Indian Institutes of Technology, Delhi conducts the Joint Admission Test for M.Sc. (JAM ) for admission to Integrated Ph.D. Degree Programmes at IISc Bangalore and M.Sc. (Two Years), Joint M.Sc.-Ph.D., M.Sc.-Ph.D. Dual Degree, M.Sc.-M.Tech., M.Sc.-M.S.(Research)/Ph.D. Dual Degree and other Post-Bachelor Degree Programmes at IITs

the Syllabus of the Mathematics Section of the IIT JAM Examination is given below

Mathematics Syllabus

Sequences and Series of Real Numbers

Convergent and divergent sequences

Bounded and monotone sequences

Convergence criteria for sequences of real numbers

Cauchy sequences

Absolute and conditional convergence

Tests of convergence for series of positive terms – comparison test

Ratio test

Root test

Leibnitz test for convergence of alternating series

Limit

Continuity

Differentiation

Rolle’s Theorem

Mean value theorem

Taylor’s theorem

Maxima and minima

Partial Derivatives

Differentiability

Maxima and minima

Method of Lagrange multipliers

Homogeneous functions including Euler’s theorem

Integration as the inverse process of differentiation

Definite integrals and their properties

Fundamental theorem of integral calculus

Double and triple integrals

Change of order of integration

Calculating surface areas and volumes using double integrals and applications

Calculating volumes using triple integrals and applications

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-separable solutions

Linear differential equations of second and higher order with constant coefficients

Method of variation of parameters

Cauchy-Euler equation

Vector Calculus

Scalar and vector fields

Gradient

Divergence

Curl and Laplacian

Scalar line integrals and vector line integrals

Scalar surface integrals and vector surface integrals

Green’s

Stokes and Gauss theorems and their applications

Groups

Subgroups

Abelian groups

Non-abelian groups

Cyclic groups

Permutation groups

Normal subgroups

Lagrange’s Theorem for finite groups

Group homomorphism’s and basic concepts of quotient groups (only group theory)

Vector spaces

Linear dependence of vectors

Basis

Dimension

Linear transformations

Matrix representation with respect to an ordered basis

Range space and null space

Rank-nullity theorem

Rank and inverse of a matrix

Determinant

Solutions of systems of linear equations

Consistency conditions

Eigenvalues and eigenvectors

Cayley-Hamilton theorem

Symmetric

Skew-symmetric

Hermitian

Skew-hermitian

Orthogonal and unitary matrices

Real Analysis: Interior points

Limit points

Open sets

Closed sets

Bounded sets

Connected sets

Compact sets

Completeness of R

Power series (of real variable) including Taylor’s and Maclaurin’s

Domain of convergence

Term-wise differentiation and integration of power series.