Are Engineering Mathematics and GATE Mathematics (MA) the same syllabus?

No. Engineering Mathematics is a 13-mark sub-section included in papers like Computer Science (CS), Mechanical (ME), Civil (CE), and Electrical (EE), while GATE Mathematics (MA) is a standalone core paper carrying 85 marks dedicated to pure and applied postgraduate mathematics topics, such as Functional Analysis, Topology, and Measure Theory.

What types of questions are asked in the GATE MA paper, and is there negative marking?

Multiple Choice Questions (MCQs): Have 4 choices with 1 correct option. Negative marking applies—1/3 mark is deducted for incorrect 1-mark MCQs and 2/3 mark for incorrect 2-mark MCQs. Multiple Select Questions (MSQs): Can have one or more correct options. There is no negative marking and no partial marking. Numerical Answer Type (NATs): Require entering a numeric value using an on-screen virtual keypad. There is no negative marking for NATs.

Is the GATE Mathematics (MA) syllabus updated for GATE 2027?

The 11 core sections in the GATE Mathematics (MA) syllabus remain identical to previous years. Candidates can check the official PDF released by the organizing institute (IIT Madras) to verify exact sub-topic formulations.

Which topics carry the highest weightage in the GATE Mathematics syllabus?

Linear Algebra (Eigenvalues, Diagonalization, Canonical forms) Real & Complex Analysis (Residues, Uniform Convergence, Analytic Functions) Differential Equations (ODE & PDE) (Cauchy-Euler, Laplace/Fourier transforms, Separation of Variables) Numerical Analysis (Matrix Solvers, Root Finding, Integration Rules)

What is the total mark distribution and weightage for the GATE MA paper?

General Aptitude (GA): 10 questions carrying 15 marks (5 questions of 1 mark and 5 questions of 2 marks). Core Mathematics (MA): 55 questions carrying 85 marks (25 questions of 1 mark and 30 questions of 2 marks).

GATE Mathematics Syllabus 2027, Check (MA) Exam Pattern & Important Topics Here

Table of Contents

The Indian Institute of Technology Madras (IIT Madras) has released the official syllabus for the Mathematics (MA) paper. The GATE MA syllabus consists of 11 core sections (72 Marks), General Aptitude(15 Marks), & Engineering Mathematics(13 MArks). Understanding the detailed GATE Mathematics Syllabus is important for candidates preparing for the GATE 2027 Mathematics examination.

GATE Mathematics Syllabus 2027: Overview

Candidates can check a quick overview of the GATE 2027 Syllabus for Mathematics in the table below

Objective	Details
Exam Conducting Body	IIT Madras
Exam Name	GATE 2027 Exam
Paper Name	Mathematics (MA)
Exam Structure	General Aptitude Common Section
Total Marks	100
Total Duration	3 Hours (180 Minutes)
Question Types	MCQs, MSQs, & NATs
Official Website	gate.iitm.ac.in

GATE Mathematics Exam Pattern 2027

Objective	Details
General Aptitude (GA)	15 Marks
Common Section	85 Marks
Optional Section(s)	—
Total Marks	100 Marks
Total Time (Minutes)	180 Minutes (3 Hours)

GATE Mathematics Syllabus: Subject-Wise Topics

Part	Topics Covered
Common Section	Calculus, Linear Algebra, Real Analysis, Complex Analysis, Ordinary Differential Equations, Algebra, Functional Analysis, Numerical Analysis, Partial Differential Equations, Topology, & Linear Programming

GATE Mathematics Syllabus 2027

Subject	Important Topics
Calculus	Functions of two or more variables, continuity, directional derivatives, partial derivatives, total derivative, Taylor’s theorem, maxima and minima, saddle point, method of Lagrange’s multipliers; Double and Triple integrals, Jacobians and Change of variables, 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, Baire category theorem, connectedness, compactness, completeness; Continuity and Uniform continuity of functions; 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, Lp spaces.
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; Definition and basic properties of Laplace transforms, Applications of Lapalce transform 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, Finite Abelian groups, 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, Bounded linear operators and compact linear operators, Banach spaces, Separability, Dual 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, Maximum Principle; 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.
Topology	Basic concepts of topology, bases, subbases, subspace topology, order topology, product topology, quotient topology, metric topology, connectedness, path connectedness, compactness, sequentially compact, limit point compact, Tychonoff theorem, countability and separation axioms, Urysohn’s Lemma, Tietze extension theorem.
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 (MA)Syllabus 2027 PDF

IIT Madras has released the official syllabus for the Mathematics (MA) paper on its official website. Candidates can download the Mathematics Syllabus PDF from gate.iitm.ac.in. A direct link to download the GATE Mathematics (GE) Syllabus PDF is given below.