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GATE Mathematics (MA) Syllabus 2023: Important Topics, Topic-Wise Weightage, Complete Guide

Dipanjana Sengupta
Dipanjana SenguptaUpdated On: December 20, 2022 01:44 pm IST | GATE
The GATE 2023 syllabus for Mathematics has been released by IIT Kanpur. Check the important topics, topic-wise weightage, and a complete guide in this article.
GATE Mathematics (MA) Syllabus: Important Topics, Topic-Wise Weightage, Complete Guide

GATE Mathematics (MA) Syllabus 2023 - The Indian Institute of Technology (IIT) Kanpur has released the syllabus of GATE 2023 on its official website gate.iitk.ac.in. As per the official syllabus of GATE 2023, there are no changes observed in the latest syllabus from the last year. According to the GATE 2023 mathematics syllabus, candidates will have to appear for a total of 65 questions. In GATE 2023 exam, out of 65 questions, 55 questions will be based on Mathematics and the remaining 10 questions will be asked from the General Aptitude section. Candidates who wish to appear for the mathematics exam can refer to the syllabus on the official website as well as in this article. 
LATEST: GATE Mathematics 2023: Download previous year papers to enhance accuracy

GATE Mathematics Syllabus 2023

The table below highlights the mathematics syllabus of GATE 2023 as per the latest syllabus. 

Chapter

Detailed View of the GATE Mathematics Chapters

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, 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.

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
  • Gauss divergence theorem

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

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

Complex Analysis

  • Functions of a complex variable: continuity, differentiability, analytic functions,
  • Radius of convergence
  • Taylor’s series and Laurent’s series
  • Residue theorem and applications for evaluating real integrals
  • Harmonic functions
  • Complex integration: Cauchy’s integral theorem and formula
  • Liouville’s theorem
  • Maximum modulus principle
  • Morera’s theorem
  • Zeros and singularities
  • Power series
  • Rouche’s theorem
  • Argument principle
  • Schwarz lemma
  • Conformal mappings
  • Mobius transformations

Ordinary Differential Equations

  • First order ordinary differential equations
  • 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
  • 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
  • Planar autonomous systems of ordinary differential equations
  • Stability of stationary points for linear systems with constant coefficients
  • Sturm's oscillation and separation theorems
  • Sturm-Liouville eigenvalue problems
  • Linearized stability
  • Lyapunov functions

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

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
  • Principle ideal domains
  • Euclidean domains
  • Polynomial rings
  • Eisenstein’s irreducibility criterion Fields
  • Finite fields
  • Field extensions
  • Algebraic extensions
  • Algebraically closed fields

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 the 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

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

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

GATE 2023 Exam Pattern of Mathematics

It is very important for a candidate to understand the exam pattern of the GATE 2023 exam prior to the commencement preparation. This will ensure that the candidates will know the weightage of the exam, duration of the exam, mode of the exam, types, the number of questions, total marks, and marking scheme. The exam pattern of GATE 2023 exam will vary for different categories. Therefore we have mentioned the mathematics exam pattern of GATE 2023.

Particulars 

Details 

Mode of Examination

Online

Duration 

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

GATE Mathematics Marking Scheme 2023

Candidates who are aspiring to appear for GATE 2023 mathematics exam are advised to check the marking scheme as given in the table below.

Type of question

Negative markings 

MCQ

  • 1/3 for 1 mark questions
  • 2/3 for 2 marks questions

NAT

No negative marking

GATE Mathematics 2023 Sectional Weightage

The sectional weightage of GATE 2023 mathematics has been listed in the table below. 

Section 

Distribution of Marks

Total Marks

Types of questions

MA- Subject-Based

  • 25 questions of 1 mark each 
  • 30 questions of 2 marks each 

85 marks

  • MCQs
  • NATs

GA

  • 5 questions of 1 mark each 
  • 5 questions of 2 marks each

15 marks 

MCQs

GATE Mathematics Syllabus 2023 Topic Wise Weightage 

The preparation for the GATE 2023 exam requires innovative preparation rather than wasting time on topics that are irrelevant. Therefore, candidates are advised to focus and emphasize the topics with more weightage and not miss out on topics with lesser weightage. Candidates who are willing to commence their GATE 2023 preparation for the mathematics exam are advised to check the topic-wise weightage prior to the preparation for the exam. Therefore we have sketched the topic-wise weightage in the table below. 

