IIT JAM Mathematics Best Online Resources

The IIT JAM Mathematics syllabus is designed to assess a student’s understanding of undergraduate-level mathematics. It broadly includes:
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 (of one real variable), radius and interval of convergence, term-wise differentiation and integration of power series.
Functions of One Real Variable:
Limit, continuity, intermediate value property, differentiation.
Rolle’s Theorem, mean value theorem, L’Hospital rule, Taylor’s theorem, Taylor’s series, maxima and minima.
Riemann integration (definite integrals and their 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 using double integrals, calculating volumes using triple integrals.
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.
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 of vectors, basis, dimension.
Linear transformations, matrix representation, range space, null space, rank-nullity theorem.
Groups:
Cyclic groups, abelian groups, non-abelian groups, permutation groups.
Normal subgroups, quotient groups, Lagrange’s theorem for finite groups, group homomorphisms.
A clear understanding of each unit and its interconnections is essential for conceptual clarity and effective problem-solving.