# GATE MA Syllabus 2025: Mathematics

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Explore the comprehensive GATE Mathematics (MA) syllabus for 2024 to kickstart your exam preparation and achieve success.

GATE MA Syllabus 2024 – GATE 2024 exam will be conduct by IISc, Bangalore on dates 3, 4 and 10, 11 February, 2024.

Here we have provided latest Mathematics syllabus & paper pattern for GATE 2024 aspirants. All candidates with Mathematics subject are advised to download this latest syllabus before starting their GATE 2024 exam preparation.

### GATE 2024 Highlights

 GATE 2024 Conducting Body IISc, Bangalore GATE 2024 Exam Date 3, 4, 10, 11 February, 2024 GATE 2024 Total Subjects 30 GATE 2024 Exam Mode ONLINE Computer Based Test (CBT) GATE 2024 Exam Duration 3 hours (180 minutes) GATE 2024 Total Questions 10 (GA) + 55 (subject)= 65 GATE 2024 Total Marks 100 GATE 2024 Question Type MCQ, MSQ, NAT

### GATE Mathematics Engineering Paper Pattern 2024

Paper SectionsMarks Distribution
Subject Questions85% of the total marks.
General Aptitude15% of the total marks.

### GATE Mathematics Syllabus for Core Subjects 2024

 Chapters Topics 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. 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. 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 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. 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, 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. 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 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. 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. 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. 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. 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 Mathematics Syllabus Weightage 2024

 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%

## What is the syllabus for GATE Mathematics?

The syllabus for GATE Mathematics includes subjects like Calculus, Linear Algebra, Abstract Algebra, Real Analysis, Ordinary Differential Equations, Partial Differential Equations, Numerical Methods, Complex Analysis, Probability and Statistics, and General Aptitude.

## Is the GATE Mathematics syllabus subject to change?

The core subjects of the GATE Mathematics syllabus remain relatively stable. However, it's important to check the official GATE website for any updates or changes in the syllabus before starting your preparation.

## Are there any specific topics within each subject that are more important for GATE Mathematics?

While the entire syllabus is important, some topics carry more weightage than others. For example, in Calculus, topics like limits, continuity, and differentiability are crucial.

In Linear Algebra, topics like matrix algebra, eigenvalues, and eigenvectors are significant.

## What is the exam pattern for GATE Mathematics?

The GATE Mathematics exam consists of a total of 65 questions, with a duration of 3 hours. The question paper is divided into two sections: Multiple Choice Questions (MCQs) and Numerical Answer Type (NAT) questions.

MCQs carry 1 or 2 marks each, while NAT questions carry 1 or 2 marks each. There is negative marking for incorrect answers in MCQs.

## Is there a specific weightage assigned to each subject in the GATE Mathematics exam?

No, there is no specific weightage assigned to each subject. The distribution of questions can vary from year to year.

However, it is generally observed that questions related to core subjects like Calculus, Linear Algebra, and Real Analysis have a significant presence in the exam.

## Are there any recommended books or resources to cover the entire GATE Mathematics syllabus?

Some popular books for GATE Mathematics preparation include 'Higher Engineering Mathematics' by B.S. Grewal, 'Linear Algebra and Its Applications' by Gilbert Strang, 'Mathematical Analysis' by S.C. Malik and Savita Arora, 'Numerical Methods: Principles, Analysis, and Algorithms' by G. Dahlquist and Å. Björck, and 'Probability and Statistics' by Morris H. DeGroot and Mark J. Schervish. Additionally, previous years' question papers and study materials from reputed coaching institutes can be helpful.

## Are there any specific reference books for numerical problem-solving in GATE Mathematics?

Yes, books like 'Numerical Methods: Principles, Analysis, and Algorithms' by G. Dahlquist and Å. Björck and 'Numerical Analysis' by Richard L. Burden and J. Douglas Faires provide insights into numerical problem-solving in Mathematics.

## Is it necessary to study Probability and Statistics for the GATE Mathematics exam?

Yes, Probability and Statistics are important topics in the GATE Mathematics syllabus. It's essential to have a solid understanding of concepts such as probability distributions, hypothesis testing, and estimation.

## Are there any online resources or mock tests available for GATE Mathematics preparation?

Yes, there are several online platforms and websites that offer free and paid resources for GATE Mathematics preparation. Some popular ones include Gradeup, GateForum, and Made Easy.

These platforms provide study materials, video lectures, mock tests, and previous years' question papers.

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1. i m prsuing mechanical engg. final year.
i m intrested in maths.
can i apply for maths ?
is there any chance that i can apply for gate maths being an mech engg. passout

• Hello Ashis ,

Yes you can apply.
But you must first check which institutes are going to accept your GATE score in maths while completing graduation in Mech.

2. Sir I have completed my B.E. degree in petrochemical engineering and I have filled the form in gate MA .I want to know if am I eligible for taking admission in any IIT for M.Sc in after securing required marks in gate ?

3. Sir I have completed BSc in maths and stats and now I am pursuing MCA …so Am I eligible for MA maths in GATE?and how it benefits me in future…?

