JRF Physics, M.Tech Computer Science ISI Kolkata Entrance Syllabus

ISI Kolkata M.Tech Computer Science, M.Tech (QROR), JRF (CS), JRF(QROR), JRF (Physics & Applied Mathematics) Entrance Syllabus

Analytical Reasoning

Algebra – Arithmetic, Geometric and Harmonic Progression. Continued fractions, Permutations and Combinations, Binomial theorem. Theory of equations. Inequalities. Complex numbers and De Moivre’s theorem. Elementary Set Theory. Functions and relatins. Elementary Number Theory : divisibility, congruence, primality. Matrices : determinant, rank and inverse, properties of symmetric and idempotent matrices, Eigenvalues and eigenvectors, quadratic forms. System of linear equations. Basic properties of a group.

Coordinate Geometry – Straight line, Circle, Parabola, Ellipse and Hyperbola.

Calculus – Sequences and its properties. Series : Power series, Taylor series and Maclaurin series, convergence. Limits and continuity of functions of one variable. Differentiation and integration of functions of one variable with applications. Definite integrals. Maxima and minima. Functions of serveral variables : limits, continuity, differentiability. Double integrals and their applications. Ordinary linear differential equations.

Elementary discrete probability theory – Combinatorial probability, Conditinal probability, Bayes theorem. Binomial and Poisson distributions.