GATE Mathematics Syllabus, Exam Pattern, Eligibility

The paper

IIT Madras's pattern page puts this paper in the group whose 85 subject marks are split into 13 of "Engineering Mathematics" and 72 of core subject. For a science paper that line is left over from a table written for the engineering papers. Plan for 15 marks of General Aptitude and 85 of mathematics.

Question types and negative marking

MSQ has no partial credit: you need every correct option and no wrong one. An on-screen virtual calculator is provided; physical calculators are not allowed.

Two papers

You may sit two papers from a published list of allowed pairs. With MA as the primary paper, the second can only be CS, DA, PH or ST.

From the official GATE 2027 MA syllabus published by IIT Madras.

Section 1: Calculus

Functions of two or more variables; continuity, directional derivatives, partial derivatives, total derivative, Taylor's theorem, maxima and minima, saddle points, Lagrange multipliers; double and triple integrals, Jacobians and change of variables, applications to area, volume and surface area.

Vector Calculus: gradient, divergence and curl; line and surface integrals; the Green, Stokes and Gauss divergence theorems.

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, eigenvalues and eigenvectors, diagonalization, minimal polynomial, the Cayley-Hamilton theorem; finite dimensional inner product spaces, Gram-Schmidt orthonormalization; 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, the Baire category theorem, connectedness, compactness, completeness; continuity and uniform continuity; sequences and series of functions, uniform convergence, the Ascoli-Arzela theorem; the Weierstrass approximation theorem; the contraction mapping principle; power series; differentiation of functions of several variables, the inverse and implicit function theorems; Lebesgue measure on the real line, measurable functions; the Lebesgue integral, Fatou's lemma, the monotone and dominated convergence theorems, L^p spaces.

Section 4: Complex Analysis

Continuity, differentiability, analytic and harmonic functions; Cauchy's integral theorem and formula, Liouville's theorem, the maximum modulus principle, Morera's theorem; zeros and singularities; power series, radius of convergence, Taylor and Laurent series; the residue theorem and its use in evaluating real integrals; Rouche's theorem, the argument principle, the Schwarz lemma; conformal mappings and Mobius transformations.

Section 5: Ordinary Differential Equations

First order equations, existence and uniqueness for initial value problems; higher order linear equations with constant coefficients; second order linear equations with variable coefficients; the Cauchy-Euler equation; Laplace transforms and their use in solving ODEs; series solutions by power series and the Frobenius method; Legendre and Bessel functions and their orthogonality; systems of linear first order ODEs; Sturm's oscillation and separation theorems; Sturm-Liouville eigenvalue problems; planar autonomous systems: 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 actions, finite abelian groups, Sylow's theorems and their applications; rings, ideals, prime and maximal ideals, quotient rings, unique factorization domains, principal 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; bounded and compact linear operators; Banach spaces, separability, dual spaces; the Hahn-Banach theorem, the open mapping and closed graph theorems, the principle of uniform boundedness; inner-product spaces, Hilbert spaces, orthonormal bases, the projection theorem, the Riesz representation theorem, the spectral theorem for compact self-adjoint operators.

Section 8: Numerical Analysis

Systems of linear equations: direct methods (Gaussian elimination, LU decomposition, Cholesky factorization) and iterative methods (Gauss-Seidel, Jacobi) with their convergence for diagonally dominant matrices; numerical solution of nonlinear equations by bisection, secant, Newton-Raphson and fixed point iteration; interpolation by the Lagrange and Newton forms and the error in polynomial interpolation; numerical differentiation and its error; numerical integration by the trapezoidal and Simpson rules, Newton-Cotes formulae, composite rules and their mathematical errors; numerical solution of initial value problems by the Euler method and the second-order Runge-Kutta method.

Section 9: Partial Differential Equations

The method of characteristics for first order linear and quasilinear equations; second order equations in two independent variables, their classification and canonical forms; separation of variables for the Laplace equation in Cartesian and polar coordinates; the maximum principle; heat and wave equations in one space variable; the wave equation (the Cauchy problem, d'Alembert's formula, domains of dependence and influence, the non-homogeneous equation); the heat equation and its Cauchy problem; Laplace and Fourier transform methods.

Section 10: Topology

Bases and subbases; subspace, order, product, quotient and metric topologies; connectedness and path connectedness; compactness, sequential compactness, limit point compactness, the Tychonoff theorem; countability and separation axioms; Urysohn's lemma and the Tietze extension theorem.

