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GATE Mathematics Syllabus 2025 with Topic Wise Weightage

GATE Mathematics Syllabus 2025 with Topic Wise Weightage

Edited By Team Careers360 | Updated on Aug 22, 2024 06:03 PM IST | #GATE

GATE Mathematics Syllabus 2025: IIT Roorkee released the GATE 2025 Mathematics syllabus on the official website, gate2025.iitr.ac.in. Candidates can check the GATE Mathematics 2025 syllabus to identify important topics for exam preparation. The GATE exam syllabus pdf available for download on the official website. Aspirants must follow the GATE exam pattern and syllabus to prepare for the Graduate Aptitude Test in Engineering. The authority will prepare the GATE Maths question paper based on topics mentioned in the GATE 2025 syllabus of Maths. Candidates must focus on the GATE Mathematics syllabus rather than focusing on unnecessary topics. GATE 2025 exam will be held in online mode. For more details, candidates can refer to the GATE Mathematics syllabus 2025 page.

GATE Mathematics Syllabus 2025

The syllabus for GATE Mathematics is updated below. Candidates can refer to the previous GATE Mathematics syllabus provided. Aspirants should review the GATE Maths syllabus and commence their preparation accordingly.

GATE General Aptitude Syllabus 2025 for Mathematics

ChapterTopics
GATE GA Syllabus for Verbal Aptitude
  • Basic English grammar: tenses, articles, adjectives, prepositions, conjunctions, verb-noun agreement, and other parts of speech
  • Basic vocabulary: words, idioms, and phrases in context, reading and comprehension, Narrative sequencing.
GATE GA Syllabus for Quantitative Aptitude
  • Data interpretation: data graphs (bar graphs, pie charts, and other graphs representing data), 2- and 3-dimensional plots, maps, and tables
  • Numerical computation and estimation: ratios, percentages, powers, exponents and logarithms, permutations and combinations, and series Mensuration and geometry Elementary statistics and probability.
GATE GA Syllabus for Analytical AptitudeLogic: deduction and induction, Analogy, Numerical relations and reasoning
GATE GA Syllabus for Spatial AptitudeTransformation of shapes: translation, rotation, scaling, mirroring, assembling, and grouping paper folding, cutting, and patterns in 2 and 3 dimensions.

GATE Maths Syllabus 2025

Topics

Sub Topics

GATE Mathematics Syllabus for 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

GATE Mathematics Syllabus for 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

GATE Mathematics Syllabus for 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

GATE Mathematics Syllabus for 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.

GATE Mathematics Syllabus for 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

GATE Mathematics Syllabus for 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

GATE Mathematics Syllabus for 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

GATE Mathematics Syllabus for 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

GATE Mathematics Syllabus for 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 Mathematics Syllabus for 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

GATE Mathematics Syllabus for 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

Direct link for download the GATE 2025 syllabus for Mathematics

GATE Mathematics Exam Pattern 2025

The authority has released the exam pattern for GATE Maths on the official website. The GATE exam pattern consists of a marking scheme, mode of exam, types of questions, and more. Candidates can check the GATE Maths exam pattern 2025 below.

GATE exam pattern for Maths 2025

Mode of examComputer Based Test (CBT)
Duration of exam3 hours
Number of questions
  • Multiple Choice Questions (MCQs)
  • Multiple Select Questions (MSQs)
  • Numerical Answer Type (NAT) questions
Total Number of questions65 questions
Total marks100
Sections
  • General Aptitude (GA)
  • Candidates selected subject
Distribution of marks
  • General Aptitude - 15 marks
  • Subject marks - 85 marks
Marking Scheme1 mark or 2 marks
Negative marking
  • 1 mark MCQs – 1/3 mark will be deducted for every wrong answer
  • 2 mark MCQs – 2/3 mark will be deducted for every wrong answer
  • Zero marks will be awarded for unattempted questions
  • No negative marking will be done for Numerical Answer Type (NAT) questions
  • No partial marks for MSQs
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GATE Mathematics Syllabus with Wise Weightage 2025

Candidates can check the GATE Mathematics topic weightage to know the topics that can help to score well in the exam. GATE Mathematics topic wise weightage is prepared based on the previous year's GATE analysis and question papers. Below is the GATE Mathematics syllabus with weightage.

