GATE 2021 Mathematics Syllabus, Preparation Tips and Books

Updated On - May 19th, 2020

Nikkil Visha

Exams Prep Master

Mathematics includes the study of topics like quantity, structure, space, and change. The syllabus of GATE 2021 Mathematics paper will be based on the topics studied at the graduation level. The question asked in paper will be based on formulas, equations, and graphs.

The major topics of included in the syllabus are Calculus, Linear Algebra, Real Analysis, Algebra, Functional Analysis, Numerical Analysis, etc. In the exam, there will be a total of 65 questions. Out of these total questions, 55 questions will be based on Mathematics and the remaining questions will be based on the General Aptitude section.  Check GATE 2021 Exam Pattern

GATE is conducted online and candidates need to solve the paper within 3 hours duration. After qualifying GATE 2021 candidates will be able to get admission in M.Tech courses offered at IITs, NITs, etc. 

Must Read IIT Bombay Admission Process

GATE 2021 Syllabus of 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 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 matrices; Finite dimensional inner product spaces, Gram-Schmidt orthonormalization process, definite forms.

Chapter 2 – 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

Chapter 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.

Chapter 4 – 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.

Chapter 5 – 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.

Chapter 6 – Functional Analysis

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

Chapter 7 – 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.

Chapter 8 – 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.

Chapter 9 – Topology

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

Chapter 10 – 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.

Chapter 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.

Direct link to download GATE Mathematics (MA) Syllabus PDF 

Important Topics in GATE 2021 Mathematics Paper

• Sample Question 1: 

• Sample Question 2:

Weightage of Important Topics

Check GATE Paper Analysis

GATE 2021 Exam Pattern of Mathematics

Every candidate can apply for one stream among all the 25 papers. GATE exam is conducted in online mode (Computer based). The total weightage of the GATE Exam is 100 marks. GATE 2021 Exam Pattern is quite tricky as it varies for different disciplines.

Note: There is also Negative marking 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.

Weightage of Sections in Paper

Preparation Books for GATE 2021 Mathematics

Mathematics section in  GATE  is considered 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:

Also Check GATE Recommended Books

Preparation Tips for GATE 2021 Mathematics (MA) Paper 

1. Know your Syllabus and Exam Pattern

• Candidates must have accurate information about the exam pattern. This will help them in understanding the weightage of sections, marking schemes, etc.
• After that, candidates must go through their syllabus again and again so that they won’t miss any topic.
• Candidates are advised to follow the syllabus prescribed by the exam conducting body.
• With the help of the right syllabus, you can easily plan your preparation. 

2. Prepare a Productive Plan

Candidates are suggested to prepare a plan as per their capabilities. Do not overburden yourself. You can follow the below-mentioned tips to prepare a plan:

• Long Term Plan: In long term planning you can divide your syllabus based on the months that are left for preparations. 
• Short Term Plan: In short term plan, you can divide the topics that you want to cover in a week. You can also call it a weekly plan. This plan is more defined in comparison to long term plan because here you would know exactly which topics you have to cover in a particular week. 

Read Preparation tips from GATE Topper

3. Manage your Time Properly

• Time management is a must in GATE Preparations. 
• Candidates need to give 6-8 hours of time for GATE preparations (considering you have 3-4 months left for the exam)
• Take frequent breaks to avoid laziness and to get refreshed.
• Dedicate 1-2 hours especially for revisions. 

4. Practice Papers

• Candidates solve the practice papers after completion of the whole syllabus or simultaneously after completion of each topic. 
• You can improve the accuracy and speed of solving questions.
• With the help of practice papers, you can judge the level of your performance. 
• You can get a better idea about the exam pattern, the difficulty level of questions, type of questions, etc.

Download GATE Practice Papers

5. Revision from Notes

• During the time of preparation prepare handwritten notes for each topic.
• These notes should include all the important points, tips, tricks, short cut methods, formulas, etc.
• Revise these notes on a daily basis. This will help you in memorizing important thinks. 
• Notes are helpful for a quick look before the exam

GATE 2021 Syllabus of Other Subjects

Other than Mathematics there are other 24 subjects for which GATE 2021 will be conducted. Candidates can check the syllabus of their respective subjects from the links provided below in the table:

GATE 2021 Mathematics Syllabus FAQs

*The article might have information for the previous academic years, which will be updated soon subject to the notification issued by the University/College