GATE MATHEMATICS 2016

GATE MATHEMATICS 2015 INFORMATION BROCHURE

The Graduate Aptitude Test in Engineering (GATE) is an all-India examination that basically tests the complete understanding of various undergraduate subjects in engineering and science. GATE is conducted jointly by the Indian Institute of Science, Bangalore and the seven Indian Institutes of Technology on behalf of the National Coordination Board – GATE, Department of Higher Education, Ministry of Human Resources Development (MHRD), Government of India.

The GATE score of a candidate reflects the relative performance level of a candidate. The score is used for admissions to various post-graduate programs (e.g. Master of Engineering, Master of Technology, Doctor of Philosophy) in Indian higher education institutes, with financial assistance provided by MHRD and other government agencies. Recently, GATE scores are also being used by several Indian public and private sector undertakings for recruiting graduates in entry-level positions. It is one of the most competitive examinations in India.

The Indian Institute of Science (IISc) and seven Indian Institutes of Technology (IITs at Bombay, Delhi, Guwahati, Kanpur, Kharagpur, Madras and Roorkee) jointly conduct the GATE. The Organizing Institute (OI) is responsible for the end-to-end process and coordination amongst the administering  Institutes. The Organizing Institute for GATE 2015 is IIT Kanpur.

1) Important dates related to GATE 2015:

2) Duration and Examination Type:

The GATE MATHEMATICS examination consists of a single paper of 3-hour duration that contains 65 questions carrying a maximum of 100 marks. The question paper will consist of both multiple choice questions (MCQ) and numerical answer type questions. The examination for all the papers will be carried out in an ONLINE Computer Based Test (CBT) mode where the candidates will be shown the questions in a random  sequence on a computer screen. The candidates are required to either select the answer  (for MCQ type) or enter the answer for numerical answer type question using a mouse on a virtual keyboard (keyboard of the computer will be disabled). Candidates will be  provided with scribble pad for rough work and these have to be returned back after the examination. At the end of the 3-hour window, the computer will automatically close the screen from further actions.

3) Pattern of Question Papers:

In all the papers, there will be a total of 65 questions carrying 100 marks, out of which 10 questions carrying a total of 15 marks are in General Aptitude (GA). The General Aptitude section will carry 15% of the total marks and the remaining 85% of the total  marks is devoted to the subject of the paper.

GATE MATHEMATICS 2015 would contain questions of two different types in various papers:

(i) Multiple Choice Questions (MCQ) carrying 1 or 2 marks each in all papers and  sections. These questions are objective in nature, and each will have a choice of four  answers, out of which the candidate has to mark the correct answer(s).

(ii) Numerical Answer Questions of 1 or 2 marks each in all papers and sections. For these questions the answer is a real number, to be entered by the candidate using the virtual keypad. No choices will be shown for this type of questions.

4) Marking Scheme:

For 1-mark multiple-choice questions, 1/3 marks will be deducted for a wrong answer. Likewise, for 2-mark multiple-choice questions, 2/3 marks will be deducted for a wrong answer. There is NO negative marking for numerical answer type questions.

            NO negative marking for a wrong answer in numerical answer type questions.

GATE Questions:

GA questions carry a total of 15 marks. The GA section includes 5 questions carrying 1-mark each (sub-total 5 marks) and 5 questions carrying 2-marks each (sub-total 10 marks).

The GATE MATHEMATICS paper would contain 25 questions carrying 1-mark each (sub-total 25 marks) and 30 questions carrying 2-marks each (sub-total 60 marks). The question paper will consist of questions of multiple choice and numerical answer type. For numerical answer questions, choices will not be given. Candidates have to enter the answer (which will be a real number, signed or unsigned, e.g., 25.06, -25.06, 25, -25 etc.) using a virtual keypad. An appropriate range will be considered while evaluating the numerical answer type questions so that the candidate is not penalized due to the usual round-off errors.

5) GATE MATHEMATICS Syllabus:

5.1) General Aptitude (GA):

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

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

5.2) Mathematics (MA):

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.

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.

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.

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.

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.

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.

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 Legendrequadrature, 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.

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.

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

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

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.

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 -u method for solving transportation problems; Hungarian method for solving assignment problems.

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.

6) GATE MATHEMATICS 2015 Results:

GATE 2015 results will be announced on March 12, 2015 at 17:00 hrs and will be available on the GATE Online Application Website. GATE 2015 score is valid for THREE YEARS from the date of announcement of the results.

7) GATE MATHEMATICS 2015 Score Card:

After the declaration of the results, candidates can download their GATE MATHEMATICS 2015 Score Card. Downloadable score cards will be available to only those candidates whose marks are equal to or above the qualifying marks of SC/ST/PwD candidates in that paper. The GATE 2015 score cards can be downloaded between March 27, 2015 to May 29, 2015 and for that the candidate should access the zonal websites from where he/she has taken the GATE 2015 examination.

In case any candidate requires the soft copy of his/her GATE Score Card after May 29, 2015 till December 31, 2015, then they can do so by sending a demand draft of 500 (five hundred only) in the name of Chairman GATE, payable at Kanpur and send to GATE Office, IIT Kanpur.