# GATE Mathematics Syllabus 2020 - Study Material (PDF)

GATE 2020 Mathematics Syllabus: GATE 2020 application form process ended on October 5, 2019. IIT Delhi notified the syllabus for all the 25 subjects for GATE 2020.

The GATE syllabus for Mathematics is mentioned in the article below in a structured manner. The exam consists of 65 questions, out of which 55 questions shall be from Mathematics, and the remaining 10 will be based on General Aptitude. The syllabus is also available on the official website.
Every aspirant needs to go through the syllabus for GATE 2020 in a comprehensive manner to structure their preparation accordingly. The GATE syllabus for Mathematics is spread across 11 sections. For candidates planning to appear for the GATE exam, the most recent GATE Mathematics syllabus is given below for your reference:

## GATE Mathematics Syllabus 2020

 Topics Syllabus Section 1: Calculus Finite, countable and uncountable sets, Real number system as a complete ordered field, Archimedean property; Sequences and series, convergence; Limits, continuity, uniform continuity, differentiability, mean value theorems; Riemann integration, Improper integrals; Functions of two or three variables, continuity, directional derivatives, partial derivatives, total derivative, maxima and minima, saddle point, method of Lagrange’s multipliers; Double and Triple integrals and their applications; Line integrals and Surface integrals, Green’s theorem, Stokes’ theorem, and Gauss divergence theorem. Section 2: Linear Algebra Finite dimensional vector spaces over real or complex fields; Linear transformations and their matrix representations, rank and nullity; systems of linear equations, eigenvalues and eigenvectors, minimal polynomial, Cayley-Hamilton Theorem, diagonalization, Jordan canonical form, symmetric, skew-symmetric, Hermitian, skew-Hermitian, orthogonal and unitary matric Section 3:Real Analysis Metric spaces, connectedness, compactness, completeness; Sequences and series of functions, uniform convergence; Weierstrass approximation theorem; Power series; Functions of several variables: Differentiation, contraction mapping principle, Inverse and Implicit function theorems; Lebesgue measure, measurable functions; Lebesgue integral, Fatou’s lemma, monotone convergence theorem, dominated convergence theorem. Section 4: Complex Analysis Analytic functions, harmonic functions; Complex integration: Cauchy’s integral theorem and formula; Liouville’s theorem, maximum modulus principle, Morera’s theorem; zeros and singularities; Power series, radius of convergence, Taylor’s theorem and Laurent’s theorem; residue theorem and applications for evaluating real integrals; Rouche’s theorem, Argument principle, Schwarz lemma; conformal mappings, bilinear transformations. Section 5: Ordinary Differential equations First order ordinary differential equations, existence and uniqueness theorems for initial value problems, linear ordinary differential equations of higher order with constant coefficients; Second order linear ordinary differential equations with variable coefficients; Cauchy-Euler equation, method of Laplace transforms for solving ordinary differential equations, series solutions (power series, Frobenius method); Legendre and Bessel functions and their orthogonal properties; Systems of linear first order ordinary differential equations. Section 6: Algebra Groups, subgroups, normal subgroups, quotient groups, homomorphisms, automorphisms; cyclic groups, 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. Section 7: Functional Analysis Normed linear spaces, Banach spaces, Hahn-Banach theorem, open mapping and closed graph theorems, the principle of uniform boundedness; Inner-product spaces, Hilbert spaces, orthonormal bases, Riesz representation theorem. Section 8:Numerical Analysis Numerical solutions of algebraic and transcendental equations: bisection, secant method, Newton-Raphson method, fixed point iteration; Interpolation: error of polynomial interpolation, Lagrange and Newton interpolations; Numerical differentiation; Numerical integration: Trapezoidal and Simpson’s rules; Numerical solution of a system of linear equations: direct methods (Gauss elimination, LU decomposition), iterative methods (Jacobi and Gauss-Seidel); Numerical solution of initial value problems of ODEs: Euler’s method, Runge-Kutta methods of order 2. Section 9: Partial Differential Equations Linear and quasi-linear 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 and wave equations 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 equations mentioned above. Section 10: Topology Basic concepts of topology, bases, subbases, subspace topology, order topology, product topology, metric topology, connectedness, compactness, countability and separation axioms, Urysohn’s Lemma. Section 11: Linear Programming Linear programming problem and its formulation, convex sets and their properties, graphical method, basic feasible solution, simplex method, two phase methods; infeasible and unbounded LPP’s, alternate optima; Dual problem and duality theorems; Balanced and unbalanced transportation problems, Vogel’s approximation method for solving transportation problems; Hungarian method for solving assignment problems.

