GATE Mathematics Syllabus for exam is mentioned below as per which the candidates can prepare for the exam. The applicants of the exam needs to be very particular about the following the syllabus for preparation. Be focussed on the exam, then you can achieve nice score in exam. All Mathematics topics are described below which are the part of exam. Mathematics is a matter of practice only, so be very keen in solving the questions of each topic.

Real Analysis: Fourier series, Fatou’s lemma, maxima, minima, integrals, Lebesgue Lebesgue integral, dominated convergence theorem, functions of several variables, measure, measurable functions

Linear programming: Graphical method, basic feasible solution, simplex method, big-M and two phase methods, dual simplex method and its application in post optimality analysis

Calculus of Variation and Integral Equations: Variation problems, sufficient conditions for extremum

Algebra: Normal subgroups, homomorphism theorems, automorphisms, Group actions, Sylow’s theorems and their applications, Euclidean domains, Principle ideal domains, Fields, finite fields

Functional Analysis: Banach spaces, Hahn-Banach extension theorem, principle of uniform boundedness, Hilbert spaces, orthonormal bases, Riesz representation theorem

Numerical Analysis: Fixed point iteration, numerical differentiation, method of undetermined parameters, Newton-Raphson method, interpolation, polynomial interpolation, iterative methods (Jacobi and Gauss-Seidel), initial value problems, secant method, Bisection, Lagrange, Newton interpolations, numerical solution of systems of linear equations

Linear Algebra: Skew Hermitian matrices, Cayley- Hamilton theorem, linear transformations, linear equations, Gram- Schmidt orthonormalisaion process

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Complex Analysis: Bilinear transformations, Analytic functions, Cauchy’s integral theorem and formula, Liouville’s theorem, Taylor and Laurent’s series, conformal mappings

Partial Differential Equations: Linear & quasilinear first order partial differential equations, second order linear equations in two variables, Cauchy, Dirichlet & Neumann problems, Fourier series and Fourier transform, Laplace transform

Mechanics

Topology

Probability and Statistics: Bayes theorem, independence, conditional distributions, standard probability distributions, Conditional probability, central limit theorem, Sampling distributions, UMVU estimators, maximum likelihood estimators, Testing of hypotheses, Random variables

Ordinary Differential Equations: Laplace transforms, First order, systems of linear first order ordinary differential equations, linear second order ordinary differential equations with variable coefficients, higher order with constant coefficients

Download the full set of syllabus from below given PDF. The candidates should note that above topics are limited and the detailed syllabus can be obtained from below.

**GATE Mathematics Syllabus DOWNLOAD**

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