GATE Mathematics Syllabus: Sections, Important Topics

GATE Mathematics Syllabus Overview

GATE Mathematics syllabus 2024 collects the important topics released by the officials (IISc Bangalore) for the exam. The GATE Mathematics (MA) syllabus is considered a relatively challenging subject for the exam. It is important not to confuse the GATE Mathematics syllabus with the Engineering Mathematics syllabus.

The GATE Mathematics paper will have a total of 65 questions with 100 marks. A total of 15 questions will be from the General Aptitude section, and the remaining 55 will be based on the GATE Mathematics syllabus.

Sections in GATE Mathematics Syllabus

There are a total of 10 sections in the core GATE Mathematics syllabus:

• Section 1: Calculus
• Section 2: Linear Algebra
• Section 3: Real Analysis
• Section 4: Complex Analysis
• Section 5: Ordinary Differential Equations
• Section 6: Algebra
• Section 7: Functional Analysis
• Section 8: Numerical Analysis
• Section 9: Partial Differential Equations
• Section 10: Topology

GATE Mathematics Syllabus PDF

Along with the detailed description of the GATE syllabus for Mathematics, we have provided a PDF for candidates to download. It is advised to keep the GATE Mathematics syllabus PDF saved on their devices and a hard copy to prepare for the exam efficiently.

Download GATE Mathematics 2024 Syllabus PDF

Section-wise GATE Mathematics Syllabus

The GATE Maths syllabus is divided into different sections, and each section includes specific topics that candidates are expected to know and understand. By studying and mastering the topics in each section, candidates can prepare themselves for success on the GATE Mathematics exam. Let us see the syllabus of each section:

Calculus Syllabus

The calculus section is one of the most famous branches of the GATE Mathematics syllabus. Basically, it is concerned with continuous change. Calculus emphasizes some important topics in math, such as integration, differentiation, limits, functions, and so on. The complete list of the topics covered in the Calculus section of the GATE Mathematics syllabus are:

GATE Mathematics Syllabus of Calculus
Functions of two or more variables	Partial derivatives	Total derivative
Continuity	Directional derivatives	Green’s theorem
Method of Lagrange’s multipliers	Maxima and minima	Double and Triple integrals and their applications to the area
Saddle point	Line integrals and Surface integrals	Vector Calculus: Gradient divergence and curl
Volume and surface area	Gauss divergence theorem	Stokes’ theorem

Linear Algebra Syllabus

The linear algebra section of the GATE Mathematics syllabus 2024 deals with the study of linear sets of equations and the transformation properties of equations. In this section, some important topics are covered, such as:

• Finite-dimensional vector spaces over real or complex fields;
• Linear transformations and their matrix representations, rank, and nullity;
• Systems of linear equations, characteristic polynomials,
• 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 Syllabus

Real Analysis is a branch of Mathematics that was made to formalize the study of numbers & functions. It is used to investigate important concepts such as limits and continuity. It comprises a few topics in the GATE Mathematics syllabus 2024, such as 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 Syllabus

Basically, Complex analysis is the study of complex numbers combined with their derivatives, manipulation, and a few other properties. In the GATE Mathematics syllabus 2024, the Complex analysis contains the following topics:

• 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, the 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 Syllabus

In Mathematics, an ordinary differential equation is a differential equation that contains one or more functions of one independent variable and also the derivatives of those functions. This section of the GATE Mathematics syllabus includes the following:

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 Syllabus

Algebra is a branch of Mathematics that deals with symbols and the rules for manipulating the symbols. In this section of the GATE MA syllabus, some important topics are included, such as:

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, and algebraically closed fields.

Functional Analysis Syllabus

Functional analysis is a branch of mathematical analysis that deals with functionals, or functions of functions y = f(x). It comprises a few topics in the Mathematics syllabus, such as:

Projection theorem	Orthonormal bases	Hilbert spaces	Riesz representation theorem
Hahn-Banach theorem	Open mapping	Inner-product spaces	Spectral theorem for compact self-adjoint operators
Normed linear spaces	Banach spaces	Principle of uniform boundedness	Closed graph theorems

Numerical Analysis Syllabus

In the GATE Mathematics syllabus 2024, this section covers the various numerical methods for solving equations (roots), Bisection or Half-interval as the foundation, and the other technique. Other important topics covered in this section are given below:

• 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 an interpolating polynomial, Error in the 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 Syllabus

A Partial differential equation is a type of differential equation. In this topic, the equation contains multi-unknown variables with their partial derivatives. It is also called a special case of an ordinary differential equation. The PDE section of the GATE Mathematics Syllabus includes the following topics:

• 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 Syllabus

The Topology section in Mathematics deals with Mathematical Analysis and is used for proving the convergence results in various numerical methods for partial differential equations. Topics in this section include Basic concepts of topology, bases, subbases, subspace topology, order topology, product topology, quotient topology, metric topology, connectedness, compactness, accountability, and separation axioms, and Urysohn’s Lemma.

Linear Programming Syllabus

Linear programming is used to determine the best outcome of a linear function. In Mathematics, Linear programming is the best method to perform linear optimization by taking a few simple assumptions. Important topics in this section of the GAT Mathematics (MA) syllabus include:

Linear programming models, extreme points, convex sets	Infeasible and unbounded linear programming models, alternate optima	Initial basic feasible solution to balanced transportation problems
Basic feasible solution, graphical method, simplex method	Duality theory, weak duality, and strong duality	Balanced and unbalanced transportation problems
Hungarian method, two-phase methods, revised simplex method	Optimal solution modified distribution method	Least cost method, the north-west corner rule, Vogel’s approximation method

Preparation Tips GATE Mathematics Syllabus 2024

With the growing competition and difficulty level of the GATE Mathematics syllabus 2024, it is important for candidates to invest their time in the preparation smartly. Here we have provided a few important tips to tackle the GATE MA syllabus to achieve a good rank.

• Allot specific time per topic and track your GATE Mathematics preparation weekly.
• Understand your weak and strong points in the GATE MA syllabus.
• Select and prepare from the trusted study material.
• Clear your doubts as and when faced.
• Attempt mock tests to test your strength.

Important Topics in GATE Mathematics Syllabus

The important topic from the GATE Mathematics syllabus is the list of chapters covering most marks from the exam perspective. Candidates are advised not to miss these topics and to provide some extra time for preparing these topics. The important topics for the 2024 exam are:

• Linear Programming
• Real and Complex Analysis
• Partial Differential Equations
• Algebra
• General Aptitude

You can refer to the following video for a complete understanding of the GATE Mathematics syllabus.

Best Books for GATE MA Syllabus 2024

In order to have effective preparation for the GATE MA exam and cover an adequate amount of syllabus, it is important to use trusted study material. We have provided a list of books best suited for your exam preparation and completing the GATE Mathematics syllabus.

Best GATE Mathematics Books
Chapterwise Solved Papers Mathematics	Arihant Publication
Wiley Acing the Gate: Engineering Mathematics and General Aptitude	Anil K. Maini, Wiley
Engineering Mathematics	Made Easy Publications
Engineering Mathematics(Higher)	B.S. Grewal

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