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# isical.ac.in ISI Admission Test JRF Computer Science Syllabus : Indian Statistical Institute

Organisation : Indian Statistical Institute
Announcement : Syllabus
Name of Examination : ISI Admission Test
Degree : JRF Junior Research Fellowship
Subject : Computer Science

## JRF Computer Science Syllabus :

GROUP A :
** Analytical reasoning.
** Basics of programming (using pseudo-code), elementary data structures (array, stack and queue).

Related : ISI Admission Test M.Tech QROR Syllabus Indian Statistical Institute : www.syllabus.gen.in/1241.html

** Basics of Set Theory, functions and relations.
** Basic combinatorics : basic counting, inclusion-exclusion principle, pigeonhole principle.
** Basic probability theory including conditional probability, Binomial distribution.

GROUP B :
Mathematics :
Graph theory and combinatorics : Graphs, paths and cycles, trees, Eulerian graphs, Hamiltonian graphs, chromatic numbers, planar graphs, digraphs and tournaments.

Linear algebra : Vector spaces, basis and dimension, orthogonality, linear transformations, matrices, rank, inverse, determinant, systems of linear equations, eigenvalues and eigenvectors, Cayley-Hamilton theorem, canonica forms, quadratic forms.

Abstract algebra : Groups, subgroups, products, cosets, Lagranges Theorem, group homomorphism, normal subgroups and quotient groups, permutation groups, Sylow theorems, rings, subrings, ring homomorphism, ideals and quotient rings, prime and maximal ideals, products

Chinese remainder theorem, integral domains, Prime and irreducible elements, elds, characteristic of a eld, polynomial rings, division algorithm, roots of polynomials, principal ideal domain, unique factorization domains, eld extensions, nite fields.

Elementary number theory : Elementary number theory, divisibility, congruences, primality.

Calculus and real analysis
: Real numbers, convergence of sequences and series, limits, continuity, uniform continuity of functions, dierentiability of functions, indenite integral, fundamental theorem of integral calculus, Riemann integration, improper integrals, sequences and series of functions, convergence.

Statistics :
Probability theory and distributions : Basic probability theory, discrete and continuous distributions, moments, characteristic functions, Markov chains.

Estimation and inference : Unbiased estimation, maximum likelihood estimation, suficiency, completeness, consistency of estimates, most powerful and uniformly most powerful tests, unbiased tests and uniformly most powerful unbiased tests, condence sets, Bayesian methods.

Linear models : Gauss-Markov set up and least squares theory, multiple linear regression, one and two way analysis of variance.
Multivariate analysis : Multiple and canonical correlations, multivariate normal distribution, principal component analysis, discriminant analysis.

Physics :
Classical mechanics : Lagrangian and Hamiltonian formulation of Newtonian mechanics, symmetries and conservation laws, motion in centraleld of force, small oscillations and normal modes, wave motion, special theory of relativity.

Electrodynamics : Electrostatics and magnetostatics, electric and magnetic phenomena in dielectrics, Maxwell’s equations, conservation laws, electromagnetic waves, optics.

Thermodynamics and statistical physics : Laws of thermodynamics, statistical basis of thermodynamics, thermodynamic potentials and Maxwell’s relations, density matrix formulation, ensembles, partition function, classical and quantum statistics, blackbody radiation and Planck’s distribution law.

Quantum physics : Basic postulates of quantum mechanics, Schrodinger equation, Exactly solvable Eigenvalue problems: Particle in a box, Potential well, Harmonic oscillator, Matrix mechanics: Creation and annihilation operators, Angular momentum algebra, Spin, Symmetries and conservation laws, Quantum particle in electromagnetic eld.

Atomic and nuclear physics : Energy spectrum of an electron in hydrogen atom, electron spin, relativistic correction, selection rules, Zeeman eect, Stark eect, basic nuclear properties, nuclear force, nuclear models, radioactive decays.