Section 11: Linear Programming

Linear programming models, convex sets, extreme points; basic feasible solutions, the graphical method, the simplex method, two-phase and revised simplex methods; infeasible and unbounded models, alternate optima; duality theory, weak and strong duality; balanced and unbalanced transportation problems, initial basic feasible solutions by least cost, north-west corner and Vogel's approximation methods; optimal solution by the modified distribution method; assignment problems and the Hungarian method.

General Aptitude (15 marks, common to every GATE paper)

Verbal Aptitude: basic English grammar: tenses, articles, adjectives, prepositions, conjunctions, verb-noun agreement and other parts of speech; basic vocabulary: words, idioms and phrases in context; reading and comprehension; narrative sequencing.

Quantitative Aptitude: data interpretation: bar graphs, pie charts and other data graphs, 2- and 3-dimensional plots, maps and tables; numerical computation and estimation: ratios, percentages, powers, exponents and logarithms, permutations and combinations, series; mensuration and geometry; elementary statistics and probability.

Analytical Aptitude: logic: deduction and induction; analogy; numerical relations and reasoning.

Spatial Aptitude: transformation of shapes: translation, rotation, scaling, mirroring, assembling and grouping; paper folding, cutting, and patterns in 2 and 3 dimensions.

Qualification

You must be in the 3rd or higher year of any undergraduate degree, or already hold a government-approved degree in Engineering, Technology, Architecture, Science, Commerce, Arts or Humanities.

Qualifying degrees include B.E., B.Tech., B.Pharm., B.Arch., three-year B.Sc./B.A./B.Com., M.Sc./M.A./MCA and equivalents, professional degrees such as MBBS, BDS and B.V.Sc., and professional society exams recognised as equivalent to B.E./B.Tech./B.Arch. With an international degree you must be in the 3rd year or higher, or hold a bachelor's degree of at least three years.

Not required

• No age limit.
• No limit on attempts.
• Your degree doesn't have to match the paper you sit.

Full rules: GATE 2027 eligibility.

Fee per paper

Two papers double it: Rs 2,000 / Rs 4,000 in the regular window, Rs 2,500 / Rs 4,500 in the extended one. Every female candidate pays the concessional fee, whatever her category. PwBD means Person with Benchmark Disability.

The portal

You apply through GOAPS, the GATE Online Application Processing System, from gate2027.iitm.ac.in. GATE 2027 adds live facial verification and DigiLocker to registration.

A paid rectification window follows the closing date for correcting details you already submitted. It isn't a second chance to register.

Admission

A GATE score is used for M.Tech, M.E., M.S. and direct PhD admission at the IITs, IISc, NITs, IIITs and many central and state institutions, and for MoE assistantships.

The IITs and IISc admit through COAP, which sequences offers so you hold one at a time. NITs and IIITs admit through CCMT. Each needs its own registration; a GATE score alone admits nobody.

Recruitment

A GATE Mathematics score is used mainly for M.Sc., M.Tech. and PhD admission in mathematics, computing and statistics, and for MoE assistantships. It's rarely a PSU route, because most PSU advertisements name engineering disciplines. Read each advertisement's eligibility list before counting on it.

Each PSU sets its own eligibility, shortlisting ratio and interview or group discussion. GATE gives you the score, not the vacancy, and the list of recruiters changes every year.

GATE runs at centres across India and a few abroad. You list preferred cities in order when you apply. The allotted city is announced separately (4 January 2027 this cycle), before the admit card, so you can plan travel early.

Allotment follows your preference where capacity allows and isn't guaranteed. The centre address is on the admit card.

GATE 2027, organised by IIT Madras.

The opening date moved twice this cycle: first 14 August 2026, then 27 August, then 2 September. IIT Madras says all dates are liable to change, so check its dates page.

There are six exam days, against four in GATE 2026, because there are now 30 papers including the new Robotics and Automation paper.

Download the admit card from GOAPS with your enrolment ID or email and password. The exam city comes first, on 4 January 2027. The admit card and centre address follow later; IIT Madras hasn't fixed that date yet.

Bring the admit card and the original photo ID whose details you entered in the application. A different document or a photocopy isn't accepted.

