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 
• Saddle Point 
• 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
• Bilinear And Quadratic Forms

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