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GATE 2018 Mathematics Syllabus

Last Updated - August 30, 2017

GATE Syllabus is set by the conducting authority. For the academic year 2018, Indian Institute of Technology, Guwahati will conduct GATE. There are total 23 papers in GATE exam. The syllabus of each discipline is different.

  • GATE 2018 is scheduled for February 03, 04, 10 and 11, 2018 in multiple sessions.
  • GATE Syllabus is based on the topics studied at graduation level. 
  • GATE Mathematics syllabus includes the subject topics and general aptitude.
  • 85% of the questions are asked from core subject and remaining 15% questions are asked from general aptitude section.
  • The question paper consists of 65 questions worth 100 marks. 

GATE (Graduate Aptitude Test in Engineering) is a national level test conducted 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 mode (Computer Based Test). It consists of 65 questions. Candidates need to solve the paper in three hours. There is negative marking for every incorrect response. In this article, we are providing the complete Mathematics syllabus for GATE 2018. 

GATE Syllabus for Mathematics

There are 11 chapters in GATE Syllabus for Mathematics paper. It is tabulated below. Each chapter has many sub topics. The complete syllabus of Mathematics paper is given below.

Linear AlgebraAlgebraTopology
Complex AnalysisFunctional AnalysisProbability and Statistics
Real AnalysisNumerical AnalysisLinear Programming
Ordinary Differential EquationsPartial Differential Equations-

Chapter 1 – 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, Skew-Hermitian and unitary matrices; Finite dimensional inner product spaces, Gram-Schmidt orthonormalization process, self-adjoint operators, definite forms.

Chapter 2 – Complex Analysis

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.

Chapter 3 – Real Analysis

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, completeness, Weierstrass approximation theorem; Lebesgue measure, measurable functions; Lebesgue integral, Fatou’s lemma, dominated convergence theorem.

Chapter 4 – Ordinary Differential Equations

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; method of Laplace transforms for solving ordinary differential equations, series solutions (power series, Frobenius method); Legendre and Bessel functions and their orthogonal properties.

Chapter 5 – Algebra

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.

Chapter 6 – Functional Analysis

Normed linear spaces, Banach spaces, Hahn-Banach extension theorem, open mapping and closed graph theorems, principle of uniform boundedness; Inner-product spaces, Hilbert spaces, orthonormal bases, Riesz representation theorem, bounded linear operators.

Chapter 7 – Numerical Analysis

Numerical solution of algebraic and transcendental equations: bisection, secant method, Newton-Raphson method, fixed point iteration; interpolation: error 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.

Chapter 8 – Partial Differential Equations

Linear and quasilinear first order partial differential equations, method 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 method 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.

Chapter 9 – Topology

Basic concepts of topology, bases, subbases, subspace topology, order topology, product topology, connectedness, compactness, countability and separation axioms, Urysohn’s Lemma.

Chapter 10 – 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.

Chapter 11 – 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.

Preparation Books for Mathematics

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. Good books is one of the best ways of better preparation. 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. 

Preparation books for Mathematics
Chapterwise Solved Papers Mathematics GATE – 2018Suraj Singh, Arihant Publication
GATE Engineering Mathematics for All StreamsAbhinav Goel, Arihant Publication
GATE 2017: Engineering MathematicsME Team, Made Easy Publications
Wiley Acing the Gate: Engineering Mathematics and General AptitudeAnil K. Maini, Wiley
Higher Engineering MathematicsB.S. Grewal, Khanna Publishers

GATE 2018 Exam Pattern

Every candidate can apply for one stream among all the 23 papers for which GATE 2018 is conducted. GATE is an online mode examination conducted with 65 questions to be solved in 3 hours. The total weightage of the GATE Exam is 100 marks. GATE Exam Pattern is quite tricky as it varies for different disciplines.

Mode of ExaminationOnline/ Computer-based Test
Total no. of questions65
Question Type2 types- Multiple Choice type (MCQ) and Numerical Answer Type (NAT).
Maximum Marks100
Duration of Exam3 hours
Sections in paperTwo, i.e. General Aptitude and Subject Specific



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