# GATE Mathematics Syllabus 2018

Last Updated - March 10 2018

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 2018 is scheduled for February 03, 04, 10 and 11, 2018 in multiple sessions.
• GATE Mathematics syllabus comprises 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.
• GATE Syllabus is based on the topics studied at graduation level.
• The question paper consists of 65 questions worth 100 marks.

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.

### Syllabus for Mathematics GATE 2018

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.

 Linear Algebra Algebra Topology Complex Analysis Functional Analysis Probability and Statistics Real Analysis Numerical Analysis Linear Programming Ordinary Differential Equations Partial 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 procedure, 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, clearness, 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; mode 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, the 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: 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.

#### Chapter 8 – Partial Differential Equations

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.

#### 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 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.

### Preparation Books for Mathematics GATE 2018

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.

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

### Exam Format for GATE 2018

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). Maximum Marks 100 Period of Exam 3 hours Sections in paper Two, i.e. General Aptitude and Subject Specific

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