This course will be very challenging and loaded with very tough assignments. So if you feel that you don’t have time for some advanced level coursework and you already feel burdened with your semester syllabus then this course is not for you.

We will be covering the syllabus of I.S.I. M.Math/M.Stat entrance and focus on the subjective problems from some of the standard books and in parallel, we will focus on the MCQ problems which will help the students in the first paper of the entrance exam and also in other exams like TIFR, IITJAM, etc.

Every week we meet for 4 hours for learning and then there are assignments every week, and we will periodically take tests to evaluate your progress.

For further details, you can contact Arkabrata Das, Phone no.- +91-8247590347, Whatsapp no.-+91-9700803692.

I myself have cracked ISI M.Math exam in the year 2015, so I will be sharing my experience with you all.
https://www.isical.ac.in/~deanweb/MMATHINTLIST2015.pdf

First, let’s talk about I.S.I. M.Math/M.Stat, the syllabus has recently changed from the year 2019. The first part i.e. the PMA/PSA section will no longer have questions from 10+2 level, now the mcqs will be mostly from college-level mathematics. The syllabus mainly focuses on the real analysis part from where half of the questions come in the subjective paper and the other half comes from linear algebra and abstract algebra for M.Math and also for the M.Stat we separately focus on the Statistics part. For real analysis start reading Introduction to Real Analysis by Robert G. Bartle & Donald R. Sherbert and then when you are done with your basics go for these two books Mathematical Analysis by Tom Apostol and Principles of Mathematical Analysis by Walter Rudin. One will help you with a much better theory coverage and the latter one will have superb exercises. That’s what even I did when I was preparing for the exam. Then there is a part from metric space for which the book Topology of Metric Spaces by S. Kumaresan is the best with some nice examples and exercises and which will help you to solve the continuity problems from the book by Walter Rudin. You will have added advantage if you know complex analysis and topology.
Coming to the algebra part, you have one of the best video lecture series by Gilbert Strang from MIT which is available on youtube. You can read the book Introduction to Linear Algebra by Serge Lang, and solve its exercises. This book has a different approach in Linear algebra and the eigenvalue exercise will have some questions which will be easier to solve if you had followed the approach of the book for eigenvalues. Solve the exercises from Linear Algebra by Hoffman & Kunze.
For the abstract part, the best book is Abstract Algebra by David S. Dummit and Richard M. Foote, if you can cover this book then you are very much done, but for starters, I would suggest Topics in algebra by Israel Nathan Herstein and Contemporary Abstract Algebra by Gallian. You will feel like reading a storybook when you read the book by I.N. Herstein, the book has used group action to prove many things but hasn’t used the word, “Group Action” and also the challenging problems in the exercises will be thrilling. The book by Gallian will have most of the theories covered and the exercises will help you clear your fundamentals.

For Probability Theory follow A First Course in Probability by Sheldon Ross, and for statistics follow Statistical Inference by Casella Berger, Mathematical Statistics and Data Analysis by J.A.Rice.

Along with these solve the previous year’s papers and this will be enough for your written exam as well as the interview if you get a chance. 

For ISI M.Math:
Test Codes: PMA (Multiple-choice Type) and
PMB (ShortAnswerType).

Questions will be set on the following and related topics.

• 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.

For M.Stat:

Test Codes: PSA (Multiple-choice Type) and
PSB (ShortAnswerType).

Mathematics Arithmetic, geometric and harmonic progressions. Trigonometry. Two-dimensional coordinate geometry: Straight lines, circles, parabolas, ellipses, and hyperbolas. Elementary set theory. Functions and relations. Elementary combinatorics: Permutations and combinations, Binomial and multinomial theorem. Theory of equations. Complex numbers and De Moivre’s theorem. Vector spaces. Determinant, rank, trace, and inverse of a matrix. System of linear equations. Eigenvalues and eigenvectors of matrices. Limit and continuity of functions of one variable. Differentiation and integration. Applications of differential calculus, maxima, and minima. Statistics and Probability Notions of sample space and probability. Combinatorial probability. Conditional probability and independence. Bayes Theorem. Random variables and expectations. Moments and moment generating functions. Standard univariate discrete and continuous distributions. Distribution of functions of a random variable. Distribution of order statistics. Joint probability distributions. Marginal and conditional probability distributions. Multinomial distribution. Bivariate normal and multivariate normal distributions. Sampling distributions of statistics. Statement and applications of Weak law of large numbers and Central limit theorem. Descriptive statistical measures. Pearson product-moment correlation and Spearman’s rank correlation. Simple and multiple linear regression. 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. Basic experimental designs such as CRD, RBD, LSD and their analyses. ANOVA. Elements of factorial designs. Conventional sampling techniques (SRSWR/SRSWOR) including stratification.