GATE Mathematics Syllabus (2019 PDF Download Maths)

GATE Mathematics Syllabus (GATE Mathematics Notes PDF and also Books, Mathematics Question Papers) : Download GATE Mathematics Syllabus in PDF for the upcoming year updated as per recent official notifications from the Indian Institute of Science. The overall GATE Mathematics Syllabus for next exam has been officially released recently and we have provided below the updated details on that. With Proper preparation, GATE Mathematics Syllabus can be easily taken over to the perfection. Mathematics is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics.

GATE Mathematics Syllabus Details

Over Syllabus Scope 11 Sections
GATE Maths Syllabus PDF Download
Total Subtopics Twenty Seven
Ideal Preparation Time 810 Hours

Prelude to GATE Mathematics Syllabus

Mathematics is probably one among the few streams of engineering that has not got the same level of popularity as other flashy departments. Probably Mathematics doesn’t need publicity to increase the scope, as India is the land of billion people.

Even through the Mathematics Syllabus portion in GATE looks very huge and hard to study, once you start reading through few chapters, you will come to an absolute conclusion that GATE Mathematics Syllabus is one of the most interesting and easiest of all the papers in entire GATE Syllabus.

GATE Mathematics Question Papers

Below we have provided the exclusive downloads of GATE Mathematics Question Papers. These Mathematics Question Papers have been compressed so that the download will be much faster and it will consume less internet data.

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Section A: GATE Mathematics Syllabus

Linear Algebra

  1. Finite dimensional vector spaces;
  2. Linear transformations and their matrix representations, rank;
  3. systems of linear equations, eigenvalues and eigenvectors,
  4. minimal polynomial, Cayley-Hamilton Theorem, diagonalization,
  5. Jordan-canonical form, Hermitian, SkewHermitian and unitary matrices;
  6. Finite dimensional inner product spaces,
  7. Gram-Schmidt orthonormalization process,
  8. self-adjoint operators, definite forms.

Section B: GATE Mathematics Syllabus

Complex Analysis

  1. Analytic functions, conformal mappings, bilinear transformations;
  2. complex integration: Cauchy’s integral theorem and formula;
  3. Liouville’s theorem, maximum modulus principle;
  4. Zeros and singularities; Taylor and Laurent’s series;
  5. residue theorem and applications for evaluating real integrals.

Section C: GATE Mathematics Syllabus

Real Analysis

  1. Sequences and series of functions, uniform convergence, power series,
  2. Fourier series, functions of several variables, maxima, minima;
  3. Riemann integration, multiple integrals, line, surface and volume integrals,
  4. theorems of Green, Stokes and Gauss;
  5. metric spaces, compactness, completeness, Weierstrass approximation theorem;
  6. Lebesgue measure, measurable functions;
  7. Lebesgue integral, Fatou’s lemma, dominated convergence theorem.

Section D: GATE Mathematics Syllabus

Ordinary Differential Equations

  1. First order ordinary differential equations,
  2. existence and uniqueness theorems for initial value problems,
  3. systems of linear first order ordinary differential equations,
  4. linear ordinary differential equations of higher order with constant coefficients;
  5. linear second order ordinary differential equations with variable coefficients;
  6. method of Laplace transforms for solving ordinary differential equations,
  7. series solutions (power series, Frobenius method);
  8. Legendre and Bessel functions and their orthogonal properties.

Section E: GATE Mathematics Syllabus

GATE Mathematics Syllabus PDF Download Maths


  1. Groups, subgroups, normal subgroups, quotient groups and homomorphism theorems, automorphisms;
  2. cyclic groups and permutation groups, Sylow’s theorems and their applications;
  3. Rings, ideals, prime and maximal ideals, quotient rings,
  4. unique factorization domains, Principle ideal domains,
  5. Euclidean domains, polynomial rings and irreducibility criteria;
  6. Fields, finite fields, field extensions.

