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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 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 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.

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

### 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 Examination Online/ Computer-based Test Total no. of questions 65 Question Type 2 types- Multiple Choice type (MCQ) and Numerical Answer Type (NAT). Maximum Marks 100 Duration of Exam 3 hours Sections in paper Two, i.e. General Aptitude and Subject Specific

sumit kumar

I m expecting 52 in gate 2018 civil and m belong to sc category.. Can I get any PSU?

15 Mar, 2018 10:56
Sakshi Garg Expert

Hi Sumit, You get information about the GATE Cutoff list through this link: PSU Cutoff List.

21 Mar, 2018 12:12
Prashant kumar

Sir my gate marks 65 in gate 2018 in civil engineering can I get it Delhi?

14 Mar, 2018 02:37
Sakshi Garg Expert

Hi Prashant, Please check the Cutoff list of Delhi through this link: GATE Delhi Cutoff

17 Mar, 2018 11:20
Avinash Chauhan

I m expecting 32 number in gate 2018 mechanical and belong to sc category can i get admisiion in dtu??

09 Mar, 2018 00:22
Sakshi Garg Expert

Hi Avinash, I am giving you the Cutoff list of DTU college please check the list through this link: GATE Cutoff List.

09 Mar, 2018 12:58
sama raju

what is the expected cut off marks for physics ( OBC Category)

23 Feb, 2018 13:53
Sakshi Garg Expert

Hi Sama, To get information about the Cutoff by this link: GATE Cutoff List

23 Feb, 2018 16:04

how much mark is required to get admission in iit kharakpur..

16 Feb, 2018 21:16
Sakshi Garg Expert

Hi Arvind, I am giving you the Cutoff list of IIT Kharagpur please check the list through this link: Gate Cutoff List

17 Feb, 2018 15:19
abhishek sharma

I am from commerce background and I have done MBA with specialization in hr can I eligible for filling the form for the post of personal and hr pls rep me fast

30 Jan, 2018 11:05
Sakshi Garg Expert

Hi Abhishek, GATE (Graduate Aptitude Test in Engineering) is a national level test for admission to M.Tech/ Ph.D. and other Government Scholarships/Assistantships in the field of engineering and technology. So you can not fill this exam for MBA. But you can apply for MBA by filling the CAT, XAT, CMAT, GMAT entrance exam.

15 Feb, 2018 16:34
suraj rohila

how to prepare for gate and when we will get the forms of gate exam and now a i am in fourth year

15 Jun, 2017 00:20
Kalpana Sharma Expert

Hi Suraj, The GATE 2018 Online Application Processing System (GOAPS) website opens from September 01, 2017. You can check form status from the official website. For know about the preparing tips, please check this link Prepare for GATE

01 Sep, 2017 18:24
NIKHIL SAHU

about nsr round in ccmt 2017

12 Apr, 2017 00:20

Hi Nikhil, to get details on GATE counseling and its rounds, please find the link http://exams.collegedunia.com/gate/counselling

12 Apr, 2017 17:03
Sumitra chakraborty

plz tell me gate exam 2017 when will be held

24 Mar, 2017 11:06

Hi Sumitra, GATE 2017 Examination has been completed, you may apply for GATE 2018.To get details on GATE 2018, please find the link http://exams.collegedunia.com/news/e-60-gate-2018

24 Mar, 2017 11:19
kanivarshini

GATE exam updtes and cut off for colleges in Tamilnadu

06 Mar, 2017 11:59
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