Important Topics

Weightage of Topics

Vector Calculus

20%

Probability & Statistics

20%

Numerical Methods

20%

Differential Equation

10%

Linear Algebra

10%

Calculus

10%

Complex Variables

10%

Topic Wise GATE Mathematics Preparation Strategy 2023

In order to score well in GATE 2023 mathematics exam, candidates should prepare for the exam sectionally. This will help the candidates to get the maximum marks out of their full preparation. Below are the selection-wise proportion tips for mathematics papers in the GATE 2023 exam. 

  • First, concentrate on the topics that carry the maximum weightage such as Vector Calculus, Probability & Statistics, and Numerical Methods. This will help the candidates to cover the maximum portion of the high-weight topics. Covering the high-weightage topics is always recommended to wrap up earlier to ensure that high-scoring topics are covered and prioritized
  • Second, never leave the other topics for the topics with low weightage such as Differential Equations, Linear Algebra, Calculus, and Complex Variables. Since the GATE entrance exam is a tricky entrance exam that requires smart preparation more than emphasizing on hardworking preparation, candidates should also focus on the topics that carry lesser weightage' than the ones mentioned above. 
  • It's compulsory to remember the mathematical formulas, including Simpson's rule and the trapezoidal rule
  • Since Eigenvalue problems and matrix algebra are two of the most commonly requested questions in linear algebra, it is crucial to thoroughly cover these concepts
  • Another critical subject is probability and statistics; candidates should keep in mind terms like the Bayes Theorem, Poisson, etc
  • It is important to keep in mind specific equations for differential equations, such as Bernoulli's Equation and the Differential Equation of Euler

GATE Mathematics 2023 Preparation Tips

In order to score healthy marks in the GATE 2023 exam, candidates who are willing to appear for the mathematics exam are always advised to prepare in a smarter way.  Therefore we have discussed the preparation tips to score a healthy marks in GATE 2023 mathematics exam in the headers below. 

Spring Up Early for the GATE 2023 Exam Preparation

The preparation for the GATE 2023 exam requires early preparation, so it is better to prepare beforehand. Analyze the time left for preparation, revise, and prepare a timetable based on it. Jot down the important topics carrying more weightage in the GATE 2023 question paper and cover the GATE 2023 syllabus first. Do not preoccupy with other activities that are time taking other than study schedule and plan. Devise when required but do not revise it halfway. Candidates who start preparing beforehand get an ample amount of time to prepare and revise for the exam.

Understand the GATE Syllabus and GATE Exam Pattern 2023

Candidates preparing for the GATE mathematics exam are required to analyze the syllabus and the exam pattern of GATE 2023 exam. Understanding the syllabus will make them know the chapters that will be asked to prepare and make sure that the candidates are covering all the topics. Knowing the GATE 2023 exam pattern will make the candidates to know about the exam pattern, weighatge, duration, etc.

Prepare a GATE 2023 Timetable

After gathering all of the relevant information on the test and GATE 2023 syllabus, candidates should create a reasonable, quantifiable, and persuasive preparation strategy. The timetable should include adequate time for each topic as well as time for reexamination. Study for at least 6-7 hours a day. Set daily, weekly, and monthly objectives and aim to complete them. This will not only improve confidence but will also help in understanding problems in more generous profundity.

Attempt Mock Test Series and Solve GATE Year Papers

Candidates will have a better acquaintance of the kinds of questions asked in the GATE exam, their weightage in terms of marks, and the frequency of the questions asked in the GATE previous year's papers. In upsurging to improving morale, mock tests and these previous years' papers can help in time management. 

Refer to the Best GATE 2023 Mathematics Books

Candidates preparing for the GATE 2023 Mathematics exam are advised to refer to the limited amount of resources and not refer to a lot of books. This creates confusion and may lead to stress. The motive of the candidates should be “Minimum Resources, Maximum Preparation”. 

