← Back to Graduate Aptitude Test in Engineering Hub
View Complete Graduate Aptitude Test in Engineering Syllabus
GovtJobsNet.com MA · Mathematics
SYLLABUS GATE Mathematics Syllabus 2027: MA PDF and Exam Pattern
GATE MA syllabus 2027 with the official PDF, 100-mark exam pattern and complete section-wise topic tables for Mathematics.
Updated:
GATE MA syllabus 2027MathematicsGATE 2027 PDFIIT Madras
Use the available GATE MA Syllabus 2027 download resources and review the detailed syllabus, unit-wise topics, exam pattern information, preparation guidance below.
📸
Tired of resizing your photo for every exam?
Save your photo & signature once — auto-format for SSC, UPSC, TNPSC & 45+ portals.
Key Highlights
- MA is the official GATE code for Mathematics.
- The official syllabus contains 11 sections: Calculus; Linear Algebra; Real Analysis; Complex Analysis; Ordinary Differential Equations; Algebra; Functional Analysis; Numerical Analysis; Partial Differential Equations; Topology; Linear Programming.
- The paper is a 3-hour Computer-Based Test for 100 marks, including 15 marks of General Aptitude.
- Allowed second-paper codes when MA is primary: CS, DA, PH, ST.
- The official IIT Madras PDF is available in the download section.
GATE MA Syllabus 2027 Overview
The official GATE MA syllabus 2027 for Mathematics is organized into 11 sections, covering Calculus, Linear Algebra, Real Analysis, Complex Analysis and the remaining paper-specific areas listed below. This page follows the IIT Madras syllabus order, provides the correct 100-mark exam pattern, and links the official PDF so aspirants can prepare from a complete, verified checklist.
How to Prepare from the GATE MA Syllabus
- Create one checklist for every official section and retain the same sequence used in the PDF.
- Start with a diagnostic test, then allocate more study time to weak high-coverage sections instead of dividing time equally.
- Solve previous-year GATE questions immediately after completing each topic and record errors by concept, calculation and time pressure.
- Revise formulas, definitions and frequently confused conditions in short weekly cycles, followed by mixed-section tests.
- Use the official PDF as the final scope document; coaching notes should expand a listed topic, not introduce an unrelated syllabus.
GATE MA Official Source and Internal Links
The syllabus tables were checked against the IIT Madras GATE 2027 MA PDF. Use the download section for the database-hosted copy, the GATE syllabus hub to switch papers, and the notification page for registration dates and policy updates.
Exam Pattern
GATE MA Exam Pattern 2027
| Section | Marks | How it applies |
|---|---|---|
| General Aptitude | 15 | Common to all GATE papers |
| Core subject questions | 85 | Selected test-paper syllabus |
| Total | 100 | 3-hour CBT |
General Aptitude
Marks
15
How it applies
Common to all GATE papers
Core subject questions
Marks
85
How it applies
Selected test-paper syllabus
Total
Marks
100
How it applies
3-hour CBT
GATE MA Question and Marking Rules
| Question type | Possible marks | Negative marking |
|---|---|---|
| MCQ | 1 or 2 | Yes: 1/3 for a wrong 1-mark MCQ; 2/3 for a wrong 2-mark MCQ |
| MSQ | 1 or 2 | No negative marking and no partial marking |
| NAT | 1 or 2 | No negative marking |
MCQ
Possible marks
1 or 2
Negative marking
Yes: 1/3 for a wrong 1-mark MCQ; 2/3 for a wrong 2-mark MCQ
MSQ
Possible marks
1 or 2
Negative marking
No negative marking and no partial marking
NAT
Possible marks
1 or 2
Negative marking
No negative marking
Syllabus Breakdown
GATE MA Syllabus 2027 - Official Section-wise Topics
The tables below preserve the section order and complete topic coverage published by IIT Madras for the GATE 2027 MA paper. Use each table as a study and revision checklist, and verify any later corrigendum against the official PDF.
