IIT JAM Mathematics Paper Pattern

The syllabus for IIT JAM Mathematics broadly covers undergraduate-level mathematics and is divided into three major sections.
Section 1: Real Analysis
Sequences and Series of Real Numbers: Convergence (including bounded, monotone, and Cauchy sequences), Bolzano-Weierstrass theorem, absolute convergence, and tests for series convergence (comparison, ratio, root). Power series (radius/interval of convergence, term-wise differentiation/integration).
Functions of One Real Variable: Limit, continuity (including intermediate value property), differentiation (Rolle’s Theorem, mean value theorem, L’Hospital rule, Taylor’s theorem and series), maxima and minima. Riemann integration (definite integrals and properties, fundamental theorem of calculus).
Section 2: Multivariable Calculus and Differential Equations
Multivariable Calculus: Functions of two or three real variables (limit, continuity, partial/total derivatives, maxima and minima).
Integral Calculus: Double and triple integrals, change of order of integration, calculation of surface areas and volumes.
Differential Equations: First-order equations (Bernoulli’s, exact, integrating factors, orthogonal trajectories, homogeneous, separation of variables). Second-order linear equations with constant coefficients (including variation of parameters and Cauchy-Euler equation).
Section 3: Linear Algebra and Algebra
Basic Algebra: Permutations, Combinations, and Binomial Theorem.
Linear Algebra: 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/null space, rank-nullity theorem).
Group Theory: Cyclic groups, abelian/non-abelian groups, permutation groups, normal subgroups, quotient groups, Lagrange’s theorem for finite groups, group homomorphisms.