The GATE Mathematics syllabus is released officially on the official website and remains the same across years, with very minimal changes it. In this article, we will be covering the GATE Mathematics exam pattern, topic-wise division, topic-wise weightage, and important books.
Table of Contents
The GATE Mathematics paper is one of the 30 subject papers in the GATE examination. The paper code for the Mathematics subject in the GATE exam is MA. If you are appearing in this subject and give an outstanding performance, you can actually open the doors for admission to top GATE participating colleges. Because the GATE syllabus is broad and conceptually deep, you must know the entire GATE Mathematics syllabus and plan your preparation accordingly.
The GATE Mathematics syllabus is released officially on the official website and remains the same across years, with very minimal changes it. In this article, we will be covering the GATE Mathematics exam pattern, topic-wise division, topic-wise weightage, and important books.
GATE Mathematics Exam Pattern
The GATE Mathematics Exam pattern is a very important part to be considered while preparing a strategic plan. The below given table below contains the detailed GATE Mathematics exam Pattern.
|
Particulars |
Details |
|
Total Duration |
180 minutes (3 hours) |
|
Total Marks |
100 marks |
|
Total Questions |
65 questions |
|
Sections |
- General Aptitude – 15 marks - Mathematics (Core/Subject) – 85 marks |
|
Question Distribution |
- General Aptitude: 10 questions (5 × 1 mark + 5 × 2 marks) - Mathematics Section: 55 questions (approx. 25 × 1 mark + 30 × 2 marks) |
|
Question Types |
- MCQ: Multiple Choice Questions - MSQ: Multiple Select Questions - NAT: Numerical Answer Type |
|
Negative Marking |
- 1-mark MCQ → –⅓ mark for wrong answer - 2-mark MCQ → –⅔ mark for wrong answer - No negative marking for MSQ & NAT |
|
Exam Mode |
Computer-Based Test (CBT) |
|
Conducting Body (2026) |
IIT Guwahati |
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GATE Mathematics Detailed Syllabus: Topics & Subtopics
Below is the breakdown of the major topics and subtopics in the GATE Mathematics syllabus (MA).
|
Section |
Key Topics & Subtopics |
|
Calculus |
- Functions of two or more variables - Continuity, directional & partial derivatives - Total derivative, maxima & minima, saddle point, method of Lagrange multipliers - Double & triple integrals and their applications (area, volume, surface area) - Vector calculus: gradient, divergence, curl - Line & surface integrals - Green’s theorem, Stokes’ theorem, Gauss divergence theorem |
|
Linear Algebra |
- Finite dimensional vector spaces (ℝ or ℂ) - Linear transformations & matrix representation - Rank, nullity & systems of linear equations - Characteristic polynomial, eigenvalues & eigenvectors - Diagonalization, minimal polynomial, Cayley–Hamilton theorem - Inner product spaces, Gram–Schmidt orthonormalization - Symmetric, skew-symmetric, Hermitian, unitary, normal matrices - Jordan canonical form, bilinear & quadratic forms |
|
Real Analysis |
- Metric spaces: definitions, topology, completeness, compactness, connectedness - Sequences & series of functions, uniform convergence, Ascoli–Arzelà theorem - Power series, Weierstrass approximation theorem - Differentiation in several variables, inverse & implicit function theorems - Lebesgue measure & integration - Measurable functions, Lebesgue integral, Fatou’s lemma, monotone & dominated convergence theorems |
|
Complex Analysis |
- Analytic & harmonic functions, Cauchy–Riemann equations - Complex integration: Cauchy’s theorem & integral formula - Power series, Taylor & Laurent expansions - Singularities, residues & applications to real integrals - Rouche’s theorem, Argument Principle, Schwarz lemma - Conformal mappings, Möbius transformations - Liouville’s theorem, Maximum Modulus Principle, Morera’s theorem |
|
Ordinary Differential Equations (ODE) |
- First-order ODEs, existence & uniqueness theorems - Linear ODEs of higher order with constant coefficients - Variable coefficient second order ODE, Cauchy–Euler equations - Laplace transform & Frobenius series method - Special functions: Legendre, Bessel & orthogonality - Systems of first-order ODEs, phase plane analysis - Sturm–Liouville problems, eigenvalue problems, stability |
|
Partial Differential Equations (PDE) |
- Basic classification (first-order, second-order) - Method of separation of variables - Heat, wave & Laplace equations - Boundary value problems - Fourier series & transforms |
