 # GATE Mathematics Syllabus 2022

The GATE mathematics syllabus is accessible from the official website, where it goes live. Also, in this article here, we have provided details about the GATE Mathematics Syllabus PDF Download and information about the topics on the web page. Candidates can quickly check out the GATE Maths Syllabus and the marking scheme given in this article and prepare for GATE more efficiently.

Like every other subject, GATE Mathematics takes its mark from a combination of the General Aptitude section and the Mathematics (subject-based) section. Maths, as all are aware, is a subject that requires a lot of practice. Hence, knowing the entire GATE Mathematics Syllabus PDF will help students study accordingly and thus crack the exams well.

GATE Exam Mathematics Syllabus is a crucial subject paper, and the candidate who selects this as the primary paper can choose from either CS (Computer Science and Information Technology), PH( Physics) or ST(Statistics), as the secondary paper. The GATE Mathematics (MA) Syllabus includes topics such as Calculus, Linear Algebra, Real Analysis, Complex Analysis, Ordinary Differential Equations, Algebra, Functional Analysis, Numerical Analysis, Partial Differential Equations, Topology, and Linear Programming.

Candidates are advised to first refer to the syllabus and then the following marking scheme and reference materials to prepare for the exams. Details of topics and sub-topics are given below in this article.

### GATE Mathematics Syllabus 2022

 TOPICS SUB-TOPICS/CONCEPTS 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. 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, 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. 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, 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. 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. 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. 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, 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, compactness, countability and separation axioms, Urysohn’s Lemma. 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.

Meanwhile, find below the details of the marking scheme, as per the GATE syllabus.

### GATE Maths Syllabus Exam Pattern 2022

Knowing the GATE Mathematics Exam Pattern 2022 will help the candidates to prepare better for the exams. Find below the details:

• General Aptitude(GA) Marks of Mathematics (MA) = 15 Marks
• Subject Marks = 85 Marks
• Total Marks for MA = 100 Marks
• Total Time (in Minutes) = 180 Minutes

## Frequently Asked Questions on GATE Mathematics Syllabus 2022

### How do we access the GATE Mathematics Syllabus 2022?

IIT releases it on the official GATE website. Meanwhile, we also provide the PDF link and details of the topics on our webpage.

### Which are the main topics from the GATE MA Syllabus 2022?

The key topics covered in the syllabus are Calculus, Linear Algebra, Real Analysis, Complex Analysis, Ordinary Differential Equations, Algebra, Functional Analysis, Numerical Analysis, Partial Differential Equations, Topology and Linear Programming.

### Which are the concepts discussed under the main topic of Topology of the syllabus?

The main concepts discussed under Topology section of GATE MA Syllabus are the basic concepts of topology, bases, subbases, subspace topology, order topology, product topology, quotient topology, metric topology, connectedness, compactness, countability and separation axioms and Urysohn’s Lemma.