GATE Mathematics Syllabus 2025: Check Topics, Weightage, Download PDF

GATE 2025 Syllabus for Mathematics

IIT Roorkee has released the GATE Mathematics syllabus 2025 PDF in online mode at gate2025.iitr.ac.in. The GATE MA syllabus 2025 includes 11 sections namely Calculus, Linear Algebra, Real Analysis, Complex Analysis, Ordinary Differential Equations, Algebra, Functional Analysis, Numerical Analysis, Partial Differential Equations, Topology, Linear Programming etc. IIT Roorkee will prepare the GATE 2025 paper based on the official GATE syllabus 2025. The GATE 2025 Mathematics syllabus is divided into two sections: Core Mathematics Subjects and General Aptitude. The GATE Mathematics paper will consist of 65 questions for 100 marks. Of these, 55 questions will be asked from the core GATE Mathematics syllabus 2025 and the remaining 10 from the General Aptitude part. The GATE syllabus for Mathematics is known to be quite tough to prepare as requires memorization of various formulas and a lot of practice with practical questions. 

Candidates must keep in mind that the GATE Mathematics syllabus 2025 and the Engineering Mathematics syllabus are different from one another. Check out the detailed GATE 2025 MA syllabus, important topics, and topic-wise weightage etc on this page. 

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GATE Mathematics Syllabus 2025 Section-Wise Topics

GATE Mathematics syllabus 2025 includes 11 sections. Candidates can check the detailed GATE 2025 Mathematics syllabus below. 

Section 1: 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.

Section 2: 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, eigen values and eigen vectors, 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.

Section 3: 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.

Section 4: 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.

Section 5: 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.

Section 6: 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.

Section 7: Functional Analysis

Normed linear spaces, Banach spaces, Hahn-Banach theorem, open mapping and closed graph theorems, the principle of uniform boundedness; Inner-product spaces, Hilbert spaces, orthonormal bases, projection theorem, Riesz representation theorem, spectral theorem for compact self-adjoint operators.

Section 8: 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, RungeKutta method of order 2.

Section 9: 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.

Section 10: 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.

Section 11: 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.

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GATE Mathematics Syllabus 2025 for General Aptitude

GATE Maths exam 2025 will include 10 questions from the General Aptitude section too. The GATE General Aptitude section is common for all the GATE papers. Along with preparing the GATE Mathematics syllabus 2025, candidates must also study the General Aptitude topics. Students can check out the GATE General Aptitude syllabus 2025 below. 

GATE 2025 Mathematics Syllabus PDF

Candidates can access the official GATE Mathematics syllabus 2025 PDF by clicking on the link given below. With the help of the detailed section-wise syllabus and sub-topics, they can better prepare for the upcoming examination.

GATE Mathematics Syllabus 2025 Important Topics

The GATE Mathematics syllabus 2025 includes a list of key chapters that carry a good weightage as per the previous year's paper analysis. While studying the GATE MA syllabus 2025 candidates must focus on these important topics to score good marks in the exam. The following are the GATE 2025 Mathematics important topics. 

• Real and Complex Analysis

• Algebra

• Linear Programming

• Partial Differential Equations

• Vector Calculus

• General Aptitude

• Numerical Methods 

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GATE Mathematics Syllabus 2025 Topic-Wise Weightage (Expected)

GATE 2025 Mathematics syllabus is quite huge and includes various topics. However, among the large number of GATE Maths syllabus topics, there are few important topics that carries good weightage. These GATE Mathematics important topics have been repeated several times in the past year's GATE exam. Therefore, while studying the GATE Mathematics syllabus 2025, refer to the following topic-wise weightage and focus on high weightage topics. 

How to Prepare for GATE Mathematics 2025 Syllabus

Preparing for the GATE Mathematics exam 2025 can be quite challenging keeping in mind that the syllabus is huge. However, if you are dedicated towards your studies you can prepare the complete syllabus and perform well in the exam. To help you with that, we have provided some of the important preparation tips for GATE 2025 Mathematics syllabus below. 

• Firstly, go through the GATE Mathematics syllabus 2025 and GATE exam pattern 2025 to get an idea about the topics and chapters to be studied. It will help you analyze the marking scheme, section-wise weightage, exam mode, etc.

• Since the GATE Mathematics exam syllabus 2025 is huge, you should begin your preparation early so that you have enough time to study the syllabus and practice numerical questions. 

• The Maths GATE syllabus 2025 includes various formulas and equations you must thoroughly grasp and learn them. Memorizing formula is important as you can solve questions through it only. 

• If any part of the GATE Maths syllabus involves learning theoretical concepts learn and understand them.

• Practicing numerical questions is very important for the GATE Maths paper preparation. Daily solving numerical questions will give you clarity. 

• Time management is an important aspect of the GATE Maths paper. Solving numerical questions is time taking so you must work on your time management skills. Practicing with the GATE mock test will help you improve your time accuracy.

• Frequently solving GATE previous year question papers and GATE sample papers will help you analyze your preparation and improve your shortcomings. 

• Do timely revision of the formulas and equations. Make short notes of formulas and equations for quick revision. 

Best Books for GATE Mathematics 2025 Syllabus

To prepare for GATE Mathematics syllabus 2025, candidates should strictly refer to the best books by renowned authors as those have clear explanations/ solutions and several worked out problems based on the fundamental concepts. Following are some of the GATE best books 2025 for Mathematics that must be referred to.