GATE Mathematics Syllabus 2026, Check Topic-Wise Syllabus
Riya Sharma4 Apr, 2025
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GATE Mathematics Syllabus 2026: The Indian Institute of Technology, Guwahati is going to organize the GATE 2026 examination for 30 various disciplines including Mathematics. Candidates who are aiming to take the GATE 2026 for the Mathematics paper must be well acquainted with the GATE Syllabus to prepare systematically.
Usually, the GATE syllabus remains similar every year, so based on the last year examination, we have provided the comprehensive GATE Mathematics Syllabus 2026 in this article to aid the aspirant's GATE preparation.
In the GATE exam, Mathematics is identified by the subject code MA. Acquiring the GATE Maths Syllabus is an essential foundation for preparing for the upcoming exam. Candidates must ace their test preparation to secure the highest marks in the upcoming examination.
GATE Mathematics Syllabus 2026
The GATE Mathematics syllabus 2026 covers 11 different chapters to assess the candidate's calculation and problem-solving skills. The GATE MA Syllabus covers a wide range of topics that requires enough time and practice to cover. Candidates are advised to commence their preparation as early as possible to cover the extensive syllabus and devote sufficient time for practice and revision.
The GATE MA Syllabus covers a variety of topics across Calculus, Linear Algebra, Real Analysis, Complex Analysis, Ordinary Differential Equations, Algebra, Functional Analysis, Numerical Analysis, Partial Differential Equations, Topology, and Linear Programming. In order to check the topic-wise breakdown of the entire syllabus for GATE Mathematics, candidates must read this article.
GATE Mathematics Syllabus
The GATE Mathematics syllabus for 2026 is a compilation of all the essential topics across various chapters. The GATE Mathematics (MA) syllabus is known to be relatively difficult compared to other subjects in the exam. It's crucial to differentiate between the GATE Mathematics syllabus and the Engineering Mathematics syllabus.
The GATE Mathematics paper will consist of a total of 65 questions, carrying 100 marks. Out of these, 15 questions will be from the General Aptitude section, while the remaining 55 questions will be based on the topics covered in the GATE Mathematics syllabus.
| 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: 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. |
| 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
The GATE Mathematics Syllabus 2026 PDF will be released by IIT Guwahati on the official website, gate.iitg.ac.in. Candidates can find the Mathematics syllabus PDF for GATE 2026 from the direct link given below. This syllabus consists of the topics from which questions will be asked in the Graduate Aptitude Test in Engineering.
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% |
| Numerical Methods | 20% |
Important Topics in GATE Mathematics Syllabus 2026
The GATE Mathematics syllabus includes a list of crucial chapters that carry significant weightage in terms of marks in the exam. It is highly recommended for candidates not to overlook these topics and allocate extra time for their preparation. Here are the important topics for the GATE 2026 exam:
- Linear Programming
- Real and Complex Analysis
- Partial Differential Equations
- Algebra
- General Aptitude
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GATE Mathematics Syllabus 2026 FAQs
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