Topics

Weightage in %

Vector Calculus

20%

Probability & Statistics

20%

Numerical Methods

20%

Differential Equation

10%

Calculus

10%

Linear Algebra

10%

Complex Variables

10%

Related links:

GATE 2025 Syllabus
Candidates preparing for GATE 2025 can now access the official syllabus. The detailed syllabus PDF is available for download as PDF here.
Download Now

Best Books for GATE 2025 Mathematics Syllabus

Books are the best resource to prepare for the GATE Mathematics exam. Candidates must know the GATE Mathematics syllabus to select the best book for preparation. While selecting the best book for the GATE 2025 Mathematics syllabus, candidates must check the language is easy to understand and the topics are mentioned as per the syllabus. The books help to understand the topics in more simple steps. When the concepts are clear it becomes easy to solve the problems which will result in good scores. Below is the list of best books for GATE Mathematics syllabus 2025.

Book Name

Author Name

MADE EASY Engineering Mathematics

MADE EASY Editorial Board

GATE GENERAL APTITUDE & ENGINEERING MATHEMATICS

Trishna

Higher Engineering Mathematics

B.S. Grewal

Engineering Mathematics for GATE

T.K. Mandal and A.K. Chakraborty

GATE Mathematics

Arihant Publications

GATE Mathematics Solved Papers

Made Easy Publications

Engineering Mathematics for GATE

T.K. Mandal and A.K. Chakraborty

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GATE Mathematics Syllabus 2025: Important Topics

The important topics in GATE are those topics that have a high weightage of questions in the exam. Moreover, these topics are covered almost in all exams. Based on the GATE Mathematics syllabus and the previous year question paper below are the most important topics in the GATE Mathematics syllabus.

  • Real Analysis

  • Complex Analysis

  • Functional analysis

  • Topology

  • Calculus

  • Linear Algebra

  • Linear programming

  • Real Analysis

  • Ode and Pde

  • Numerical analysis

  • Probability & Statistics

Frequently Asked Questions (FAQs)

1. When will the authorities release GATE 2025 syllabus Mathematics?

The GATE Mathematics syllabus 2025 has been released on the official website, gate2025.iitr.ac.in.

2. Can I download the GATE Maths syllabus in pdf format?

Yes, the GATE Maths syllabus 2025 is available in pdf format.

3. Is calculus included in the GATE Mathematics syllabus?

Yes, Calculus is one of the topics included in the GATE syllabus for Mathematics.

4. What is the syllabus for GATE 2025?

The GATE Syllabus 2025 includes three major sections viz. General Aptitude, Engineering Mathematics, and Core Engineering subjects included in the graduation level.

5. When should I start preparing for GATE 2025?

Early preparation is the best option. Currently, candidates have plenty of months for preparation. If the candidate chooses early preparation then they will have much time for the revision.

6. Who will take GATE 2025?

IIT Roorkee is the conducting body for GATE 2025.

7. What is the GATE Mathematics syllabus for CSE?

The GATE Mathematics syllabus for CSE is as follows

  • Discrete Mathematics

  • Linear Algebra

  • Calculus

  • Probability and Statistics

8. How can I download GATE 2025 Mathematics syllabus pdf?

Candidates can download the GATE Mathematic syllabus on the official website, gate2025.iitr.ac.in.