## Important Topics and Question-Related for GATE Mathematics

 Sections Important Topics Question-Related to the Topics Linear Algebra (For all streams) Eigenvalues and vectors Finding rank and determinant of matrices System of linear equations Find the Matrix for the given Eigenvalues and Eigenvectors Find the rank of determinant matrix Find the sum for the given system of linear equation Calculus (For all streams) Limit Maxima and Minima Gradient, Divergence, and Curl Find the maximum and minimum values for the given functions Simple questions on limit and continuity Find the Divergence of given Vector field Differential Equations (For all streams) First order equations (linear and non-linear) Cauchy s and Euler s equations Find the solution of given differential equation Complex Analysis (Except GATE CS) Analytic functions Cauchy-Riemann equations Taylor s series Find the expression for one of u(x,y) and v(x,y) for given analytical function f(z) = u(x,y) + iv(x,y) and also provide value of i with other expression Integration of given complex function in either clockwise or anticlockwise direction Numerical Methods (Except GATE CS) Newton-Raphson method Integration by Trapezoidal and Simpson s rules Find the iteration value of equation using the Newton-Raphson method Find the values of given integral using Trapezoidal and Simpson s rules Probability and Statistics (For all streams) Joint and conditional probability Uniform, Normal, Exponential Distributions Finding the probability of coin based problems, dice-based problems, etc Finding the probability using distributions Transform Theory (For GATE EE and ME) Laplace Transform Find the Laplace transform and Inverse Laplace transform on the given function Discrete Mathematics (Only for GATE CS) Mathematical Logic (Propositions and Predicate Logic) Relations and Functions Graph Connectivity and Colouring Find the first order logic sentence for the given English statement and with predicates Find is the given relation is reflective, symmetric or transitive Simple properties of various graphs such as complete graphs, bipartite graphs, regular graphs, cycle graph, and line graph

## GATE Mathematics Exam Pattern 2020

 Exam Section Marks Weightage General Aptitude 15% of the total marks Subject questions 85% of total marks

## GATE Mathematics Eligibility Criteria 2020

Graduates or final year student of Bachelor's degree/Master's degree (or equivalent) in engineering/architecture are eligible to appear for GATE 2020.

## Reference/Study Books Related to Each Topic for GATE Mathematics 2020

• Linear Algebra: Higher Engineering Mathematics by S Grewal
• Complex Analysis: Complex Analysis by Dr. A.P. Singh
• Real Analysis: Real Analysis by Dr. A.P. Singh
• Ordinary Differential Equations: Advanced Differential Equations by M D Raisinghania
• Algebra: GATE Engineering Mathematics for all Streams by Arihant Publications
• Functional Analysis & Numerical Analysis: GATE General Aptitude & Engineering Mathematics 2019 by GK Publications
• Partial Differential Equations, Topology: GATE Engineering Mathematics by Made Easy Publications
• Probability and Statistics & Linear programming: Advanced Engineering Mathematics by Erwin Kreyszig

## Tips and Tricks to Excel the Examination

1. Engineering Mathematics has a lot of formulae and noting them down as and when you complete one topic or referring to a set of formulae will help you memorise them for the exam later.
2. Solve all types of questions you come across in different books and be prepared for all question patterns
3. Solve previous year s papers and mock test series to help you adapt to the exam pattern. It will also help you evaluate your preparation and based on the test you can concentrate on areas where you re weak and prepare for those.

## FAQs

• How to prepare for GATE Mathematics exam?

Practice all the topics that are relevant to the syllabus, and make revision notes for each topic wherein you cover all important formulas and point while practising the problems.

• How much time does it require to prepare for GATE Mathematics exam?

It may take minimum one month for beginners, but since many aspirants already have studied engineering mathematics in their undergraduate courses, it is easier to complete the syllabus in less than 20 days with a preparation time of 2 to 3 hours in a day.

• How to remember and practice the formulas and concepts?

It is best to follow the recommended books and practice 2-3 times to remember the concepts and revise the formulas in one week.

## Important Points About GATE Examination

• Candidates should solve practice papers, mock tests, and previous year question papers for GATE preparation to acquire a clear idea concerning the type of questions which normally come and the upcoming paper pattern.
• For GATE preparation, it would be best to create notes for important topics which hold more weightage in the paper than others.

GATE Official Website:http://gate.iitg.ac.in/

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