Msc (math) entrance exam syllabus

Hello aspirant,

Here is the link for msc mathematics entrance syllabus..https://admission.examdevils.com/du-msc-entrance-syllabus-papers/.

Good luck.

Dear Amit, you haven't mentioned which entrance exam are you talking in particular. Neverthless, because the basic concepts for M.Sc entrance exam is evaluating you on your Mathematical skills at B.Sc level, here is a general syllabus as laid by the JNU for its M.Sc Mathematics Entrance Examination. However if you have any particular Entrance exam in mind, do let us know.



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), Taylors 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, Cayleys 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, Eulers e- function.