Content Curator  Updated On  Jan 12, 2022
IIT Kharagpur has released GATE Mathematics (MA) Syllabus 2022 on the official website. No changes have been made to the syllabus this year. GATE 2022 Mathematics Paper will have 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. The candidates who opted for Mathematics as their first paper in GATE 2022 can appear for Computer Science and Information Technology (CS), Geomatics Engineering (GE), Physics (PH), or (ST) as their second paper. Check GATE 2022 Exam Pattern
Major topics that are covered in GATE Mathematics Syllabus 2022 include Calculus, Linear Algebra, Real Analysis, Algebra, Functional Analysis, Numerical Analysis, etc. The students are advised to attempt as many previous year question papers as possible and analyze their mistakes. This would enable them to gain confidence and form a better judgment regarding GATE Mathematics Syllabus 2022. Check GATE Paper Analysis.
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GATE Mathematics Syllabus 2022
There are 11 chapters in the GATE Mathematics Syllabus. Each chapter has many subtopics. The complete syllabus of Mathematics paper is given below.
Section 1: Calculus
 Functions of two or more 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 to area, volume and surface area; Vector Calculus: gradient, divergence and curl, 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, characteristic polynomial, eigenvalues and eigenvectors, diagonalization, minimal polynomial
 CayleyHamilton Theorem, Finite dimensional inner product spaces, GramSchmidt orthonormalization process, symmetric, skewsymmetric
 Hermitian, skewHermitian, normal, orthogonal and unitary matrices; diagonalization by a unitary matrix, Jordan canonical form; bilinear and quadratic forms.
Section 3: Real Analysis
 Metric spaces, connectedness, compactness, completeness; Sequences and series of functions, uniform convergence, AscoliArzela theorem;Weierstrass approximation theorem; contraction mapping principle
 Power series; Differentiation of functions of several variables, Inverse and Implicit function theorems; Lebesgue measure on the real line, measurable functions; Lebesgue integral, Fatou’s lemma, monotone convergence theorem, dominated convergence theorem.
Section 4: Complex Analysis
 Functions of a complex variable: continuity, differentiability, 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 series and Laurent’s series; Residue theorem and applications for evaluating real integrals; Rouche’s theorem, Argument principle, Schwarz lemma; Conformal mappings, Mobius 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; CauchyEuler 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
 Sturm's oscillation and separation theorems, SturmLiouville eigenvalue problems, Planar autonomous systems of ordinary differential equations: Stability of stationary points for linear systems with constant coefficients, Linearized stability, Lyapunov functions.
Section 6: Algebra
 Groups, subgroups, normal subgroups, quotient groups, homomorphisms, automorphisms; cyclic groups, permutation groups,Group action,Sylow’s theorems and their applications; Rings, ideals, prime and maximal ideals, quotient rings, unique factorization domains
 Principal ideal domains, Euclidean domains, polynomial rings, Eisenstein’s irreducibility criterion; Fields, finite fields, field extensions,algebraic extensions, algebraically closed fields.
Section 7: Functional Analysis
 Normed linear spaces, Banach spaces, HahnBanach theorem, open mapping and closed graph theorems, principle of uniform boundedness; Innerproduct spaces
 Hilbert spaces, orthonormal bases, projection theorem,Riesz representation theorem, spectral theorem for compact selfadjoint operators.
Section 8: Numerical Analysis
 Systems of linear equations: Direct methods (Gaussian elimination, LU decomposition, Cholesky factorization), Iterative methods (GaussSeidel and Jacobi) and their convergence for diagonally dominant coefficient matrices; Numerical solutions of nonlinear equations: bisection method, secant method, NewtonRaphson method, fixed point iteration; Interpolation
 Lagrange and Newton forms of interpolating polynomial, Error in polynomial interpolation of a function; Numerical differentiation and error.
 Numerical integration: Trapezoidal and Simpson rules, NewtonCotes integration formulas, composite rules, mathematical errors involved in numerical integration formulae; Numerical solution of initial value problems for ordinary differential equations: Methods of Euler, RungeKutta method of order 2.
Section 9: Partial Differential Equations
 Method of characteristics for first order linear and quasilinear partial differential equations; Second order partial differential equations in two independent variables: classification and canonical forms, method of separation of variables for Laplace equation in Cartesian and polar coordinates, heat and wave equations in one space variable
 Wave equation: Cauchy problem and d'Alembert formula, domains of dependence and influence, nonhomogeneous wave equation; Heat equation: Cauchy problem; Laplace and Fourier transform methods.
Section 10: Topology
 Basic concepts of topology, bases, subbases, subspace topology, order topology, product topology, quotient topology, metric topology, connectedness, compactness, countability and separation axioms, Urysohn’s Lemma.
Section 11: Linear Programming
 Linear programming models, convex sets, extreme points;Basic feasible solution,graphical method, simplex method, two phase methods, revised simplex method ; Infeasible and unbounded linear programming models, alternate optima; Duality theory, weak duality and strong duality; Balanced and unbalanced transportation problems
 Initial basic feasible solution of balanced transportation problems (least cost method, northwest corner rule, Vogel’s approximation method); Optimal solution, modified distribution method; Solving assignment problems, Hungarian method.
GATE 2022 Exam Pattern of Mathematics
GATE 2022 Exam Pattern varies for different disciplines. Given below is the examination pattern for GATE Mathematics.
 Mode of Examination: Online
 Duration of Exam: 3 hours
 Types of Questions: MCQs and NAT
 Sections: 2 sections – General Aptitude and Subjectbased
 Total Questions: 65 questions
 Total Marks: 100 marks
 Negative Marking: For MCQs only
Weightage of Sections in GATE Mathematics 2022
GATE Mathematics Syllabus 2022 is divided into two sections. The below table describes the distribution of marks in each section.
Section  Distribution of Marks  Total Marks  Types of questions 

