GATE Mathematics Syllabus and Exam Pattern 2022 | Know The Updated Details!

GATE Mathematics Syllabus and Exam Pattern 2022: IIT Kharagpur has released GATE Mathematics (MA) Syllabus 2022 on the official website. No changes have been made to the syllabus this year. GATE 2022 Mathematics Paper will have a total of 65 questions.

To know more about the GATE Syllabus For Mathematics and Exam Pattern 2022, read the whole blog.

GATE Mathematics Syllabus 2022

GATE 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.

There are 11 chapters in the GATE Mathematics Syllabus. You can find the GATE Mathematics Syllabus 2022 here.

Section 1: 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.

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
• 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

• 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.

Section 4: 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.

Section 5: 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.

Section 6: 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
• 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, 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.

Section 8: 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.

Section 9: 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.

Section 10: 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.

Section 11: 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 Syllabus 2022 For General Aptitude 

Subject	GATE Mathematics Syllabus 2022
Verbal Aptitude	English grammar – articles, verb-noun agreement, tenses, adjectives, conjunctions, prepositions, other parts of speech etc.; vocabulary – words, phrases, idioms; comprehension & reading; narrative sequencing.
Analytical Aptitude	Logic – Induction & Deduction; analogy; number relations & reasoning.
Spatial Aptitude	Shape transformation – mirroring, rotation, translation, grouping, assembling, and scaling; Paper cutting, folding & 2-D and 3-D patterns.
Numerical Aptitude	Elementary statistics & probability; geometry; data and graphs (bar graph, histogram, pie chart, and other data graphs), 2- and 3- dimensional plots, maps, and tables; mensuration; numerical computation & estimation – powers, exponents, percentages, permutations & combinations, ratios, logarithms, etc.

Download GATE Mathematics Syllabus 2022 PDF

GATE Mathematical Exam Pattern 2022

Here you can check GATE Mathematical Exam Pattern 2022.

• Mode of Examination: Online
• Duration of Exam: 3 hours
• Types of Questions: MCQs and NAT
• Sections: 2 sections – General Aptitude and Subject-based
• Total Questions: 65 questions
• Total Marks: 100 marks
• Negative Marking: For MCQs only

Weightage of Sections in GATE Mathematics 2022

GATE Mathematics Syllabus 2022 is divided into two sections. The below table describes the distribution of marks in each section.

GATE Mathematics Marking Scheme 2022

Weightage of Topics Of GATE Mathematics Syllabus 2022

The students are advised to commence their GATE Preparation after going through the weightage of each topic mentioned. This will save them a lot of trouble and effort. 

Other Important Information for GATE Mathematics 2022

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GATE Mathematics Books

GATE Mathematics Previous Year Question Papers

Best Books for GATE Mathematics (MA) 2022

Here you can check the recommended books based on GATE Mathematics Syllabus 2022.

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