Masters Programmes ADMISSIONS 2019

M. Sc. Mathematics

M.Sc. Mathematics Entrance Test Syllabus

  • Sequences and Series of Real Numbers Sequence of real num- bers, convergence of sequences, bounded and monotone sequences, con- vergence 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.
  • Functions of One Real Variable: Limit, continuity, intermediate value property, differentiation, Rolles Theorem, mean value theorem, L’Hospital rule, Taylor’s theorem, maxima and minima.
  • Functions of Two or Three Real Variables: Limit, continuity, partial derivatives, differentiability, maxima and minima.
  • Integral Calculus: Integration as the inverse process of differenti- ation, 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, calculat- ing volumes using triple integrals.
  • Differential Equations: Ordinary differential equations of the first order of the form y’=f(x,y), Bernoullis equation, exact differential equa- tions, integrating factor, orthogonal trajectories, homogeneous differ- ential equations, variable separable equations, linear differential equa- tions of second order with constant coefficients, method of variation of parameters, Cauchy-Euler equation.
  • Vector Calculus: Scalar and vector fields, gradient, divergence, curl, line integrals, surface integrals, Green, Stokes and Gauss theo- rems.
  • Group Theory: Groups, subgroups, Abelian groups, non-Abelian groups, cyclic groups, permutation groups, normal subgroups, Lagrange’s Theorem for finite groups, group homomorphisms and basic concepts of quotient groups.
  • Linear Algebra: Finite dimensional vector spaces, linear indepen- dence of vectors, basis, dimension, linear transformations, matrix rep- resentation, range space, null space, rank-nullity theorem. Rank and inverse of a matrix, determinant, solutions of systems of linear equa- tions, consistency conditions, eigenvalues and eigenvectors for matrices, Cayley-Hamilton theorem.
  • Real Analysis: Interior points, limit points, open sets, closed sets, bounded sets, connected sets, compact sets, completeness of R. Power series (of real variable), Taylors series, radius and interval of conver- gence, term-wise differentiation and integration of power series.
M. Sc. Physics
M.Tech. / MS in Computer Science & Engineering (CSE)
M.Tech. / MS in Electronics & Communication Engineering (ECE)
MS in Communication and Computer Engineering (CCE)