Section 1: Calculus
| Topic area | Official syllabus coverage |
|---|---|
| Official coverage | 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. |
| Topic area | Official syllabus coverage |
|---|---|
| Official coverage | 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. |
Section 2: Linear Algebra
| Topic area | Official syllabus coverage |
|---|---|
| Official coverage | 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 eigen - vectors, diagonalization, minimal polynom ial, 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. |
| Topic area | Official syllabus coverage |
|---|---|
| Official coverage | 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 eigen - vectors, diagonalization, minimal polynom ial, 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
| Topic area | Official syllabus coverage |
|---|---|
| Official coverage | 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. |
| Topic area | Official syllabus coverage |
|---|---|
| Official coverage | 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. |
Section 4: Complex Analysis
| Topic area | Official syllabus coverage |
|---|---|
| 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 rea l integrals; Rouche’s theorem, Argument principle, Schwarz lemma; Conformal mappings, Mobius transformations. |
| Topic area | Official syllabus coverage |
|---|---|
| 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 rea l integrals; Rouche’s theorem, Argument principle, Schwarz lemma; Conformal mappings, Mobius transformations. |
Section 5: Ordinary Differential Equations
| Topic area | Official syllabus coverage |
|---|---|
| Official coverage | 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. |
| Topic area | Official syllabus coverage |
|---|---|
| Official coverage | 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. |
Section 6: Algebra
| Topic area | Official syllabus coverage |
|---|---|
| Official coverage | 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, un ique factorization domains, Principle ideal domains, Euclidean domains, polynomial rings, Eisenstein’s irreducibility criterion; Fields, finite fields, field extensions, algebraic extensions, algebraically closed fields. |
| Topic area | Official syllabus coverage |
|---|---|
| Official coverage | 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, un ique 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
| Topic area | Official syllabus coverage |
|---|---|
| Official coverage | 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, orth onormal bases, projection theorem, Riesz representation theorem, spectral theorem for compact self-adjoint operators. |
| Topic area | Official syllabus coverage |
|---|---|
| Official coverage | 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, orth onormal bases, projection theorem, Riesz representation theorem, spectral theorem for compact self-adjoint operators. |
Section 8: Numerical Analysis
| Topic area | Official syllabus coverage |
|---|---|
| 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. |
| Topic area | Official syllabus coverage |
|---|---|
| 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. |
Section 9: Partial Differential Equations
| Topic area | Official syllabus coverage |
|---|---|
| Official coverage | 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. |
| Topic area | Official syllabus coverage |
|---|---|
| Official coverage | 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. |
Section 10: Topology
| Topic area | Official syllabus coverage |
|---|---|
| Official coverage | 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. |
| Topic area | Official syllabus coverage |
|---|---|
| Official coverage | 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. |
Section 11: Linear Programming
| Topic area | Official syllabus coverage |
|---|---|
| Official coverage | 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 dualit y and strong duality; Balanced and unbalanced transportation problems, Initial basic feasible solution of balanced transportation problems (least cost method, north-west corner rule, V ogel’s approximation method); Optimal solution, modified distribution me thod; Solving assignment problems, Hungarian method. |
| Topic area | Official syllabus coverage |
|---|---|
| Official coverage | 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 dualit y and strong duality; Balanced and unbalanced transportation problems, Initial basic feasible solution of balanced transportation problems (least cost method, north-west corner rule, V ogel’s approximation method); Optimal solution, modified distribution me thod; Solving assignment problems, Hungarian method. |
Download Official PDFs & Question Papers
Official GATE MA Syllabus 2027 PDF
Prepare for Graduate Aptitude Test in Engineering
Frequently Asked Questions
Use the featured PDF button on this page. It opens the database-hosted copy of the official IIT Madras MA syllabus.
Yes. General Aptitude is compulsory in every GATE 2027 test paper and carries 15 marks.
The paper uses Multiple Choice Questions, Multiple Select Questions and Numerical Answer Type questions carrying one or two marks.
Negative marking applies only to incorrect MCQs. MSQ and NAT questions have no negative marking, and MSQs have no partial marking.
Follow the official section order, complete topic-level concepts and examples, solve previous-year questions after each unit, and use full-length mock tests only after completing the major sections.