus: Double and triple integrals, change of order of integration, surface areas and volume calculations.
Differential Equations: Bernoulli’s equation, exact differential equations, integrating factors, orthogonal trajectories, homogeneous differential equations, method of separation of variables, linear differential equations of second order with constant coefficients, method of variation of parameters, Cauchy-Euler equation.
These topics form the foundation for applied mathematics and engineering mathematics. Candidates should practice solving integrals, differential equations, and optimization problems, as these are frequently tested in the IIT JAM Mathematics paper.
Linear Algebra and Algebra
Matrices and Vector Spaces: Systems of linear equations, rank, nullity, rank-nullity theorem, inverse, determinant, eigenvalues, and eigenvectors.
Finite-Dimensional Vector Spaces: Linear independence, basis, dimension, linear transformations, matrix representation, range space, null space.
Group Theory: Cyclic groups, abelian and non-abelian groups, permutation groups, normal subgroups, quotient groups, Lagrange’s theorem, group homomorphisms.
Linear algebra is an essential topic in modern mathematics, with applications in data science, physics, and computer science. Mastery of matrices, vector spaces, and eigenvalues can help candidates tackle a significant portion of the exam efficiently.