Post Name : GATE Mathematics Syllabus 2025
Post Date : 02 March , 2024
Post Description : The institution will make the GATE Mathematics Syllabus 2025 available on the official IIT Roorkee website, @gate.iitr.ac.in, for the exam scheduled for February 2025. Applicants can begin studying in accordance with the GATE Mathematics Syllabus since it is nearly same.
The 2025 GATE Mathematics Syllabus
The Indian Institute of Technology Roorkee’s official website, gate.iitr.ac.in, will shortly host the GATE Mathematics syllabus 2025. Every subject covered in the syllabus will be the source of questions in the engineering graduate aptitude test. The prior year’s mathematics syllabus is also available to students.
The GATE Mathematics syllabus for 2025 will be added to this page on a regular basis in accordance with the official GATE syllabus. Students can also review the Mathematics GATE question papers from prior years to improve their preparation. Read the entire article to learn more about the GATE Mathematics syllabus for 2025.
The GATE Mathematics Curriculum
The IIT Roorkee administrators have compiled a list of key topics exclusively for the GATE Mathematics exam, which is scheduled for May 2025. It is well known that the GATE Mathematics (MA) syllabus is more challenging than other exam subjects. It is important to understand the differences between the Engineering Mathematics syllabus and the GATE Mathematics syllabus. There will be 65 questions in the GATE Mathematics exam, each worth 100 points. Of these, fifteen will come from the General Aptitude part, while the other fifty-five will center around the subjects found in the GATE Mathematics syllabus.
| Sl. No | Chapters | Topics |
|---|---|---|
| 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. |
| 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, 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. |
| 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 |
| 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. |
| 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; 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. |
| 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 |
| 7. | 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. |
| 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, Runge-Kutta method of order 2. |
| 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: ification 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. |
| 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. |
| 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. |
GATE Mathematics Syllabus PDF
IIT Roorkee will soon release the GATE Mathematics Syllabus PDF specifying all the topics at its the official website gate.iitr.ac.in. Candidates can find the Mathematics syllabus PDF for GATE 2025 in the official notification. This syllabus consists of the topics from which questions will be asked in the Graduate Aptitude Test in Engineering. Aspirants preparing for GATE 2025 can download the GATE Mathematics Syllabus PDF given below.
GATE Mathematics Syllabus – Topic Wise weightage
It is recommended that students begin their GATE preparation by reviewing the weightage assigned to each topic. This step can save them significant trouble and effort in their exam preparation. By understanding the importance and distribution of marks across different topics, students can prioritize their study plan effectively.
| GATE Mathematics Topic wise Weightage | |
|---|---|
| Important Topics | Weightage of Topics (In %) |
| Linear Algebra | 10% |
| Complex Variables | 10% |
| Vector Calculus | 20% |
| Calculus | 10% |
| Differential Equation | 10% |
| Probability & Statistics | 20% |
Key Subjects in the GATE Mathematics Curriculum 2025
There is a list of important chapters in the GATE Mathematics syllabus that are worth a lot of points in the test. It is strongly advised that candidates pay close attention to these subjects and allot additional time for their preparation. The following are the key subjects for the GATE 2025 test:
- Programming in Lines
- Practical and Intricate Evaluation
- Equations using Partial Differentials
- Math
- All-around Ability
| GATE 2025 | |
|---|---|
| GATE Application Form 2025 | GATE Registration 2025 |
| GATE CSE Syllabus 2025 | GATE ME Syllabus 2025 |
| GATE Aerospace Engineering Syllabus 2025 | GATE Agricultural Engineering Syllabus 2025 |
