- GATE SYLLABUS
- GATE Syllabus - Home
- GATE - General Aptitude
- GATE - Aerospace Engineering
- GATE - Agricultural Engineering
- GATE - Architecture and Planning
- GATE - Biotechnology
- GATE - Biomedical
- GATE - Chemical Engineering
- GATE - Chemistry
- GATE - Civil Engineering
- GATE - Computer Science & IT
- GATE - Ecology and Evolution
- GATE - Electrical Engineering
- Electronics & Communications
- GATE - Geology and Geophysics
- GATE - Instrumental Engineering
- GATE - Mathematics
- GATE - Mechanical Engineering
- GATE - Metallurgical Engineering
- GATE - Mining Engineering
- GATE - Petroleum Engineering
- GATE - Physics
- Production & Industrial Engineering
- Textile Engineering & Fibre Science
- PART I – ENGINEERING SCIENCE (XE)
- GATE - Engineering Mathematics
- GATE - Fluid Mechanics
- GATE - Materials Science
- GATE - Solid Mechanics
- GATE - Thermodynamics
- Polymer Science and Engineering
- GATE - Food Technology
- Atmospheric & Ocean Science
- PART II – LIFE SCIENCE (XL)
- GATE - Chemistry
- GATE - Biochemistry
- GATE - Botany
- GATE - Microbiology
- GATE - Zoology
- GATE - Food Technology
GATE Mathematics Syllabus
Subject Code: MA
Course Structure
Sections/Units | Topics |
---|---|
Section A | Linear Algebra |
Section B | Complex Analysis |
Section C | Real Analysis |
Section D | Ordinary Differential Equations |
Section E | Algebra |
Section F | Functional Analysis |
Section G | Numerical Analysis |
Section H | Partial Differential Equations |
Section I | Topology |
Section J | Probability and Statistics |
Section K | Linear programming |
Course Syllabus
Section A: Linear Algebra
- Finite dimensional vector spaces
- Linear transformations and their matrix representations −
- Rank
- Systems of linear equations
- Eigenvalues and eigenvectors
- Minimal polynomial
- Cayley-hamilton theorem
- Diagonalization
- Jordan-canonical form
- Hermitian
- Skewhermitian
- Unitary matrices
- Finite dimensional inner product spaces −
- Gram-Schmidt orthonormalization process
- Self-adjoint operators, definite forms
Section B: Complex Analysis
- Analytic functions, conformal mappings, bilinear transformations
- complex integration −
- Cauchy’s integral theorem and formula
- Liouville’s theorem
- Maximum modulus principle
- Zeros and singularities
- Taylor and Laurent’s series
- Residue theorem and applications for evaluating real integrals
Section C: Real Analysis
- Sequences and series of functions −
- Uniform convergence
- Power series
- Fourier series
- Functions of several variables
- Maxima
- Minima
- Riemann integration −
- Multiple integrals
- Line
- Surface and volume integrals
- Theorems of green
- Stokes
- Gauss
- Metric spaces −
- Compactness
- Completeness
- Weierstrass approximation theorem
- Lebesgue measure −
- Measurable functions
- Lebesgue integral −
- Fatou’s lemma
- Dominated convergence theorem
Section D: Ordinary Differential Equations
First order ordinary differential equations −
Existence and uniqueness theorems for initial value problems
Systems of linear first order ordinary differential equations
Linear ordinary differential equations of higher order with constant coefficients
Linear second order ordinary differential equations with variable coefficients
Method of Laplace transforms for solving ordinary differential equations, series solutions (power series, Frobenius method)
Legendre and Bessel functions and their orthogonal properties
Section E: Algebra
Groups, subgroups, normal subgroups, quotient groups and homomorphism theorems
Automorphisms
Cyclic groups and permutation groups
Sylow’s theorems and their applications
Rings, ideals, prime and maximal ideals, quotient rings, unique factorization domains, Principle ideal domains, Euclidean domains, polynomial rings and irreducibility criteria
Fields, finite fields, and field extensions
Section F: Functional Analysis
- Normed linear spaces
- Banach spaces
- Hahn-Banach extension theorem
- Open mapping and closed graph theorems
- Principle of uniform boundedness
- Inner-product spaces
- Hilbert spaces
- Orthonormal bases
- Riesz representation theorem
- Bounded linear operators
Section G: Numerical Analysis
- Numerical solution of algebraic and transcendental equations −
- Bisection
- Secant method
- Newton-Raphson method
- Fixed point iteration
- Interpolation −
- Error of polynomial interpolation
- Lagrange, newton interpolations
- Numerical differentiation
- Numerical integration −
- Trapezoidal and Simpson Rules
- Numerical solution of systems of linear equations −
- Direct methods (Gauss Elimination, Lu Decomposition)
- Iterative methods (Jacobi and Gauss-Seidel)
- Numerical solution of ordinary differential equations
- Initial value problems −
- Euler’s method
- Runge-Kutta methods of order 2
Section H: Partial Differential Equations
Linear and quasilinear first order partial differential equations −
Method of characteristics
Second order linear equations in two variables and their classification
Cauchy, Dirichlet and Neumann problems
Solutions of Laplace, wave in two dimensional Cartesian coordinates, interior and exterior Dirichlet problems in polar coordinates
Separation of variables method for solving wave and diffusion equations in one space variable
Fourier series and Fourier transform and Laplace transform methods of solutions for the above equations
Section I: Topology
- Basic concepts of topology
- Bases
- Subbases
- Subspace topology
- Order topology
- Product topology
- Connectedness
- Compactness
- Countability
- Separation axioms
- Urysohn’s lemma
Section J: Probability and Statistics
Probability space, conditional probability, Bayes theorem, independence, Random
Variables, joint and conditional distributions, standard probability distributions and their properties (Discrete uniform, Binomial, Poisson, Geometric, Negative binomial, Normal, Exponential, Gamma, Continuous uniform, Bivariate normal, Multinomial), expectation, conditional expectation, moments
Weak and strong law of large numbers, central limit theorem
Sampling distributions, UMVU estimators, maximum likelihood estimators
Interval estimation
Testing of hypotheses, standard parametric tests based on normal, distributions
Simple linear regression
Section H: Linear programming
Linear programming problem and its formulation, convex sets and their properties, graphical method, basic feasible solution, simplex method, Big-M and two phase methods
Infeasible and unbounded LPP’s, alternate optima
Dual problem and duality theorems, dual simplex method and its application in post optimality analysis
Balanced and unbalanced transportation problems, Vogel’s approximation method for solving transportation problems
Hungarian method for solving assignment problems
To download pdf Click here.