Subject questions 85% of total marks
General aptitude 15% of total marks
Finite and infinite dimensional vector space, basis, linear transformation and their matrix representation, range space and null space, determinant, eigenvalues and eigenvectors, minimal polynomial, cayley Hamilton theorem, diagonalisation, inner product space, norms , Jordan canonical forms
Binary operation, groups and subgroups, cyclic groups, permutation group, normal subgroup. Homeomorphism and isomorphism, sylow’s theorem, rings and sub-rings, ideals , prime and maximal ideals, quotient rings, unique factorization domains, principal ideal domains, euclidean domains, polynomial rings and their irreducibility, fields and their extensions.
Set , countable and uncountable set, supremum and infimum, sequence and series and their convergence, continuous and different able function, uniform continuous, conditional convergence and uniform convergence, Riemann integral, power series and radius of convergence, double and triple integration, surface and line integrals, Gauss theorem, Lebesgue measures, measurable function, Lebesgue integrals.
Analytic functions, bi-linear transformation, con-formal mapping, complex integration, Cauchy’s integral formula, Louisville’s theorem, maximum modulus principle, zeros and singularities, Taylor,s and Laurent series, argument principle and residue theorem.
Ordinary differential equation
First order ordinary differential equation, uniqueness and existence theorem for initial value problems, singular and particular solution, homogeneous and non homogeneous equation, Bernoulli equation, Laplace transform, linear independent solutions of higher order differential equation.
Partial differential equation
Linear and quasi-linear first order partial differential equations, Dirichlet and neumann problems, boundary value problems, solutions of heat and wave equations,
General concept of topology, bases and sub bases, subspace topology, order topology and product topology, compactness and contentedness.
Probability and statistics
Basic definition of probability, conditional probability, Bayes theorem, independence, random variables, sample space, standard probability distributions ( discrete uniform, binomial, Poisson , geometric, normal, exponential) probability distribution function, weak and strong law of large numbers, central limit theorem, sampling distributions, interval estimation, testing of hypothesis
Linear programming problems, convex sets , graphical methods of linear programming problems, feasible solution, simplex method, big-M and two phase problems, infeasible and unbounded linear programming problems, dual problems and duality theorems, dual simplex method.
Average marks from each section
Section average marks
Real analysis 12 – 18
Complex analysis 4 – 8
Linear algebra 10 – 18
Abstract algebra 6 – 10
Ordinary differential equation 10 – 12
Partial differential equation 2 – 4
Numerical methods 8 – 12
Topology 2 – 4
Probability and statistics 6 – 20
Lpp 4 – 8
General aptitude 10
Tips to crack gate (maths)
- Prepare 3 or 4 topics (choose according to the average marks)
- Don’t leave linear algebra because it covers an average marks of 10 and it is the easiest topic .
- MSC ( maths ) students should not prepare probability and statistics because this section is for MSC (stats.) students.
- Practice previous year question ( it is necessary)