ISI and CMI Entrance Course 2027: B.Stat, B.Math and BSc Mathematics

The ISI and CMI entrance in one paragraph

The Indian Statistical Institute (ISI) and the Chennai Mathematical Institute (CMI) run the two hardest undergraduate mathematics entrances in India. ISI admits to B.Stat (Kolkata) and B.Math (Bangalore); CMI admits to BSc Mathematics and Computer Science and BSc Mathematics and Data Science. Both papers are written in May, both have an objective section and a subjective section, and both reward a kind of mathematics that school does not teach: you are asked to prove things, to construct counterexamples, and to solve problems you have never seen before. A student who has only practised board-exam questions will not pass, however strong their marks.

Who this course is for

This is a course for students in Class 11 and Class 12, and for droppers taking a second attempt, who intend to sit ISI and CMI in May 2027. You do not need olympiad medals to join. You do need genuine comfort with Class 10 algebra and geometry, and the willingness to spend time on a single problem without being told the method first. Students who have done RMO or INMO will find the first weeks familiar; students who have not will be brought up to that level deliberately.

What the papers actually demand

ISI B.Stat and B.Math

Paper 1 is UGA, thirty objective questions in two hours. Paper 2 is UGB, eight to ten subjective problems in two hours, of which you are expected to write complete solutions to a handful. The objective paper punishes slow arithmetic and rewards recognising structure. The subjective paper is marked on the proof, not the answer: a correct final number with no argument earns very little.

CMI

Part A is objective and short-answer. Part B is entirely subjective, typically six problems, and CMI is explicit that partial credit is given for genuine progress. CMI leans slightly more towards algebra and combinatorics; ISI leans slightly more towards inequalities and classical geometry. The overlap is large enough that one preparation serves both, which is why this course prepares for them together.

How the course runs

Thirty-two weeks, two live sessions a week, plus one full-length paper every fortnight. Sessions are ninety minutes and capped at eight students, so every student writes on the board and every proof gets read aloud and criticised. The first half of the course builds the four pillars: algebra, combinatorics, number theory and geometry. The second half is entirely past papers and timed practice, working backwards from the actual ISI and CMI papers of the last fifteen years.

Every fortnightly paper is marked by hand the way ISI marks: for the argument. You get the script back with the gaps circled, not just a score. This is the single most useful thing in the course, and it is the part students underestimate most at the start.

Proof writing, which is the real subject

Most students who fail ISI and CMI can solve more problems than their score suggests. They lose marks because they cannot write a proof that a reader will accept: they assert what needs justifying, they handle one case and ignore three, they write the discovery rather than the argument. A substantial part of every session is spent on writing. By week twelve students are expected to produce a proof that another student can read without the author explaining it, and by week twenty they are marking each other's work against the real scheme.

Topics covered

Algebra: polynomials and their roots, functional equations, inequalities from AM-GM through Cauchy-Schwarz, complex numbers and roots of unity. Combinatorics: bijections, recursions, the pigeonhole principle, generating functions and counting in two ways. Number theory: divisibility, congruences, Fermat and Euler, order and primitive roots, Diophantine equations. Geometry: classical Euclidean configurations, similar triangles and power of a point, coordinate and trigonometric methods. Calculus and analysis to the level ISI expects: limits, continuity, differentiability and the standard theorems, sequences and series.

Mock papers and the last eight weeks

From week twenty-four the course becomes an examination rehearsal. Students sit full ISI UGA and UGB papers and full CMI papers under real time pressure, in the same morning slot as the actual exam. Each paper is followed by a session that works only the problems the group failed, which is a more efficient use of time than reviewing problems most people solved. Students finish the course having written at least twelve full papers under timed conditions.

Interviews

B.Math and B.Stat shortlist candidates for interview. The interview is mathematical, not personal: you are given a problem and watched while you think. Students who reach the shortlist get interview sessions at no extra cost, run as one-to-one mock interviews with a written report on what the panel is likely to probe.