# GATE

HomeGATE

- About Gate
- Graduate Aptitude Test in Engineering (GATE) is an examination that primarily tests the comprehensive understanding of the candidates in various undergraduate subjects in Engineering /Technology / Architecture and post-graduate level subjects in Science. The GATE score of a candidate reflects a relative performance level in a particular subject in the examination across several years. The score is used for admissions to post-graduate programs (e.g.,M.E./M.Tech/ Direct Ph.D.) in centrally funded Indian Institutes of higher education (i.e., Institutes which are provided with financial assistance by MHRD and other Government agencies). The score is also used by some Public and Private Sector Undertakings for employment processes in India. Direct recruitment to Group ‘A’ level posts i.e., Senior Field Officer (SFO Tele), Senior Research Officer (SRO) (Crypto) and SRO (S&T) in Cabinet Secretariat is now being done on the basis of GATE scores.

## SYLLABUS FOR MATHEMATICS

#### TOPICS

- Section 1: Linear Algebra
- Section 2: Complex Analysis
- Section 3: Real Analysis
- Section 4: Ordinary Differential Equations
- Section 5: Algebra
- Section 6: Functional Analysis
- Section 7: Numerical Analysis
- Section 8: Partial Differential Equations
- Section 9: Topology
- Section 10: Probability and Statistics
- Section 11: Linear programming

Linear Algebra Finite dimensional vector spaces; Linear transformations and their matrix representations, rank; systems of linear equations, eigenvalues and eigenvectors, minimal polynomial, Cayley-Hamilton Theorem, diagonalization, Jordan-canonical form, Hermitian, SkewHermitian and unitary matrices; Finite dimensional inner product spaces, Gram-Schmidt orthonormalization process, self-adjoint operators, definite forms. Section 10: Probability and Statistics Probability and Statistics Probability space, conditional probability, Bayes theorem, independence, Random variables, joint and conditional distributions, standard probability distributions and their properties (Discrete uniform, Binomial, Poisson, Geometric, Negative binomial, Normal, Exponential, Gamma, Continuous uniform, Bivariate normal, Multinomial), expectation, conditional expectation, moments; Weak and strong law of large numbers, central limit theorem; Sampling distributions, UMVU estimators, maximum likelihood estimators; Interval estimation; Testing of hypotheses, standard parametric tests based on normal, , , distributions; Simple linear regression. Section 11: Linear programming Linear programming Linear programming problem and its formulation, convex sets and their properties, graphical method, basic feasible solution, simplex method, big-M and two phase methods; infeasible and unbounded LPP’s, alternate optima; Dual problem and duality theorems, dual simplex method and its application in post optimality analysis; Balanced and unbalanced transportation problems, Vogel’s approximation method for solving transportation problems; Hungarian method for solving assignment problems.