Organisation : Indian Statistical Institute
Announcement : Syllabus
Name of Examination : ISI Admission Test
Subject : M.Maths
Home Page : http://www.isical.ac.in/
Download Syllabus :
MMA : http://www.syllabus.gen.in/uploads/1223-MMA.pdf
PMB : http://www.syllabus.gen.in/uploads/1223-MMath-PMB.pdf
M.Maths Syllabus :
MMA : (Objective type)
Analytical Reasoning :
Algebra : Arithmetic, geometric and harmonic progression. Continued fractions. Elementary combinations : Permutations and combinations, Binomial theorem.
Related : ISI Admission Test M.Statistics Syllabus Indian Statistical Institute : www.syllabus.gen.in/1219.html
Theory of equations. Inequalities. Complex numbers and De Moivre’s theorem. Elementary set theory. Functions and relations.
Elementary number theory: Divisibility, Congruences, Primality. Algebra of matrices. Determinant, rank and inverse of a matrix. Solutions of linear equations. Eigenvalues and eigenvectors of matrices.
Basic group theory: subgroups, cosets, cyclic groups,homomorphisms, normal subgroups, quotient groups, isomorphism ofgroups.
Coordinate geometry : Straight lines, circles, parabolas, ellipses and hyperbolas.
Calculus : Sequences and series: Power series, Taylor and Maclaurin series. 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 several variables – limits, continuity, differentiability. Double integrals and their applications. Ordinary linear differential equations.
Elementary discrete probability theory : Combinatorial probability, Conditional probability, Bayes theorem. Binomial and Poisson distributions.
PMB : (Afternoon Session)
** Countable and uncountable sets;
** equivalence relations and partitions;
** convergence and divergence of sequence and series;
** Cauchy sequence and completeness;
** Bolzano-Weierstrass theorem;
** continuity, uniform continuity, differentiability, Taylor Expansion;
** partial and directional derivatives, Jacobians;
** integral calculus of one variable – existence of Riemann integral,
** fundamental theorem of calculus, change of variable, improper integrals;
** elementary topological notions for metric spaces – open, closed and
** compact sets, connectedness, continuity of functions;
** sequence and series of functions;
** elements of ordinary differential equations.
** Vector spaces, subspaces, basis, dimension, direct sum;
** matrices, systems of linear equations, determinants;
** diagonalization, triangular forms;
** linear transformations and their representation as matrices;
** groups, subgroups, quotient groups, homomorphisms, products,
** Lagrange’s theorem, Sylow’s theorems;
** rings, ideals, maximal ideals, prime ideals, quotient rings,
** integral domains, Chinese remainder theorem, polynomial rings, fields.
** Elementary discrete probability theory : Combinatorial probability, Conditional probability, Bayes’ Theorem. Binomial and Poisson distributions