IIT JAM Mathematics Syllabus 2027, Download Section Wise Syllabus, Important Chapters

Section

Chapter

Topic

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.

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.

Linear Algebra and Algebra

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.

Subject

Compulsory subjects opted in bachelor’s degree

IIT JAM Maths

Mathematics for at least two years/ four semesters

Particulars

IIT JAM Exam Pattern 2027

Medium of exam

English

Mode of exam

Online

Total marks

100 marks

Number of questions

60 questions

Type of questions

Multiple Choice Questions (MCQs), Multiple Select Questions (MSQs), and Numerical Answer Type (NAT)

IIT JAM exam time duration

3 hours (180 minutes)

Section

No of Questions

Marks

A

10 MCQs

1 mark each

20 MCQs

2 marks each

B

10 MSQs

2 marks each

C

10 NAT Questions

1 mark each

10 NAT Questions

2 marks each

IIT JAM Maths Books

Authors

Mathematical Analysis

S.C Malik

IIT JAM Mathematics

Neha Tyagi

Statistics

Murray and Spiegel

Fundamentals of Real Analysis

V.K. Krishnan

Abstract Algebra

Bhattacharya, Jain, and Nagpal

Principle of Mathematical Analysis

Rudi

Geometry and Vectors

Vasishtha

Calculus

Thomas and Finny