# GATE Mathematics Syllabus 2024

Candidates taking the GATE (Graduate Aptitude Test In Engineering) 2024 exam must be aware of the entire syllabus of the subject paper they are opting for. There are a total of 29 subject papers and one of these is mathematics. Here is the latest GATE syllabus of Mathematics (Code: MA) in detail:

## GATE Mathematics Syllabus: Calculus

• Functions Of Two Or More Variables
• Maxima And Minima
• Partial Derivatives
• Vector Calculus: Gradient, Divergence, And Curl, Line Integrals And Surface Integrals, Green’s Theorem, Stokes’ Theorem, And Gauss Divergence Theorem
• Total Derivative
• Directional Derivatives
• Continuity
• Double And Triple Integrals And Their Applications To Area, Volume, And Surface Area
• Method Of Lagrange’s Multipliers

## GATE Mathematics Syllabus: Linear Algebra

• Finite-Dimensional Vector Spaces Over Real Or Complex Fields
• Cayley-Hamilton Theorem
• Diagonalization
• Rank And Nullity
• Eigenvalues And Eigenvectors
• Gram-Schmidt Orthonormalization Process
• Characteristic Polynomial
• Diagonalization By A Unitary Matrix,  Jordan Canonical Form
• Systems Of Linear Equations
• Finite-Dimensional Inner Product Spaces
• Minimal Polynomial
• Symmetric, Skew-Symmetric, Hermitian, Skew-Hermitian, Normal, Orthogonal, And Unitary Matrices
• Linear Transformations And Their Matrix Representations, rank and Nullity

## GATE Mathematics Syllabus: Real Analysis

• Sequences And Series Of Functions, Uniform Convergence, Ascoli-Arzela Theorem
• Lebesgue Integral, Fatou’s Lemma, Monotone Convergence Theorem, Dominated Convergence Theorem
• Metric Spaces, Connectedness, Compactness, Completeness
• Contraction Mapping Principle, Power Series
• Differentiation Of Functions Of Several Variables, Inverse And Implicit Function Theorems Lebesgue Measure On The Real Line, Measurable Functions
• Weierstrass Approximation Theorem

## GATE Mathematics Syllabus: Complex Analysis

• Conformal Mappings, Mobius Transformations
• Complex Integration: Cauchy’s Integral Theorem And Formula
• Residue Theorem And Applications For Evaluating Real Integrals
• Power Series, Radius Of Convergence, Taylor’s Series, And Laurent’s Series
• Rouche’s Theorem, Argument Principle, Schwarz Lemma
• Liouville’s Theorem, Maximum Modulus Principle, Morera’s Theorem; Zeros And Singularities
• Functions Of A Complex Variable: Continuity, Differentiability, Analytic Functions, Harmonic Functions

## GATE Mathematics Syllabus: Ordinary Differential Equations:

• Systems Of Linear First-Order Ordinary Differential Equations, Sturm’s Oscillation And Separation Theorems, Sturm-Liouville Eigenvalue Problems
• First-Order Ordinary Differential Equations, Existence And Uniqueness Theorems For Initial Value Problems, Linear Ordinary Differential Equations Of Higher Order With Constant Coefficients
• Planar Autonomous Systems Of Ordinary Differential Equations: Stability Of Stationary Points For Linear Systems With Constant Coefficients, Linearized Stability, Lyapunov Functions
• Legendre And Bessel Functions And Their Orthogonal Properties
• 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)

## GATE Mathematics Syllabus: Algebra

• Fields, Finite Fields, Field Extensions, Algebraic Extensions, Algebraically Closed Fields
• 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

## GATE Mathematics Syllabus: Functional Analysis

• Inner-Product Spaces, Hilbert Spaces, Orthonormal Bases, Projection Theorem, Riesz Representation Theorem, Spectral Theorem For Compact Self-Adjoint Operators
• Normed Linear Spaces, Banach Spaces, Hahn-Banach Theorem, Open Mapping And Closed Graph Theorems, Principle Of Uniform Boundedness

## GATE Mathematics Syllabus: Numerical Analysis

• Numerical Solution Of Initial Value Problems For Ordinary Differential Equations: Methods Of Euler, Runge-Kutta Method Of Order 2
• 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 Differentiation And Error, Numerical Integration: Trapezoidal And Simpson Rules, Newton-Cotes Integration Formulas, Composite Rules, Mathematical Errors Involved In Numerical Integration Formulae
• Interpolation: Lagrange And Newton Forms Of Interpolating Polynomial, Error In Polynomial Interpolation Of a Function
• Numerical Solutions Of Nonlinear Equations: Bisection Method, Secant Method, Newton-Raphson Method, Fixed-Point Iteration