What you receive

• Marks out of 100: what you actually scored in your session.
• GATE Score out of 1000: a normalised figure computed against the qualifying mark and the top scorers. This is the number institutes and employers compare.

A paper held in more than one session is normalised across them, so the shift you sat doesn't help or hurt you.

Validity

The score is valid for three years from the result date, so one good attempt covers three admission cycles.

Response sheet and answer key

Your response sheet and the provisional answer key come out before the result, with a paid challenge window. The subject committee decides challenges, and the final key can differ from the provisional one.

GATE publishes a qualifying mark per paper per category, the bar for being declared qualified and getting a scorecard. It is set each year from that year's paper, so an older figure is only a rough guide.

Qualifying isn't the same as getting in. The score that wins an IIT M.Tech seat or a PSU interview call in Mathematics is far above the qualifying mark.

PSUs set their own cut-offs on the GATE Score in each advertisement. They swing with the discipline and that year's vacancies, so no figure is given here.

1. Don't prepare this as engineering mathematics. Sections 3, 7 and 10 (Real Analysis with Lebesgue measure, Functional Analysis and Topology) are postgraduate pure mathematics and on no engineering syllabus.
2. Section 11 is your easiest marks. Linear Programming is procedural: simplex, transportation, assignment, the Hungarian method. Against ten sections of proof-based mathematics, it pays back practice far beyond its difficulty.
3. Attempt every MSQ and NAT question. Neither carries negative marking, while a wrong MCQ costs a third or two thirds of its value.
4. Don't give away General Aptitude. 15 marks with no maths needed, and easy to neglect when the subject is this hard.
5. Numerical Analysis rewards arithmetic, not theory. NAT questions are routine there, and NAT has no penalty.
6. Practise with the on-screen calculator. Numerical Analysis and Linear Programming involve real computation, and the virtual keypad isn't what you're used to.
7. Pick the second paper for where you'll use the score. MA pairs only with CS, DA, PH and ST. For a computational or statistical programme, DA or ST fits; the fee doubles either way.
8. Work past papers section by section. Eleven sections in 85 marks means a handful of questions each, and the papers show the depth expected better than the syllabus does. Papers and answer keys back to 2007 are on the GATE 2027 downloads page.

GATE 2027 (IIT Madras): gate2027.iitm.ac.in

MA syllabus (PDF): MA_GATE2027_Syllabus.pdf

All syllabi: Test papers and syllabus

Pattern and marking: Question paper pattern

Two-paper combinations: Allowed pairs

Eligibility: Eligibility criteria

Fees: Application fees

Previous papers and answer keys, 2007 to 2026: GATE 2027 downloads

Dates: Important dates

Which IIT is conducting GATE 2027?

IIT Madras. The organising institute rotates each year among IISc Bangalore and the seven older IITs, and the website changes with it.

Is there an age limit or a limit on attempts?

Neither. Your degree doesn't have to match the paper either; you choose the paper.

How is the MA paper's 100 marks divided?

General Aptitude 15, Mathematics 85.

Which questions carry negative marking?

Only MCQs: 1/3 for a wrong 1-mark question, 2/3 for a wrong 2-mark one. MSQ and NAT have no penalty.

Does MSQ give partial credit?

No. You must select every correct option and no wrong one.

Can I sit two papers?

Yes. With MA as the primary paper, the second can be CS, DA, PH or ST. The fee doubles.

Is a calculator allowed?

Not a physical one. There's a virtual calculator on screen.

How long is a GATE score valid?

Three years from the result date.

What is the difference between marks and GATE Score?

Marks are out of 100 and are what you scored. The GATE Score is out of 1000, normalised across sessions, and is what institutes and employers compare.

Does qualifying GATE get me a seat?

No. It gets you a scorecard. Admission is through COAP for the IITs and IISc and CCMT for the NITs and IIITs, each a separate registration, and the scores that win seats are well above the qualifying mark.

Can third-year students apply?

Yes, from the 3rd year of any undergraduate degree.

Is this the same as the Engineering Mathematics section in other GATE papers?

No. That's a 13-mark section. GATE MA is a full postgraduate mathematics paper with eleven sections plus General Aptitude, including Real Analysis, Functional Analysis, Topology, Algebra and Linear Programming.

Are past GATE Mathematics papers available?

Yes. Papers and answer keys back to 2007 are on the GATE 2027 downloads page.