**IIT JAM MATHEMATICS SYLLABUS**– Dear **IIT JAM mathematics** student here I am going to discuss the details **syllabus of IIT JAM mathematics** as well as the *exam pattern of IIT JAM*.

IIT JAM exam is the most prestigious exam if you are going to join the MSc courses in the IIT.

## IIT JAM Mathematics Syllabus

The** IIT JAM Mathematics Syllabus** few main topics I will cover those one by one.

- Sequences and Series of Real Numbers
- Functions of One Real Variable
- Functions of Two or Three Real Variables
- Integral Calculus
- Differential Equations
- Vector Calculus
- Group Theory
- Linear Algebra
- Real Analysis

**Sequences and Series of Real Numbers**: Sequence of real numbers, the convergence of sequences, bounded and monotone sequences, convergence criteria for sequences of real numbers, Cauchy sequences, subsequences, Bolzano-Weierstrass theorem. Series of real numbers, absolute convergence, tests of convergence for series of positive terms – comparison test, ratio test, root test; Leibniz test for convergence of alternating series.

**Functions of One Real Variable:** Limit, continuity, intermediate value property, differentiation, Rolle’s Theorem, mean value theorem, L’Hospital rule, Taylor’s theorem, maxima, and minima.

**Functions of Two or Three Real Variables:** Limit, continuity, partial derivatives, differentiability, maxima, and minima.

**Integral Calculus**: Integration as the inverse process of differentiation, definite integrals, and their properties, fundamental theorem of 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**: Ordinary differential equations of the first order of the form y’=f(x,y), Bernoulli’s equation, exact differential equations, integrating factor, orthogonal trajectories, homogeneous

differential equations, variable separable equations, linear differential equations of second order

with constant coefficients, Method of variation of parameters, Cauchy-Euler equation.

**Vector Calculus**: Scalar and vector fields, gradient, divergence, curl, line integrals, surface integrals,

Green, Stokes, and Gauss theorems.

**Group Theory**: Groups, subgroups, Abelian groups, non-Abelian groups, cyclic groups, permutation groups, normal subgroups, Lagrange’s Theorem for finite groups, group homomorphisms, and basic

concepts of quotient groups.

**Linear Algebra**: Finite dimensional vector spaces, linear independence of vectors, basis, dimension,

linear transformations, matrix representation, range space, null space, rank-nullity theorem. Rank and

inverse of a matrix, determinant, solutions of systems of linear equations, consistency conditions,

eigenvalues, and eigenvectors for matrices, Cayley-Hamilton theorem.

**Real Analysis**: Interior points, limit points, open sets, closed sets, bounded sets, connected sets,

compact sets, completeness of R. Power series (of a real variable), Taylor’s series, radius and interval

of convergence, term-wise differentiation, and integration of power series.