4. Hello sir,
I completed three years in b-tech graduation in electronics and communication and I did engineering mathematics in one of my semesters. can I apply for MA paper in GATE and try for IIT’s ? If yes, In which stream will I have to pursue M-TECH? Please check and inform me about the qualification criteria to get into IIT’s or any such institutes.

5. Sir,
I am pursuing M.Sc final in maths. Can I eligible for GATE exam and if yes then which course I need to apply for GATE that would help me in future? And what is the use of GATE for me?
Also after my schooling there is a year lag in my career.

• Hello Nikita,

Last date of application form filling was 8 Oct. So you would not be able to fill your form now.
Yes final year candidates of M Sc were eligible for GATE 2016. As you mentioned your are pursuing M.Sc in maths so it would be better if you choose M tech or M tech + P HD in maths after qualifying GATE.

There are two main uses of qualifying GATE exam :
1. Getting job in PSUs
2. Getting admission for Higher education

Gap will not affect your career much. If you don’t let it affect your career much.

6. Sir,
I’m pursuing B.E in Electronics & Communications….i want to know that if i will chose Mathematics(MA) as one of my GATE exam paper then will i be eligible for PSUs?

also there is year lag in my career.

• Hello Danish,

There is very less jobs in PSUs for Mathematics rather than Electronics & Communications.
Check below posts for more details.
GATE Paper wise PSUs recruitment list : http://www.gate2016.info/psu-guidance/gate-paper-wise-psus-recruitment-list/
GATE Paper wise PSUs recruitment list for 2016 PSUs only : http://www.gate2016.info/psus-2016-application/

For any PSU application through GATE there are two kind of restriction for a candidate.
First in which branch candidate have done B Tech degree.
Second in which GATE paper he/she appeared.

Point to be noted here is they need a candidate with both of these combine correctly.
When you will go through any notification of any PSU which recruit through GATE then you will find that they mention GATE paper for particular post as well as your B Tech degree for that particular post.

7. Sir, I have done my MSc in statistics. I want to do m.tech .To which course I need to apply for GATE that would help me in future?

• Hello Vijeta,

As you mentioned you have done M Sc. in statistics so it would be better if you do M Tech in subject related to statistics.
So that you can find more job opportunity related to statistics in future.

8. Sir, I have done my B.Sc. in mathbvs and M.Sc. in Operational Research. Can I apply for mathematics in gate 2016?

• Hello pallvi,

First you have to complete Master’s degree in Mathematics For being eligible for GATE exam.

There are mainly two applications of GATE exam for a candidate :
(1) Job in PSU or govt sector using GATE score
(2) Higher Education using GATE score

(1) As far as I know there are very less PSUs which recruit Mathematician on the basis of GATE score But there are few Govt departments for which you can apply on the basis of your M. Sc. also there your GATE score card will have no use but if there is any interview they will surely consider your GATE/NET score card if you have good one.
You can find such high profile and reputed govt. jobs in UPSC & SSC special recruitment notification also. UPSC ask about your GATE/NET score while filling application form.

Please check GATE paper wise PSU recruitment list : http://www.gate2016.info/psu-guidance/gate-paper-wise-psus-recruitment-list/

(2) After a Masters degree, you can pursue a Ph.D. and can apply for lecturer/professor post in various universities.

9. Hello sir i am in Fe engineering i want to crack the gate so tell me the subject and my tread is mechanical engineering
& how can i study that’s all tell me

• Hello arul,

First you need to complete your masters in order to attend GATE exam.
GATE exam actually now a days have two applications :
(1) get admission into Higher education programs (like M Tech/ PHd)
(2) Job in some PSUs/Govt organiations

There are very few PSUs which will recruit a candidate which have qualified GATE with mathematics subject.
So main advantage in case you of would be that you can get admission in IISc/IITs or any reputed college using this GATE score for higher education.

• Hello Malik,

Most probably no.
Electronics discipline is not allowed in Mathematics discipline but Mathematics discipline is allowed in Electronics discipline.
However eligibility criteria depends upon the educational institute in which you want to take admission so please first check the education qualification of that institute in which you want to take admission and the respective course in which you want to take admission.

• Hello Malik,

In Indian Institute of Space Science and Technology(IIST) fot M Tech in Mathematics under ‘Machine Learning and Computing’ programme Educational Qualification is :
(i) M.Sc in Mathematics/Statistics/Physics/Computer Science.
OR
BE/B. Tech or equivalent degree in Electronics and Communication Engineering/Electrical Engineering/Chemical Engineering/Computer Science and Engineering
(ii)A valid GATE Score in Mathematics/Statistics/Physics/Computer Science/Electronics and Communication Engineering/Electrical Engineering/Chemical Engineering.

You are eligible there. So please first check education qualification of the course and institute in which you want to take admission. Education qualification criteria is different for different institutes.

10. Sir, i have done bachelors in Electrical and Electronics Engineering. Can i apply for mathematics in gate 2016.

• Hello Afaq,

For mathematics you have to have mathematics or computer science at your graduation level.
May be in some institutes they may qualify Electrical and Electronics Engineering for this course.
You please check some institutes qualification criteria for mathematics before making any decision.