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Unformatted text preview: Test Code : RC (Short Answer Type) 2008 JRF in Computer and Communication Sciences The Candidates for Junior Research Fellowship in Computer Science and Communication Sciences will have to take two tests - Test MIII (objective type) in the forenoon session and Test RC (short answer type) in the after- noon session. The RC test booklet will have two groups as follows: GROUP A A test for all candidates in logical reasoning and basics of programming, carrying 20 marks. GROUP B A test, divided into five sections, carrying equal marks of 80 in the following areas at M.Sc./M.E./M.Tech. level: (i) Mathematics, (ii) Statistics, (iii) Physics, (iv) Radiophysics/ Telecommunication/ Electronics/ Electrical Engg., and (v) Computer Science. A candidate has to answer questions from only one of these sec- tions, according to his/her choice. The syllabi and sample questions of the RC test are given overleaf. 1 Syllabus Elements of Computing: Logical reasoning, basics of programming (using pseudo-codes), Elementary data types and arrays. Mathematics: Graph theory and combinatorics: Graphs and digraphs, paths and cycles, trees, Eulerian graphs, Hamiltonian graphs, chromatic numbers, planar graphs, tournaments, inclusion-exclusion principle, pigeon-hole principle. Linear programming: Linear programming, simplex method, duality. Linear algebra: Vector spaces, basis and dimension, linear transformations, matrices, rank, inverse, determinant, systems of linear equations, character- istic roots (eigen values) and characteristic vectors (eigen vectors), orthog- onality and quadratic forms. Abstract algebra: Groups, subgroups, cosets, Lagrange’s theorem, normal subgroups and quotient groups, permutation groups, rings, subrings, ideals, integral domains, fields, characteristic of a field, polynomial rings, unique factorization domains, field extensions, finite fields. Elementary number theory: Elementary number theory, divisibility, congru- ences, primality. Calculus and real analysis: Real numbers, basic properties, convergence of sequences and series, limits, continuity, uniform continuity of functions, differentiability of functions of one or more variables and applications, in- definite integral, fundamental theorem of calculus, Riemann integration, im- proper integrals, double and multiple integrals and applications, sequences and series of functions, uniform convergence. Differential equations: Solutions of ordinary and partial differential equa- tions and applications. Statistics: Probability Theory and Distributions: Basic probability theory, discrete and continuous distributions, moments, characteristic functions, Markov chains. Estimation and Inference: Sufficient statistics, unbiased estimation, max- imum likelihood estimation, consistency of estimates, most powerful and uniformly most powerful tests, unbiased tests and uniformly most powerful unbiased tests, confidence sets....
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- Winter '11
- Normal Distribution, probability density function, maximum likelihood estimator, Elementary number theory