Section F: GATE Mathematics Syllabus

Functional Analysis

  1. Normed linear spaces, Banach spaces, Hahn-Banach extension theorem,
  2. open mapping and closed graph theorems, principle of uniform boundedness;
  3. Inner-product spaces, Hilbert spaces, orthonormal bases,
  4. Riesz representation theorem, bounded linear operators.

Section G: GATE Mathematics Syllabus

Numerical Analysis

  1. Numerical solution of algebraic and transcendental equations: bisection, secant method, Newton-Raphson method, fixed point iteration;
  2. interpolation: error of polynomial interpolation, Lagrange, Newton interpolations;
  3. numerical differentiation;
  4. numerical integration: Trapezoidal and Simpson rules;
  5. numerical solution of systems of linear equations: direct methods (Gauss elimination,
  6. LU decomposition);
  7. iterative methods  (Jacobi and Gauss-Seidel);
  8. numerical solution of ordinary differential equations: initial value problems: Euler’s method, Runge-Kutta methods of order 2.

Section H: GATE Mathematics Syllabus

Partial Differential Equations

  1. Linear and quasilinear first order partial differential equations, method of characteristics;
  2. second order linear equations in two variables and their classification;
  3. Cauchy, Dirichletand Neumann problems;
  4. solutions of Laplace, wave in two dimensional Cartesian coordinates,
  5. Interior and exterior Dirichlet problems in polar coordinates;
  6. Separation of variables method for solving wave and diffusion equations in one space variable;
  7. Fourier series and Fourier transform and Laplace transform methods of solutions for the above equations.

Section I: GATE Mathematics Syllabus


  1. Basic concepts of topology, bases, subbases, subspace topology,
  2. order topology, product topology,
  3. connectedness, compactness, countability and separation axioms,
  4. Urysohn’s Lemma.

Section J: GATE Mathematics Syllabus

Probability and Statistics

  1. Probability space, conditional probability, Bayes theorem, independence,
  2. Random variables, joint and conditional distributions,
  3. standard probability distributions and their properties (Discrete uniform, Binomial, Poisson, Geometric,
  4. Negative binomial, Normal,Exponential, Gamma, Continuous uniform,
  5. Bivariate normal, Multinomial), expectation, conditional expectation, moments;
  6. Weak and strong law of large numbers, central limit theorem;
  7. Sampling distributions, UMVU estimators, maximum likelihood estimators;
  8. Interval estimation;
  9. Testing of hypotheses, standard parametric tests based on normal, distributions;
  10. Simple linear regression.

Section K: GATE Mathematics Syllabus

Linear programming

  1. Linear programming problem and its formulation, convex sets and their properties,
  2. graphical method, basic feasible solution, simplex method,
  3. big-M and two phase methods; infeasible and unbounded LPP’s, alternate optima;
  4. Dual problem and duality theorems,
  5. dual simplex method and its application in post optimality analysis;
  6. Balanced and unbalanced transportation problems,
  7. Vogel’s approximation method for solving transportation problems;
  8. Hungarian method for solving assignment problems.

Also See Syllabus Details of Other Courses like:

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FRM Level 1 Syllabus CS Professional Syllabus
UPSC Geography Syllabus UPSC Botany Syllabus
UPSC Zoology Syllabus UPSC Statistics Syllabus
UPSC Maths Syllabus UPSC Physics Syllabus

Conclusion on GATE Mathematics Syllabus

It is always said that the wise men words are often neglected. However, we would like to again stress the fact that the Mathematics Syllabus in GATE is one of the most important and crucial things that has to be properly taken care of.

Not just for examination point of view, Mathematics Syllabus in GATE helps you in the overal development to become a good responsible officer who will play a crucial role in the development of the country in the decades to come.

Mathematics can be a good optional if you are extremely brilliant at it but i do have a few problems. Mathematics is going to help in any possible way.

If readers have any further questions on GATE Mathematics Syllabus, you can drop us a mail or even post your question below on our comments section.