IIT JAM Mathematics Syllabus 2026

The syllabus is published in the JAM information brochure. In brief:

Real Analysis

• Sequences and series of real numbers, convergence tests, limit superior and inferior
• Functions of one real variable: continuity, uniform continuity, differentiability, mean value theorems, Riemann integration

Calculus

• Functions of two and three variables: limits, partial derivatives, maxima and minima, Lagrange multipliers
• Double and triple integrals, vector calculus, Green's, Gauss's and Stokes' theorems

Differential Equations

• First-order equations, linear equations with constant coefficients, Cauchy–Euler equation

Linear Algebra and Abstract Algebra

• Vector spaces, linear transformations, rank and nullity, eigenvalues, Cayley–Hamilton theorem
• Groups, subgroups, cyclic groups, permutation groups, Lagrange's theorem, rings and fields

• Real analysis: convergence of sequences and series, limit superior and inferior, continuity and uniform continuity, compactness, mean value theorems
• Calculus: maxima and minima, double and triple integrals, Green's, Gauss's and Stokes' theorems
• Linear algebra: rank and nullity, eigenvalues, Cayley–Hamilton theorem, diagonalisation
• Differential equations: first-order methods, integrating factors, linear equations with constant coefficients
• Abstract algebra: orders of elements, cyclic groups, Lagrange's theorem, permutation groups, rings and fields

1. Weeks 1–3: real analysis: definitions first, then standard counter-examples.
2. Weeks 4–5: calculus of several variables and vector calculus.
3. Weeks 6–8: linear algebra, differential equations and group theory.
4. From week 9: previous-year JAM questions topic by topic and a timed full mock every weekend; redo every question you got wrong after three days.