Prabhav Sharma 10th Sep, 2020

Hello,

The detailed syllabus for M. Sc. Mathematics Entrance exam of JNU is as follows:

• Set Theory and related topics: Elementary set theory, Finite, countable and uncountable sets, Equivalence relations and partitions
• Real Numbers, Sequences and Series: Real number system as a complete ordered field, Archimedean property, supremum, infimum, Sequence of real numbers, 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
• Real Analysis: Interior points, limit points, open sets, closed sets, bounded sets, connected sets, compact sets. Power series (of a real variable), Taylor’s series, 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, maxima and minima
• Functions of Two and 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
• 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 homomorphism and basic concepts of quotient groups, Cayley’s theorem, class equations
• 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, Inner product spaces, Orthonormal basis
• Miscellaneous: Logical reasoning, elementary combinatorics, divisibility in Integers, Congruence, Chinese remainder theorem, Euler’s φ-function

Hope this helps!