Syllabus of Entrance Test for Admission to M.Sc. in Mathematics

(Syllabus of the following topics is as per Under Graduate Honours lavel)

• Real Analysis – Sequence, Sets in R, Continuity, Differentiability, Power series, Enumerable sets, Fourier series, Compact sets, Metric spaces.
• Dynamics – Particle Dynamics.
• Algebra – Group, Ring, Field, Vector Space, Vector Algebra, Theory of equation, Complex Number
• Calculus – Functions of several variable, Indeterminate forms, Maxima & Minima, Infinite series of real constants and their convergence. Definite integration, Ordinary Differential equation of first order, Vector Calculus, Concavity & Convexity.
• Numerical Analysis – Errors in numerical computation, Numerical integration, Solution of linear and non-linear equations.
• LPP - Mathematical Preliminaries, Characteristics of an optimal solution.
• Mathematical Theory of Probability - Random experiments, events, Axioms of probability, Independent events, Multiplication rule, Conditional Probabilities, Bayes’ theorem, Bernoulli & Poisson trials, Binomial law, Probability distributions: Binomial, Poisson, Gamma, Normal, Uniform distributions, Transformations of random variables, Mathematical Expectations, Mean, Variance, Moments, Central moments, Tchebycheff’s inequality, convergence in probability, Law of Large numbers, Bernoulli’s limit theorem, Asymptotically normal distribution, Limit theorem for equal components
• Tensor Calculus - Summation convention, Contravariant, Covariant, Invariant and Mixed tensors, Kronecker Delta, Symmetric & Skew-symmetric tensors, Outer & Inner products, Quotient laws, Reciprocal Tensor, Riemannian Space, Line element & Metric tensor, Reciprocal Metric tensor, Associated tensor, Magnitude of a vector, Orthogonal vectors.