Syllabus of ISI M.STAT Entrance Exam

MMA Paper

Analytical Reasoning

Algebra | Arithmetic, geometric and harmonic progression. Continued fractions. Elementary combinatorics: Permutations and combinations, Binomial theorem. 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. Simple properties of a group.

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. Di erentiation and integration of

functions of one variable with applications. De nite integrals. Maxima and minima.

Functions of several variables - limits, continuity, di erentiability. Double integrals

and their applications. Ordinary linear di erential equations.

Elementary discrete probability theory | Combinatorial probability, Conditional probability, Bayes theorem. Binomial and Poisson distributions.

Test Code PSB (Short answer type)Syllabus for Mathematics

Combinatorics; Elements of set theory. Permutations and combinations.

Binomial and multinomial theorem. Theory of equations. Inequalities.

Linear Algebra: Vectors and vector spaces. Matrices. Determinants. Solution of linear equations. Trigonometry. Co-ordinate geometry.

Complex Numbers: Geometry of complex numbers and De Moivres theorem.

Calculus: Convergence of sequences and series. Functions. Limits and continuity of functions of one or more variables. Power series. Diﬀerentiation.

Leibnitz formula. Applications of diﬀerential calculus, maxima and minima.

Taylor’s theorem. Diﬀerentiation of functions of several variables. Indeﬁnite

integral. Fundamental theorem of calculus. Riemann integration and properties. Improper integrals. Double and multiple integrals and applications.

Syllabus for Statistics and Probability

Probability and Sampling Distributions: Notions of sample space

and probability. Combinatorial probability. Conditional probability

and independence. Random variables and expectations. Moments and

moment generating functions. Standard univariate discrete and continuous distributions. Joint probability distributions. Multinomial distribution. Bivariate normal and multivariate normal distributions. Sampling distributions of statistics. Weak law of large numbers. Central

limit theorem.

Descriptive Statistics: Descriptive statistical measures. Contingency tables and measures of association. Product moment and other

types of correlation. Partial and multiple correlation. Simple and multiple linear regression.

Statistical Inference: Elementary theory of estimation (unbiasedness, minimum variance, suﬃciency). Methods of estimation (maximum likelihood method, method of moments). Tests of hypotheses

(basic concepts and simple applications of Neyman-Pearson Lemma).

Conﬁdence intervals. Inference related to regression. ANOVA. Elements of nonparametric inference.

Design of Experiments and Sample Surveys: Basic designs such

as CRD, RBD, LSD and their analyses. Elements of factorial designs. Conventional sampling techniques (SRSWR/SRSWOR) including stratiﬁcation. Ratio and regression methods of estimation.

MMA Paper

Analytical Reasoning

Algebra | Arithmetic, geometric and harmonic progression. Continued fractions. Elementary combinatorics: Permutations and combinations, Binomial theorem. 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. Simple properties of a group.

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. Di erentiation and integration of

functions of one variable with applications. De nite integrals. Maxima and minima.

Functions of several variables - limits, continuity, di erentiability. Double integrals

and their applications. Ordinary linear di erential equations.

Elementary discrete probability theory | Combinatorial probability, Conditional probability, Bayes theorem. Binomial and Poisson distributions.

Test Code PSB (Short answer type)Syllabus for Mathematics

Combinatorics; Elements of set theory. Permutations and combinations.

Binomial and multinomial theorem. Theory of equations. Inequalities.

Linear Algebra: Vectors and vector spaces. Matrices. Determinants. Solution of linear equations. Trigonometry. Co-ordinate geometry.

Complex Numbers: Geometry of complex numbers and De Moivres theorem.

Calculus: Convergence of sequences and series. Functions. Limits and continuity of functions of one or more variables. Power series. Diﬀerentiation.

Leibnitz formula. Applications of diﬀerential calculus, maxima and minima.

Taylor’s theorem. Diﬀerentiation of functions of several variables. Indeﬁnite

integral. Fundamental theorem of calculus. Riemann integration and properties. Improper integrals. Double and multiple integrals and applications.

Syllabus for Statistics and Probability

Probability and Sampling Distributions: Notions of sample space

and probability. Combinatorial probability. Conditional probability

and independence. Random variables and expectations. Moments and

moment generating functions. Standard univariate discrete and continuous distributions. Joint probability distributions. Multinomial distribution. Bivariate normal and multivariate normal distributions. Sampling distributions of statistics. Weak law of large numbers. Central

limit theorem.

Descriptive Statistics: Descriptive statistical measures. Contingency tables and measures of association. Product moment and other

types of correlation. Partial and multiple correlation. Simple and multiple linear regression.

Statistical Inference: Elementary theory of estimation (unbiasedness, minimum variance, suﬃciency). Methods of estimation (maximum likelihood method, method of moments). Tests of hypotheses

(basic concepts and simple applications of Neyman-Pearson Lemma).

Conﬁdence intervals. Inference related to regression. ANOVA. Elements of nonparametric inference.

Design of Experiments and Sample Surveys: Basic designs such

as CRD, RBD, LSD and their analyses. Elements of factorial designs. Conventional sampling techniques (SRSWR/SRSWOR) including stratiﬁcation. Ratio and regression methods of estimation.