GATE 2023 Mathematics Books

Candidates who are preparing for the GATE 2023 exam are advised to refer to the best books. While choosing these reference books, candidates should keep a few points in mind. These include (a) the book should cover the full syllabus of GATE 2023 examination and (b) the books should be written by an authorized author.

The table below highlights the best reference books of GATE 2023 mathematics in the table below. 

Books

Author/Publisher

Wiley Acing the Gate: Engineering Mathematics and General Aptitude

Anil K. Maini, Wiley

Chapterwise Solved Papers Mathematics GATE 

Suraj Singh, Arihant Publication

Higher Engineering Mathematics

B.S. Grewal, Khanna Publishers

GATE: Engineering Mathematics

ME Team, Made Easy Publications

GATE Engineering Mathematics for All Streams

Abhinav Goel, Arihant Publication

Master the Use of Virtual Calculators

Candidates who are preparing for the GATE exam are advised to skillfully gather the usage of the virtual calculators required in the GATE 2023 entrance test. They must utilize a virtual calculator to answer questions since carrying an actual calculator during the GATE exam is prohibited inside the hall premises. 

Follow a Schedule for GATE Preparation

It is always advisable for the candidates to follow a consolidated study schedule that will cover up all the topics in the stipulated time covering up the revision time as well. 

Below is a study schedule for 30 days that can be followed by the candidates for an effective GATE 2023 mathematics preparation.

Days of the month

Study Schedule 

Day 1 to 5

Solve all Problems of chapters 1 to 3

Day 6

Revise the 3 chapters done previously and attempt chapter-wise mock tests

Day 7 to 11

Solve all Problems of chapters 1 to 3

Day 12 and 13

Revise all the chapters done between day 7 to day 11 and attempt chapter-wise mock tests

Day 14

Solve as many questions as possible relating to past GATE question papers and test series of any coaching center

Day 15

Rest Day

Day 16 to 20

Learn all concepts of Chapters 4 to 6  and solve available problems.

Day 21

Revise all 3 chapters and attempt chapter-wise mock tests.

Day 22 to 26

Chapters  4 to 6 have to be learned and problems relating to the concept need to be practiced.

Day 27 and 28

Revise all the chapters done between days 22 and 26 and attempt chapter-wise mock tests to analyze your performance

Day 29

Solve questions related to Subject 2 from past GATE previous year question papers and test series.

Day 30

Rest Day

Day 31

Follow the same procedure

Know Time Management Skills

Since the time is very limited and a lot of question has to be covered up within this stipulated time, candidates will have to excel in the time management skills. Practicing the mock tests, previous year's question papers, and sample papers help in excelling the time management skill. 

Take Care of Your Health

Health is the biggest asset. Preparing for GATE 2023 might be a bit stressful as well as hectic for some candidates. It is always advised not to stress much and listen to soft music. Listening to soft music is proven to increase concentration and release stress. Exercise regularly and avoid junk foods. Meditate regularly. 
All the Best. Stay tuned to CollegeDekho for the latest updates on GATE and Education News.

FAQs

When will the authorities release the GATE 2023 syllabus Mathematics?

Indian Institute of Technology (IIT) Kanpur has released the syllabus of GATE 2023 on the official website gate.iik.ac.in.
 

Can I download the GATE Maths syllabus in pdf format?

The syllabus of GATE 2023 for mathematics is available to download in PDF format. 
 

Who is eligible to give the GATE mathematics paper?

Candidates who have completed their graduation in any respective fields such as Engineering or Technology or  Architecture or Science or Commerce or Arts are eligible for appearing in the GATE 2023 exam. Other than this, a candidate who is presently studying in the 3rd or higher years of any UG degree program can also apply for the GATE 2023 exam. 
 

Do I have to study calculus in GATE mathematics?

Yes, calculus is compulsory for the GATE 2023 mathematics (MA) exam. 
 

Is the Mathematics syllabus tough for the GATE 2023 exam?

The toughness of the Maths syllabus depends on the preparation of the candidate. Therefore it is always advisable for the candidates to prepare efficiently and beforehand.

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