GATE Mathematics Syllabus 2025 OUT; Check Marks Weightage, Important Topics and Download Official PDF

GATE Mathematics Syllabus 2025: Those aspiring to take the GATE 2025 Mathematics (MA) exam are encouraged to familiarize themselves with the syllabus. The detailed syllabus for GATE 2025 Mathematics has been released by IIT Roorkee.

GATE MA Syllabus 2025

The GATE syllabus for Mathematics (MA) 2025 consists of questions from topics such as Calculus, Linear Algebra, Real Analysis, Complex Analysis, Differential Equations, Algebra, Functional Analysis, etc. All prospective candidates for the GATE Mathematics 2025 exam are advised to review the syllabus carefully before starting their preparation. Check the important topics and section-wise weightage for the GATE Mathematics syllabus.

GATE Mathematics Syllabus 2025 Section Wise 

The GATE Mathematics (MA) exam consists of two parts: General Aptitude and core Mathematics subjects. The weightage of General Aptitude is 15%, while core Mathematics accounts for 85%. The detailed list of topics in the the GATE Mathematics syllabus is provided below.

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; 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.

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, nonhomogeneous 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 2025 Official PDF

IIT Roorkee has released the official GATE Mathematics syllabus PDF. Get the direct link to download the GATE Mathematics syllabus 2025 PDF here.

GATE MA Syllabus: Section-wise weightage

The GATE Mathematics exam consists of two parts: General Aptitude, which constitutes 15%, and the Mathematics subject, which comprises the remaining 85%. However the specific weightage of topics within the GATE Mathematics syllabus changes annually. A comprehensive breakdown of topic-wise weightage is provided here by analyzing previous years' papers. This breakdown offers valuable insights into significant topics within the GATE Mathematics syllabus, aiding you in creating effective preparation strategies for the exam.

How to Prepare the GATE Mathematics Syllabus 2025?

To crack the GATE exam, candidates need to follow a well-planned approach. Here, we share some tips for GATE preparation for the Mathematics (MA) paper.

• Understand the Syllabus: Candidates must carefully review the complete GATE Mathematics syllabus. Note down the important topics, prioritizing those that require more attention. Create a study plan around these requirements.
• Create a Study Schedule: Once you analyze the syllabus, make an extensive study plan that covers all the topics mentioned. Allocate ample time to each topic based on your requirements.
• Focus on Fundamental Understanding: Always prioritize understanding the core principles of each topic. Merely memorizing will not be enough for this exam.
• Create Revision Notes: Develop short revision notes with important formulas, concepts, and key points for quick last-minute review.
• Practice Previous Year Papers: Candidates should solve previous years' papers to understand the exam pattern and the types of questions asked in the GATE Mathematics exam. This will provide insights into important topics and help identify areas that require improvement.
• Take Mock Tests: Take sufficient mock tests to familiarize yourself with the real exam environment. After each mock test, analyze your performance and work on areas needing improvement. This practice will also enhance your time management skills.

Best Books to Prepare the GATE MA Syllabus 2025

Selecting study material is crucial for the preparation of the GATE Mathematics exam. For your reference, a list of highly recommended books for the GATE Mathematics syllabus is provided here.

1. Calculus of Variations by I. M. Gelfand, S. V. Formin
2. Linear Algebra and its Applications by Gilbert Strang
3. Real Analysis by H.L Royden, P.M. Fitzpatrick
4. Foundations of complex analysis by S. Ponnusamy
5. Ordinary and Partial Differential Equations by M. D. Raisinghania
6. Topology by James Munkre

GATE Mathematics Exam Pattern 

The GATE Mathematics exam has 65 questions based on General Aptitude and Mathematics with a total of 100 marks. The total allotted time for this online exam is 3 hours. The GATE Mathematics paper consists of Multiple choice questions, Multiple select questions, and Numerical Answer Type questions. All the important details about the GATE exam pattern for Mathematics are given in the table below.

Also check: The candidates can also check the detailed syllabus of the following subjects.