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GATE 2019 Mathematics Syllabus

Last Updated - September 10, 2018

Mathematics includes the study of such topics as quantity, structure, space, and change. The question asked in GATE mathematics paper are based on formulas and graphs. GATE Mathematics syllabus includes the subject topics and general aptitude. There are total 24 papers in GATE exam. The syllabus of each discipline is different.

GATE SyllabusGATE Exam PatternGATE Paper Analysis
  • The syllabus is based on the topics studied at graduation level.
  • 85% of the questions are asked from core subject and the remaining 15% questions are asked from general aptitude section.
  • The question paper consists of 65 questions worth 100 marks.

GATE 2019 will be scheduled from February 02, 03, 09 and 10, 2019 in multiple sessions. The paper is held in online mode (Computer Based Test). Candidates need to solve the paper in 3 hours. There is negative marking for every incorrect answer. In this article, we are providing the complete Mathematics syllabus for those candidates who appear for GATE Mathematics. 


GATE 2019 Syllabus for Mathematics

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

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.

Check HereGATE Paper Analysis


Preparation Books for Mathematics

Mathematics section in GATE is considered as one of the toughest subjects so the preparation of it should be awesome. Books are the best option to prepare for any exam. 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
BooksAuthor/Publisher
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

Also Check GATE Recommended Books


GATE 2019 Exam Pattern

Every candidate can apply for one stream among all the 24 papers. GATE exam is conducted in online mode (Computer based). 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

Note: There is also Negative marking include for every wrong answer. But is no negative marking for NAT but it is applicable for MCQs.  For 1 mark MCQs, 1/3 marks will be deducted for every wrong answer. Likewise, for 2 marks MCQs, 2/3 marks will be deducted


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