 GATE Mathematics (MA) Syllabus 2022: Important Topics, Weightage, Question Paper, and Preparation Books 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.

GATE MA Syllabus

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
• Cayley-Hamilton Theorem, Finite dimensional inner product spaces, Gram-Schmidt orthonormalization process, symmetric, skew-symmetric
• Hermitian, skew-Hermitian, 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, Ascoli-Arzela 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; 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
• Sturm's oscillation and separation theorems, Sturm-Liouville 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, Hahn-Banach theorem, open mapping and closed graph theorems, principle of uniform boundedness; Inner-product spaces
• Hilbert spaces, orthonormal bases, projection theorem,Riesz representation theorem, spectral theorem for compact self-adjoint operators.

Section 8: Numerical Analysis

• Systems of linear equations: Direct methods (Gaussian elimination, LU decomposition, Cholesky factorization), Iterative methods (Gauss-Seidel and Jacobi) and their convergence for diagonally dominant coefficient matrices; Numerical solutions of nonlinear equations: bisection method, secant method, Newton-Raphson 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, Newton-Cotes integration formulas, composite rules, mathematical errors involved in numerical integration formulae; Numerical solution of initial value problems for ordinary differential equations: Methods of Euler, Runge-Kutta 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, non-homogeneous 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, north-west corner rule, Vogel’s approximation method); Optimal solution, modified distribution method; Solving assignment problems, Hungarian method.

GATE MA Exam Pattern

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 Subject-based
• 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- Subject-Based 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
• 1/3 for 1 mark questions
• 2/3 for 2 marks questions
NATs No negative marking
GATE MA Weightage

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%

Check GATE Paper Analysis

GATE MA Preparation

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.

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 MA Question Paper

GATE Mathematics Sample Questions

• Sample Question 1: 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- Subject-Based 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.

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