## GATE Mathematics Syllabus: Partial Differential Equations

• Heat Equation: Cauchy Problem; Laplace And Fourier Transform Methods
• Method Of Characteristics For First-Order Linear And Quasilinear  Partial Differential Equations
• Wave Equation: Cauchy Problem And D’alembert Formula, Domains Of Dependence And Influence, Non-Homogeneous Wave Equation
• 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

## GATE Mathematics Syllabus: Topology

• Basic Concepts Of Topology
• Bases
• Product Topology
• Subspace Topology
• Order Topology
• Compactness
• Metric Topology
• Subbases
• Countability and separation axioms
• Urysohn’s Lemma
• Connectedness
• Quotient Topology

## GATE Mathematics Syllabus: Linear Programming

• Solving Assignment Problems, Hungarian Method
• Basic Feasible Solution, Graphical Method, Simplex Method, Two-Phase Methods, Revised Simplex Method
• Balanced And Unbalanced Transportation Problems, Initial Basic Feasible Solution Of Balanced Transportation Problems (Least Cost Method, North-West Corner Rule, Vogel’s Approximation Method)
• Infeasible And Unbounded Linear Programming Models, Alternate Optima;
• Linear Programming Models, Convex Sets, Extreme Points
• Optimal Solution, Modified Distribution Method
•  Duality Theory, Weak Duality, And Strong Duality

## How to Prepare for the GATE Maths Syllabus?

1. Understand the Syllabus:

• Start by thoroughly understanding the GATE mathematics syllabus. This will give you a clear picture of the topics you need to cover. The syllabus is available on the GATE official website.
2. Select the Right Study Materials:

• Choose high-quality study materials, textbooks, and reference books. Some recommended books for GATE mathematics include “Higher Engineering Mathematics” by B.S. Grewal, “Advanced Engineering Mathematics” by Erwin Kreyszig, and the “GATE Mathematics” book by previous toppers.
3. Create a Study Schedule:

• Develop a realistic study schedule that covers all topics within the given time frame. Allocate sufficient time to each topic based on its weightage in the exam.
4. Focus on the Core Topics:

• Concentrate on the core topics that carry the most weight in the GATE mathematics paper. These typically include calculus, linear algebra, differential equations, and discrete mathematics.
5. Practice Regularly:

• Mathematics requires practice. Solve a wide range of problems, particularly from previous years’ GATE papers. This will help you become familiar with the exam pattern and develop problem-solving skills.
6. Use Online Resources:

• Utilize online resources, including video lectures, online forums, and educational websites. Many platforms offer free and paid courses specifically designed for GATE mathematics.
7. Take Mock Tests:

• Regularly take GATE mock tests for mathematics. These tests will help you assess your preparation, improve your time management, and identify areas where you need more practice.
8. Review and Revise:

• Periodically review the topics you’ve covered and revise your notes. Revision is crucial to retaining information and ensuring you don’t forget what you’ve learned.
9. Seek Clarification:

• If you encounter difficulties with specific topics, don’t hesitate to seek clarification from professors, mentors, or online communities. GATE mathematics can be challenging, and it’s important to address any doubts promptly.
10. Stay Healthy and Manage Stress:

• A healthy lifestyle is essential. Get adequate sleep, eat well, and incorporate regular exercise into your routine. Managing stress is crucial for optimal performance.
11. Plan for the Exam Day:

• Familiarize yourself with the exam center, rules, and regulations. Plan your travel and ensure you reach the center well before the exam starts.
12. Stay Consistent:

• Consistency is key in GATE preparation. Stay committed to your study plan, and avoid last-minute cramming.

• Keep an eye on updates and notifications from the GATE organizing institute. Rules, patterns, and syllabus may change from year to year.

Get the most common frequently asked questions on GATE Mathematics Syllabus 2024.

## When is the release date for the GATE 2024 Mathematics syllabus by the authorities?

The GATE Mathematics syllabus for 2024 has been unveiled alongside the official brochure.

## Is calculus encompassed within the GATE Mathematics syllabus?

Indeed, Calculus stands as one of the topics covered within the GATE syllabus for Mathematics.

## Who holds the responsibility for organising GATE 2024?

The Indian Institute of Science (IISc) Bangalore serves as the conducting body for GATE 2024.

## What comprises the GATE Mathematics syllabus for CSE?

The GATE Mathematics syllabus for Computer Science and Engineering (CSE) is outlined as follows.

## Can we anticipate any modifications in the GATE Engineering Mathematics syllabus?

No, there are no anticipated changes in the Engineering Mathematics Syllabus for 2024. The entirety of the syllabus is expected to remain unaltered...Read full

## What paper code corresponds to the GATE Mathematics Syllabus for 2023?

The paper code designated for the GATE Mathematics Syllabus is MA. Prospective candidates are advised to review the eligibility criteria before par...Read full