GATE 2019 NEWS

NATIONAL LEVEL ONLINE TEST

Mathematics includes the study of such topics as quantity, structure, space, and change. The question asked in GATE mathematics paper are based on formulas and graphs. **GATE Mathematics syllabus** includes the subject topics and general aptitude. There are total **24 papers** in GATE exam. The syllabus of each discipline is different.

GATE Syllabus | GATE Exam Pattern | GATE Paper Analysis |

**The syllabus**is based on the topics studied at graduation level.**85% of the questions are asked from core subject**and the remaining**15% questions are asked from general aptitude**section.- The question paper consists of
**65 questions worth 100 marks.**

**GATE 2019** will be scheduled from **February 02, 03, 09 and 10, 2019 **in multiple sessions. The paper is held in online mode (Computer Based Test). Candidates need to solve the paper in 3 hours. There is negative marking for every incorrect answer. In this article, we are providing the complete Mathematics syllabus for those candidates who appear for GATE Mathematics.

There are 11 chapters in GATE Syllabus for Mathematics paper. Each chapter has many subtopics. The complete syllabus of Mathematics paper is given below.

Chapter 1 – 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, Skew-Hermitian and unitary matrices; Finite dimensional inner product spaces, Gram-Schmidt orthonormalization process, self-adjoint operators, definite forms.

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.

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, compactness, completeness, Weierstrass approximation theorem; Lebesgue measure, measurable functions; Lebesgue integral, Fatou’s lemma, dominated convergence theorem.

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.

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, field extensions.

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.

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.

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.

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

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.

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.

**Check HereGATE Paper Analysis**

Mathematics section in **GATE** is considered as one of the toughest subjects so the preparation of it should be awesome. Books are the best option to prepare for any exam. That is why we are providing you soma good books for mathematics preparation. Hence, below is the table represents some important books for mathematics preparation in GATE exam:

Books | Author/Publisher |
---|---|

Chapterwise Solved Papers Mathematics GATE – 2018 | Suraj Singh, Arihant Publication |

GATE Engineering Mathematics for All Streams | Abhinav Goel, Arihant Publication |

GATE 2017: Engineering Mathematics | ME Team, Made Easy Publications |

Wiley Acing the Gate: Engineering Mathematics and General Aptitude | Anil K. Maini, Wiley |

Higher Engineering Mathematics | B.S. Grewal, Khanna Publishers |

**Also Check GATE Recommended Books**

Every candidate can apply for one stream among all the 24 papers. GATE exam is conducted in online mode (Computer based). The total weightage of the GATE Exam is 100 marks. **GATE Exam Pattern** is quite tricky as it varies for different disciplines.

Mode of Examination | Online/ Computer-based Test |

Total no. of questions | 65 |

Question Type | 2 types- Multiple Choice type (MCQ) and Numerical Answer Type (NAT). |

Maximum Marks | 100 |

Duration of Exam | 3 hours |

Sections in paper | Two, i.e. General Aptitude and Subject Specific |

**Note: **There is also Negative marking include for every wrong answer. But is no negative marking for **NAT** but it is applicable for **MCQs**. For 1 mark MCQs, 1/3 marks will be deducted for every wrong answer. Likewise, for 2 marks MCQs, 2/3 marks will be deducted

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