|
Algebra |
- Group theory: subgroups, cosets, normal subgroups, quotient groups, homomorphism, automorphism - Cyclic groups, permutation groups, Sylow theorems, group actions - Ring theory: ideals, prime & maximal ideals, quotient rings - Integral domains, unique factorization & Euclidean domains - Polynomial rings, irreducibility criteria (Eisenstein) - Field theory: extension fields, algebraic extensions, splitting fields, Galois theory basics |
|
Functional Analysis |
- Normed linear & Banach spaces - Inner product & Hilbert spaces - Hahn–Banach theorem, open mapping & closed graph theorems - Uniform boundedness principle (Banach–Steinhaus) - Riesz representation theorem, orthonormal bases, projection theorem - Spectral theorem for compact self-adjoint operators |
|
Numerical Analysis |
- Nonlinear equations: bisection, Newton–Raphson, fixed-point iteration - Interpolation: Lagrange & Newton forms, error analysis - Numerical differentiation & integration: trapezoidal, Simpson’s rules - ODE initial value problems: Euler’s, Runge–Kutta methods - Systems of linear equations: Gaussian elimination, LU decomposition, Jacobi & Gauss–Seidel methods |
|
Topology |
- Open & closed sets, basis, subspace topology, product topology - Order & metric topology, quotient topology - Connectedness, compactness, countability axioms - Separation axioms (T0, T1, T2, etc.), Urysohn’s Lemma |
|
Linear Programming |
- Formulation of linear programming problems - Simplex method - Duality theory & primal-dual relationships - Sensitivity analysis & dual simplex method |
GATE Mathematics Topic-Wise Weightage & Strategy
The GATE Mathematics syllabus covers a good number of important topics. As per the previous year's trends, the expected weightage of the important topics, focus areas, and preparation strategy according to the GATE topic has been added in the table below:
|
Topic / Subject Area |
Approximate Weightage (%) |
Key Focus Areas |
Preparation Strategy |
|
Calculus |
10% |
Functions of several variables, maxima-minima, vector calculus, Green’s & Stokes’ theorems |
Revise core calculus formulas daily; solve past-year numerical problems and conceptual theorems. |
|
Linear Algebra |
10% |
Eigenvalues, eigenvectors, diagonalization, matrix operations |
Master theory first; practice solving system equations & matrix transformations quickly. |
|
Real Analysis |
8% |
Sequences, series, continuity, convergence, Lebesgue integration |
Focus on theorems; make flashcards for definitions and practice proof-based questions. |
|
Complex Analysis |
7% |
Cauchy’s theorem, residues, contour integration, conformal mapping |
Solve previous GATE questions on residues and contour integrals; memorize key theorems. |
|
Ordinary Differential Equations (ODE) |
10% |
First & higher order ODEs, special functions, Laplace transforms |
Learn standard forms; solve numerical and analytical problems from each category. |
|
Partial Differential Equations (PDE) |
8% |
Heat, wave, Laplace equations, separation of variables |
Practice boundary value problems and Fourier method derivations. |
|
Algebra |
8% |
Group, ring, and field theory, homomorphisms, Sylow theorems |
Prepare short notes on important theorems and group classifications. |
|
Functional Analysis |
6% |
Banach & Hilbert spaces, Riesz theorem, spectral theory |
Focus on conceptual clarity and relationships between function spaces. |
|
Numerical Analysis |
12% |
Interpolation, differentiation, integration, ODE solvers |
Practice problems using formulas; focus on iterative & error-based questions. |
|
Topology |
6% |
Compactness, connectedness, separation axioms |
Study definitions with examples; attempt theory-based questions. |
|
Linear Programming |
5% |
Simplex method, duality, sensitivity analysis |
Practice stepwise simplex problems; revise standard formulations. |
|
General Aptitude (GA) |
10% |
Verbal & numerical ability, logical reasoning |
Practice 1–2 aptitude questions daily; focus on accuracy and speed. |
The GATE Mathematics (MA) syllabus covers the applied mathematics part. For cracking and acing it, you need a detailed preparation plan, starting with fundamentals, gradually branching into advanced topics, combined with regular practice and KCET mock tests, which can lead you to success. Start early, revise often, and use the syllabus as your guiding roadmap. The above information will surely help you in getting a good score in the GATE Mathematics exam.
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