IIT JAM 2026 Syllabus Breakdown

The official syllabus for IIT JAM 2026 Mathematics is divided into three major sections:
Section 1: Real Analysis
Sequences and Series of Real Numbers: Convergence of sequences, bounded and monotone sequences, Cauchy sequences, Bolzano–Weierstrass theorem, absolute convergence.
Tests of Convergence for Series: Comparison test, ratio test, root test.
Power Series: Radius and interval of convergence, term-wise differentiation and integration.
Functions of One Real Variable: Limit, continuity, intermediate value property, differentiation, Rolle’s theorem, mean value theorem, L’Hospital’s rule, Taylor’s theorem, Taylor series, maxima and minima.
Riemann Integration: Definite integrals, properties, fundamental theorem of calculus.
Section 2: Multivariable Calculus and Differential Equations
Functions of Two or Three Real Variables: Limit, continuity, partial derivatives, total derivative, maxima and minima.
Integral Calculus: Double and triple integrals, change of order of integration, calculating surface areas and volumes.
Differential Equations: Bernoulli’s equation, exact equations, integrating factors, orthogonal trajectories, homogeneous equations, separation of variables, linear second-order equations with constant coefficients, variation of parameters, Cauchy–Euler equation.
Section 3: Linear Algebra and Algebra
Basic Algebra: Permutations and combinations, binomial theorem.
Matrices: Systems of linear equations, rank, nullity, rank–nullity theorem, inverse, determinant, eigenvalues, eigenvectors.
Finite Dimensional Vector Spaces: Linear independence, basis, dimension, linear transformations, matrix representation, range space, null space.
Groups: Cyclic groups, abelian and non-abelian groups, permutation groups, normal subgroups, quotient groups, Lagrange’s theorem, group homomorphisms.