GATE Syllabus is set by the organizing authority. The syllabus of each branch is different. For the academic year 2018, Indian Institute of Technology, Guwahati will organize GATE. There are total 23 papers in GATE exam.
GATE (Graduate Aptitude Test in Engineering) is a national level test organizeed for admission to M.Tech/ Ph.D. courses and other Government Scholarships/Assistantships in the field of engineering and technology.
The paper is held in online method (Computer Based Test). In this article, we are providing the clear Mathematics syllabus for GATE 2018. Aspirants required to solve the paper in three hours. There is negative marking for every inaccurate answer. It consists of 65 questions.
There are 11 chapters in GATE Syllabus for Mathematics paper. It is tabulated below. Each chapter has many subtopics. The clear syllabus of Mathematics paper is given below.
|Complex Analysis||Functional Analysis||Probability and Statistics|
|Real Analysis||Numerical Analysis||Linear Programming|
|Ordinary Differential Equations||Partial Differential Equations||-|
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, Skew-Hermitian and unitary matrices; Finite dimensional inner product spaces, Gram-Schmidt orthonormalization procedure, self-adjoint operators, definite forms.
Analytic functions, conformal mappings, bilinear transformations; complex integration: Cauchy’s integral theorem and formula; Liouville’s theorem, maximum modulus principle; Zeros and singularities; Taylor and Laurent’s series; residue theorem and applications for evaluating real integrals.
Sequences and series of functions, uniform convergence, power series, Fourier series, functions of several variables, maxima, minima; Riemann integration, multiple integrals, line, surface and volume integrals, theorems of Green, Stokes and Gauss; metric spaces, compactness, clearness, Weierstrass approximation theorem; Lebesgue measure, measurable functions; Lebesgue integral, Fatou’s lemma, dominated convergence theorem.
First order ordinary differential equations, existence and uniqueness theorems for initial value problems, systems of linear first order ordinary differential equations, linear ordinary differential equations of higher order with constant coefficients; linear second order ordinary differential equations with variable coefficients; mode of Laplace transforms for solving ordinary differential equations, series solutions (power series, Frobenius method); Legendre and Bessel functions and their orthogonal properties.
Groups, subgroups, normal subgroups, quotient groups and homomorphism theorems, automorphisms; cyclic groups and permutation groups, Sylow’s theorems and their applications; Rings, ideals, prime and maximal ideals, quotient rings, unique factorization domains, Principle ideal domains, Euclidean domains, polynomial rings and irreducibility criteria; Fields, finite fields, field extensions.
Normed linear spaces, Banach spaces, Hahn-Banach extension theorem, open mapping and closed graph theorems, the principle of uniform boundedness; Inner-product spaces, Hilbert spaces, orthonormal bases, Riesz representation theorem, bounded linear operators.
Numerical solution of algebraic and transcendental equations: bisection, secant method, Newton-Raphson method, fixed point iteration; interpolation: mistake of polynomial interpolation, Lagrange, Newton interpolations; numerical differentiation; numerical integration: Trapezoidal and Simpson rules; numerical solution of systems of linear equations: direct methods (Gauss elimination, LU decomposition); iterative methods (Jacobi and Gauss-Seidel); numerical solution of ordinary differential equations: initial value problems: Euler’s method, Runge-Kutta methods of order 2.
Linear and quasilinear first order partial differential equations, mode of characteristics; second order linear equations in two variables and their classification; Cauchy, Dirichlet and Neumann problems; solutions of Laplace, wave in two dimensional Cartesian coordinates, Interior and exterior Dirichlet problems in polar coordinates; Separation of variables mode for solving wave and diffusion equations in one space variable; Fourier series and Fourier transform and Laplace transform methods of solutions for the above equations.
Basic concepts of topology, bases, subbases, subspace topology, order topology, product topology, connectedness, compactness, countability and separation axioms, Urysohn’s Lemma.
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.
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 mode and its application in post-optimality analysis; Balanced and unbalanced transportation problems, Vogel’s approximation mode for solving transportation problems; Hungarian mode for solving assignment problems.
Mathematics is the study of topics such as quantity (numbers), structure, space and change. The questions asked in mathematics are based on formulas and graphs.
Mathematics section in GATE is considered as one of the toughest subjects so the preparation of it should be awesome. That is why we are providing you soma good books for mathematics preparation. Hence, below is the table represents some important books for mathematics preparation in GATE exam. Good books are one of the best ways of better preparation.
|Chapterwise Solved Papers Mathematics GATE – 2018||Suraj Singh, Arihant Publication|
|GATE Engineering Mathematics for All Streams||Abhinav Goel, Arihant Publication|
|GATE 2017: Engineering Mathematics||ME Team, Made Easy Publications|
|Wiley Acing the Gate: Engineering Mathematics and General Aptitude||Anil K. Maini, Wiley|
|Higher Engineering Mathematics||B.S. Grewal, Khanna Publishers|
Every aspirant can apply for one stream of all the 23 papers for which GATE 2018 is organizeed. The total weightage of the GATE Exam is 100 marks. GATE is an online method examination organizeed with 65 questions to be solved in 3 hours. GATE Exam Format is quite tricky as it varies for various branches.
|Method of Examination||Online/ Computer-based Test|
|Total no. of questions||65|
|Question Type||2 types- Multiple Choice types (MCQ) and Numerical Response Type (NAT).|
|Period of Exam||3 hours|
|Sections in paper||Two, i.e. General Aptitude and Subject Specific|