# Gate Syllabus of Mathematics

**GATE** (Graduate Aptitude Test for Engineering ) is one of the toughest test, an all India Examination that basically test the comprehensive understanding of various undergraduate subjects in Engineering and Technology.

It has been known for testing the engineering basics in a smart way. It need the effort of mastering an entire course of engineering(30+ subjects) which gives it a level of toughness in itself.

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**Mathematics** has been defined by Aristotle as “the science of quantity”. It can be subdivided into the study of quantity, structure, space and change. Study of mathematics is important at the basic level as well as in its applied form. Whether its economics, consultancy or computer science mathematics is required for the execution of plans. Mathematical Science plays a lead role in order to compute inventory lapses. An Interested person can choose research or teaching line. Two Best places in India which offers a bachelor’s degree is Indian Statistical Institute & Bangalore and Chennai mathematical Institute. GATE Score can be of great benefit like it can be used to get into various Post-graduate programs in Indian Higher Education Institutes that too with financial help provided by** MHRD and other government agencies.** Go through the gate mathematics syllabus 2018 in detail.

**GATE syllabus of mathematics 2018:-**

**General Aptitude(GA)**-Multiple Choice Test

**This Paper Consists of Verbal Ability:**English grammar, verbal analogies, instructions, critical reasoning and verbal deduction,Sentence completion,Word groups

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**Mathematics-**

**Linear Algebra:****It consists of vector spaces as well as linear mappings****.**It include topics- Linear transformations; Finite dimensional vector spaces and their matrix representations, rank; systems of linear equations, eigen vectors and eigen values, minimal polynomial, Cayley-Hamilton Theroem, Hermitian, diagonalisation, Skew-Hermitian and unitary matrices; Gram-Schmidt orthonormalization process, Finite dimensional inner product spaces, self-adjoint operators.**Complex Analysis:Mathematical branch which investigates functions of complex numbers**.It include topics- Analytic functions, bilinear transformations; conformal mappings ;complex integration: Cauchy’s integral theorem and formula; Liouville’s theorem, maximum modulus principle; Laurent’s and Taylor’s series; residue theorem and applications for evaluating real integrals.**Real Analysis: Mathematical branch that deals with real numbers & the real valued functions of a real variable.**It include topics**–**Sequences and series of functions, power series, uniform convergence, Fourier series, functions of several variables, minima,maxima ; multiple integrals, Riemann integration, surface, line and volume integrals, theorems of Green, Gauss and stokes; metric spaces, completeness, Weierstrass approximation theorem, Lebesgue measure, compactness; measurable functions, Fatou’s lemma, Lebesgue integral ,dominated convergence theorem.**Ordinary Differential Equations:Equation which contains a function of one independent variable and its derivatives.**It include topics- First order ordinary differential equations, existence and uniqueness theorems, linear ordinary differential equations of higher order with constant coefficients; systems of linear first order ordinary differential equations; linear second order ordinary differential equations with variable coefficients; method of Laplace transforms for solving ordinary differential equations, Legendre and Bessel functions and their orthogonality; series solutions.**Algebra:It goes together with number theory,geometry and analysis.**It include topics- Normal subgroups and automorphisms; homomorphism theorems ; Group actions, Sylow’s theorems and their applications; Euclidean domains, unique factorization domains and Principle ideal domains .Prime ideals and maximal ideals in commutative rings; finite fields, Fields**Functional Analysis:Detail study of vector spaces equipped with some kind of limit-related structure and the linear operators which act upon these spaces**.It include topics- Hahn-Banach extension theorem, Banach spaces ,open mapping and closed graph theorems, Hilbert spaces, principle of uniform boundedness ,orthonormal bases, Riesz representation theorem, bounded linear operators.

Gate mathematics syllabus

**Numerical Analysis:Study of step by step approach which uses numerical approximation to deal with the difficulties of mathematical analysis.**It include topics- Numerical solution of algebraic and transcendental equations: secant method, bisection ,Newton-Raphson method, fixed point iteration; interpolation: Lagrange ;error of polynomial interpolation, Newton interpolations; numerical differentiation; numerical integration: Trapezoidal and Simpson rules, Gauss Legendre quadrature, least square polynomial approximation; method of undetermined parameters ;numerical solution of systems of linear equations: direct methods (LU decomposition ,Gauss elimination,); iterative methods ( Gauss-Seidel and Jacobi ); matrix eigen value problems: power method, numerical solution of ordinary differential equations: initial value problems: Euler’s method, Runge-Kutta methods, Taylor series methods.**Partial Differential Equations: It contains unknown multivariable functions & partial derivatives.**It include topics- Linear and quasi linear first order partial differential equations, method of characteristics; second order linear equations in two variables and their classification; Dirichlet ,Cauchy and Neumann problems; solutions of Laplace, diffusion and wave equations in two variables; Fourier transform, Fourier series and Laplace transform methods of solutions for the above equations.**Mechanics:****It uses physical reasoning to find answer to problems.**It include topics- Lagrange’s equations for holonomic systems, Virtual work, Hamiltonian equations.**Topology:Study of shapes and spaces.**It include topics- Basic concepts of topology, connectedness, product topology, compactness, countability and separation axioms, Urysohn’s Lemma.**Probability and Statistics:**It include topics-**Probability is the way to roughly judge the occurance of a thing or to what extent a statement is true.***,*X^{2}^{ }, t,*F*– distributions; Linear regression; Interval estimation.**Linear programming:It is also referred as Linear optimization to find out the best result or outcome.**It include topics**–**Linear programming problem and its formulation, convex sets and their properties, basic feasible solution, graphical method ,simplex method, big-M and two phase methods; unbounded LPP’s and infeasible , alternate optima; Dual problem and duality theorems, dual simplex method and its application in post optimality analysis; unbalanced and balanced transportation problems, Hungarian method for solving assignment problems, u -u method for solving transportation problems.**Calculus of Variation and Integral Equations:Field that deals with maximizing or minimizing functionals which are diagramatically represented from a set of functions to the real numbers.**It include topics-

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