IIT JAM Mathematics Syllabus

IIT JAM Mathematical Statistics Syllabus

IIT JAM Mathematical syllabus will cover units and topics from the 10+2+3 level. The units included are Real Analysis, Multivariable Calculus and Differential Equations: Linear Algebra and Algebra. The table below highlights the IT JAM Mathematics syllabus.

Units	Topics and Sub-topics
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	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.

Units

Topics and Sub-topics

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.

IIT JAM Syllabus 2024 (Out): Download Syllabus PDF (Free) for Mathematics, Biotechnology, Physics, Chemistry

IIT JAM syllabus 2024 has been released by the IIT Madras for all seven subjects. The exam syllabus will remain the same as for the 2023 exam paper. Students who have successfully applied for the exam can download the IIT JAM exam syllabus and work on their exam preparation. IIT JAM 2024 will be conducted on 11th February, through which, selected candidates will be offered admission to 7 MSc courses at IITs: Biotechnology (BL), Economics (EN), Chemistry (CY), Physics (PH), Mathematical Statistics(MS), Mathematics (MA), and Geology (GG). IIT JAM exam paper consists of a total of 6 questions of 3 different types; MCQs, MSQs, and numerical based. Candidates looking forward to the exam paper need to have a proper understanding of their exam syllabus.

Therefore, to assist candidates with the best exam preparation, today, we will discuss the IIT JAM syllabus for the year 2024.

Table of Content

IIT JAM Syllabus 2024: Highlights
IIT JAM Syllabus 2024 PDF
IIT JAM Physics Syllabus
IIT JAM Biotechnology Syllabus
IIT JAM Mathematics Syllabus
IIT JAM Mathematical Statistics Syllabus
IIT JAM Chemistry Syllabus
IIT JAM Economics Syllabus
IIT JAM Geology Syllabus

IIT JAM Mathematics Syllabus

IIT JAM Syllabus 2024 (Out): Download Syllabus PDF (Free) for Mathematics, Biotechnology, Physics, Chemistry

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