# GATE MATHEMATICS COACHING

* GATE MATHEMATICS COACHING *:-We At CSR Mathematics Have Constantly Been Producing Top Ranker And Scholarship Holders In Exams Like IAS, CSIR UGC NET/JRF Mathematics, GATE Maths, IIT-JAM Mathematics, MSc/BSc Maths Entrance, TIFR, DRDO, BARC, JNU Ph.D.

### GATE MATHEMATICS COACHING

# Important Dates

GATE Online Application Processing System (GOAPS) Website Opens |
Friday |
01^{st} September 2017 |

Last Date for Submission of (Online) Application (through Website) | Monday | 09^{th} October 201720:00 Hrs (IST) |

Last Date for Requesting Change of Examination City (an additional fee will be applicable) | Friday | 17^{th} November 2017 |

Admit Card will be available in the Online Application Portal (for printing) | Friday | 05^{th} January 2018 |

GATE 2018 ExaminationForenoon: 9:00 AM to 12:00 Noon Afternoon: 2:00 PM to 5:00 PM |
Saturday Sunday Saturday Sunday |
03^{rd} February 201804 ^{th} February 201810 ^{th} February 201811 ^{th} February 2018 |

Announcement of the Results in the Online Application Portal | Saturday | 17^{th} March 2018 |

**GATE SYLLABUS AND RECOMMENDED BOOKS BY CSR MATHEMATICS**

## GATE MATHEMATICS COACHING

** **

**GENERAL APTITUDE (GA)**

**(Common to all papers)**

## GATE MATHEMATICS COACHING

**Verbal Ability-**

**Verbal Ability-**

English grammar, sentence completion, verbal analogies, word groups, instructions, critical reasoning and verbal deduction.

**Numerical Ability-**

**Numerical Ability-**

Numerical computation, numerical estimation, numerical reasoning and data interpretation.

Mathematics (MA)

**Linear Algebra-**

**Linear Algebra-**

Finite dimensional vector spaces; Linear transformations and their matrix representations, rank; systems of linear equations, eigen values and eigen vectors, minimal polynomial, Cayley-Hamilton Theroem, diagonalisation, Hermitian, Skew-Hermitian and unitary matrices; Finite dimensional inner product spaces, Gram-Schmidt orthonormalization process, self-adjoint operators.

**(CSR RECOMMENDED BOOKS)**

Linear Algebra -Schaum’s Series -(Tata McGraw-Hill Publication)Linear Algebra -Kenneth M Hoffman Ray Kunzet(PHI Publication)Linear Algebra -Vivek Sahai, Vikas Bist(Narosa Publication)

**Real Analysis-**

**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 and Gauss; metric spaces, completeness, Weierstrass approximation theorem, compactness; Lebesgue measure, measurable functions; Lebesgue integral, Fatou’s lemma, dominated convergence theorem.

**(CSR RECOMMENDED BOOKS)**

Principle of Mathematical Analysis -S.L. Gupta, N.R. Gupta(Pearson Publication)Real Analysis -Robert G Bartle(Wiley Publication)Real Analysis -M.D. Raisinghania(S. Chand Publication)

**Complex Analysis-**

**Complex Analysis-**

Analytic functions, conformal mappings, bilinear transformations; complex integration: Cauchy’s integral theorem and formula; Liouville’s theorem, maximum modulus principle; Taylor and Laurent’s series; residue theorem and applications for evaluating real integrals.

**(CSR RECOMMENDED BOOKS)**

Complex Variables -H.S. Kasana(PHI Publication )Complex Analysis -S Ponnusamy(Narosa Publication)Complex Analysis -R.V. Churchill(Tata McGraw – Hill Publication.gate maths coaching

**Algebra-**

**Algebra-**

Normal subgroups and homomorphism theorems, automorphisms; Group actions, Sylow’s theorems and their applications; Euclidean domains, Principle ideal domains and unique factorization domains. Prime ideals and maximal ideals in commutative rings; Fields, finite fields.

**(CSR RECOMMENDED BOOKS)**

Contemporary Abstract Algebra -Joseph A. Gallian(Narosa Publication )Modren Algebra -Surjeet Singh and Qazi Zameeruddin(Vikas Publication)gate maths coaching

**Ordinary Differential Equations-**

**Ordinary Differential Equations-**

First order ordinary differential equations, existence and uniqueness theorems, 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; Legendre and Bessel functions and their orthogonality.

**(CSR RECOMMENDED BOOKS)**

Ordinary Differential Equations -MD Rai Singhania( S.Chand Publication )Differential Equations -Shepley L. Ross(Wiley Publication )Differential Equations -Earl Codington(PHI Publication )gate maths coaching

**Functional Analysis-**

**Functional Analysis-**

Banach spaces, Hahn-Banach extension theorem, open mapping and closed graph theorems, principle of uniform boundedness; Hilbert spaces, orthonormal bases, Riesz representation theorem, bounded linear operators.

**Partial Differential Equations-**

**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 and diffusion equations in two variables; Fourier series and Fourier transform and Laplace transform methods of solutions for the above equations.

**(CSR RECOMMENDED BOOKS)**

Partial Differential Equations -T. Amaranath(Narosa Publication )Introduction To Partial Differential Equations -K. Sankara Rao(PHI Publication.gate maths coaching

**Numerical Analysis-**

**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, Gauss Legendre quadrature, method of undetermined parameters; least square polynomial approximation; numerical solution of systems of linear equations: direct methods (Gauss elimination, LU decomposition); iterative methods (Jacobi and Gauss-Seidel); matrix eigenvalue problems: power method, numerical solution of ordinary differential equations: initial value problems: Taylor series methods, Euler’s method, Runge-Kutta methods.

**(CSR RECOMMENDED BOOKS)**

Numerical Analysis -R.K. Jain, S.R.K. Iyengar(New Age Publication)gate maths coaching

**Topology-**

**Topology-**

Basic concepts of topology, product topology, connectedness, compactness, countability and separation axioms, Urysohn’s Lemma.

**(CSR RECOMMENDED BOOKS)**

Topology -K. D. Joshi(New Age International Publication)gate maths coaching

**Mechanics-**

**Mechanics-**

Virtual work, Lagrange’s equations for holonomic systems, Hamiltonian equations.

**Probability and Statistics-**

**Probability and Statistics-**

Probability space, conditional probability, Bayes theorem, independence, Random variables, joint and conditional distributions, standard probability distributions and their properties, expectation, conditional expectation, moments; Weak and strong law of large numbers, central limit theorem; Sampling distributions, UMVU estimators, maximum likelihood estimators, Testing of hypotheses, standard parametric tests based on normal, X2 , t, F – distributions; Linear regression; Interval estimation.gate maths coaching

**(CSR RECOMMENDED BOOKS)**

Probablity and statistics-S. C. Gupta and V. K. Kapoor(S.Chand Publication )

**Calculus of Variation and Integral Equations-**

**Calculus of Variation and Integral Equations-**

Variation problems with fixed boundaries; sufficient conditions for extremum, linear integral equations of Fredholm and Volterra type, their iterative solutions.

**Linear programming-**

**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, u -v method for solving transportation problems; Hungarian method for solving assignment problems.

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