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# Joint Admission Test JAM Mathematics (MA) Syllabus 2022 : Indian Institute Of Technology

Organisation : Indian Institute Of Technology
Exam Name : Joint Admission Test JAM
Announcement : Joint Admission Test JAM Mathematics (MA) Syllabus
Website : https://jam.iitg.ac.in/

## Joint Admission Test JAM Syllabus

JAM 2023 is a Computer Based Test (CBT) to be conducted in SEVEN different subjects: Biotechnology (BT), Chemistry (CY), Economics (EN), Geology (GG), Mathematical Statistics (MS), Mathematics (MA), Physics (PH).

Related / Similar Syllabus : GATE Engineering Mathematics (XE) Syllabus 2023 ## JAM Mathematics (MA) Syllabus

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 integr ls 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.

## Eligibility Requirements (ERs) For Admission

** Candidates who qualify in JAM 2023 must fulfill the following Eligibility Requirements (ERs) for admissions to IITs.
** Candidates should have passed an undergraduate degree or should be currently studying in their final year of undergraduate programme. Proof of having passed the undergraduate degree should be submitted by September 1, 2023.
** Candidates promoted without a marksheet should produce a certificate stating the subjects studied in that semester/year duly signed by the Head of the Institute.
** Foreign nationals with Indian degree are eligible to apply, subject to policy of the Admitting Institute. 