GA  5 questions of 1 mark each 5 questions of 2 marks each  15 marks  MCQs 
MA SubjectBased  25 questions of 1 mark each 30 questions of 2 marks each  85 marks  MCQs and NATs 
GATE Mathematics Marking Scheme 2022
Type of question  Negative marking for wrong answer 

MCQs 

NATs  No negative marking 
GATE Mathematics Syllabus 2022: Weightage of Topics
The students are advised to commence their GATE Preparation after going through the weightage of each topic mentioned. This will save them a lot of trouble and effort.
Important Topics  Weightage of Topics (In %) 

Linear Algebra  10% 
Complex Variables  10% 
Vector Calculus  20% 
Calculus  10% 
Differential Equation  10% 
Probability & Statistics  20% 
Numerical Methods  20% 
GATE Preparation 2022 for Mathematics
To assist in the GATE Mathematics Preparation 2022, the following sections have been curated. The students are advised to check out the following and avail of the benefits.
Best Books for GATE Mathematics (MA) 2022
Given below are the recommended books for GATE Mathematics 2022 that would be beneficial for the students.
Books  Author/Publisher 

Chapterwise Solved Papers Mathematics GATE  Suraj Singh, Arihant Publication 
GATE Engineering Mathematics for All Streams  Abhinav Goel, Arihant Publication 
GATE: Engineering Mathematics  ME Team, Made Easy Publications 
Wiley Acing the Gate: Engineering Mathematics and General Aptitude  Anil K. Maini, Wiley 
Higher Engineering Mathematics  B.S. Grewal, Khanna Publishers 
Also Check: GATE Recommended Books
GATE MA Previous Year Question Paper
Given below are the links for GATE MA Previous Year Question Papers along with their answer key.
Year  Link for GATE MA Question Paper  Link for GATE MA Answer Key 

2021  Check Here  Check Here 
2020  Check Here  Check Here 
2019  Check Here  Check Here 
2018  Check Here  Check Here 
2017  Check Here  Check Here 
GATE Mathematics Sample Questions

Sample Question 1:

Sample Question 2:
GATE Syllabus 2022 of Other Subjects
Other than Mathematics there are other 24 subjects for which GATE 2022 will be conducted. Candidates can check the syllabus of their respective subjects from the links provided below in the table:
GATE Mathematics Syllabus 2022 FAQs
Ques. What will be the subjects or sections that one needs to cover in the GATE 2022 Mathematics paper?
Ans: GATE 2022 Mathematics syllabus includes General Aptitude and core subject i.e. Mathematics. The engineering mathematics sections which are there in various subjects of GATE will not be the part of mathematics. The major sections from mathematics are:
 Chapter 1 – Linear Algebra
 Chapter 2 – Complex Analysis
 Chapter 3 – Real Analysis
 Chapter 4 – Ordinary Differential Equations
 Chapter 5 – Algebra
 Chapter 6 – Functional Analysis
 Chapter 7 – Numerical Analysis
 Chapter 8 – Partial Differential Equations
 Chapter 9 – Topology
 Chapter 10 – Calculus
 Chapter 11 – Linear Programming
Ques. What will be the weightage of topics and marking scheme in GATE Mathematics 2022?
Ans: The weightage and marking scheme is provided below in the table:
Section  Distribution of Marks  Total Marks  Types of questions 

GA  5 questions of 1 mark each 5 questions of 2 marks each  15 marks  MCQs 
MA SubjectBased  25 questions of 1 mark each 30 questions of 2 marks each  85 marks  MCQs and NATs 
Ques. Will there be any negative marking in GATE Mathematics 2022?
Ans: Yes. For every wrong answer, marks will be deducted depending on the total marks of those questions. Moreover, for attempting wrong NAT questions no marks will be deducted.
Type of question  Negative marking for wrong answer 

MCQs  1/3 for 1 mark questions 2/3 for 2 marks questions 
NATs  No negative marking 
Ques. What are the best books for GATE Mathematics preparation 2022?
Ans: Candidates can refer to the following books:
 Chapterwise Solved Papers Mathematics GATE – By Suraj Singh, Arihant Publication
 GATE Engineering Mathematics for All Streams – By Abhinav Goel, Arihant Publication
Ques. What is the paper code for GATE Mathematics Syllabus 2022?
Ans. The paper code for GATE Mathematics is MA. The students are advised to check the eligibility criteria before appearing for GATE 2022. Check GATE Eligibility
Ques. Which is the most important topic for GATE Mathematics Syllabus 2022?
Ans. The most important topics for GATE Mathematics Syllabus 2022 are Probability and Statistics, Numerical Methods, and Vector Calculus. However, the students are advised to go through every topic mentioned in the syllabus to score the desired marks.
Ques. What will be the difficulty level of GATE Mathematics Syllabus 2022?
Ans. The difficulty level of GATE Mathematics 2022 can be estimated by checking out GATE Paper Analysis. The candidates are advised to practice daily and try to solve every difficult question. In this case, they won’t find GATE 2022 difficult.
Ques. What is the syllabus for calculus in GATE Mathematics Syllabus 2022?
Ans. The syllabus for calculus in GATE Mathematics Syllabus 2022 consists of:
 Functions of two or more 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 to area, volume and surface area; Vector Calculus: gradient, divergence and curl, Line integrals and Surface integrals, Green’s theorem, Stokes’ theorem, and Gauss divergence theorem.
*The article might have information for the previous academic years, which will be updated soon subject to the notification issued by the University/College.