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## How to Prepare GATE Exam for Maths

Oct 18 • GATE, How to Prepare GATE Exam for Maths • 2018 Views • No Comments on How to Prepare GATE Exam for Maths

Exam pattern

Paper sections

Subject questions                                                        85% of total marks

General aptitude                                                          15% of total marks

Syllabus

Linear algebra

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

Abstract algebra

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.

Real analysis

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.

Complex analysis

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,

Topology

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

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)