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Hello,


Don't worry, a slight misalignment of the signature in the downloaded GATE 2025 application form printout is usually not a major issue. However, to avoid any potential problems, follow these steps:

Immediate Action:

1. Check the GATE 2025 guidelines: Ensure signature alignment isn't explicitly mentioned as a critical requirement.

2. Contact GATE 2025 support: Reach out to the official GATE 2025 helpline or email (gate2025@iitk.ac.in) and report the issue

Possible Solutions:

1. Re-upload signature: If permitted, re-upload a corrected signature.

2. Rectify during document verification: If selected, you can rectify the signature issue during document verification.

Precautions:

1. Verify other application details: Double-check your application form for any other errors.

2. Keep proof of payment: Ensure you have the payment receipt.

Hello Neha,

Yes, you can still apply for PSU jobs under the PwD quota later, even if you give the GATE exam under the general category for now. The GATE exam itself doesn’t restrict you from applying to jobs under a different category later, as it only reflects your score and rank, not your category.

When applying for PSU jobs, you'll have the option to apply under the PwD category, provided you have the valid UDID certificate by then. Just make sure to obtain your PwD UDID certificate before the PSU job application process begins. The key is having the certificate at the time of applying for jobs, not necessarily during the GATE exam. This way, you can still avail all the benefits of PwD reservation during the job application process.

So, it's okay to give GATE under general reservation now, as long as you plan to get your PwD certificate before applying for jobs.


After the declaration of your GATE result if you want to check the list of colleges in which you can get admission then,

I would recommend you to use GATE college predictor tool by Careers360 to get the list of possible colleges you can get with your rank.

Here is the link to the tool:

https://engineering.careers360.com/gate-college-predictor

Click on the above link, fill the required details and you will get the list of possible colleges at your rank.



I hope this answer helps you. If you have more queries then feel free to share your questions with us we will be happy to assist you.

Thank you and wishing you all the best for your bright future.


Hello aspirant,

The Graduate Aptitude Test in Engineering, or GATE, is a yearly entrance exam that is required for admission to some of the nation's most esteemed universities, such as IISc Banglore, IITs, NITs, IIITs, and many more. The official notification about the GATE 2025 exam has been released by the GATE administration, which for this year is IIT Roorkee.

To know the syllabus and get notes, you can visit the following link:

https://engineering.careers360.com/articles/gate-syllabus-for-cse-computer-science-engineering

Thank you

Hello Pankaj,

Correct any wrong details you provide in the GATE 2025 registration. You should correct any wrong details especially your mobile number. In fact, this number is for receiving important communications from GATE including the OTPs in case you wish to login or updates. While you have used a verified Gmail account, you can still login; however solely depending on the Gmail account may not be enough.

Here's what to do:

  • Do Not Submit: I f you haven't submitted the application yet, do not submit until you update the mobile number.
  • Edit Registration: Most registration portals allow you to edit your details. Check the options to update your mobile number before finalizing the submission.
  • Contact Helpdesk: In case you have already uploaded the form, contact GATE helpdesk immediately. Mention your details and the scenario; they might be able to rectify the number for you.

Keep looking for any communication from GATE in your email inbox regarding your registration. The best way to prevent future hassles is to get this done now!

Thankyou!

Hi there! Thanks for reaching out to us at Careers360. Congrats on your decent score in the DS AI domain for GATE 2024 - that's awesome!

I totally get your dilemma about which paper to write for GATE this year. It's a tough choice, especially when you're eyeing a career in AI/ML.

Based on your goals, writing the DS and AI paper again could be a solid option. It directly aligns with your career plans and you've already got experience with it. Plus, you might improve your score since you know what to expect now.

That said, the CS and IT paper could give you a broader knowledge base, which some top AI/ML programs appreciate. You could always supplement with AI courses later.

Honestly, both paths can lead you to an AI/ML career. The best choice depends on which specific programs you're targeting and how confident you feel in each subject area.

For personalized advice, you might want to check out our GATE counselling services on the Careers360 website . We've got experts who can dive deep into your specific situation.

Hope this helps! Let me know if you need anything else. Good luck with your GATE prep!

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