Recommended Books — CMI Undergraduate Entrance

Carefully selected for abstraction, proof-based thinking, and the style of problems asked in CMI entrance papers.

Absolute Essential

Begin with these alongside all topic study — not after.

  • Past Year CMI Entrance Papers
  • TOMATO — Test of Mathematics at 10+2 Level
  • Past Year ISI B.Stat Papers
  • Past Year ISI B.Math Papers

Prerequisites

Ensure these are solid before moving to problem-solving books.

  • NCERT Mathematics
  • Higher Algebra — Hall & Knight
  • Plane Trigonometry — SL Loney
  • Coordinate Geometry — SL Loney

Mathematical Thinking & Problem Solving

The heart of CMI preparation — abstraction, elegance, and independent reasoning.

  • Problems in Elementary Mathematics — Yaglom & Yaglom
  • Problem Book in Mathematics — Prelipko
  • Mathematical Circles — Dmitri Fomin
  • An Excursion in Mathematics — Modak, Shirali & Bapat
  • Challenge & Thrill of Pre-College Mathematics — Venkatachala
  • The Art and Craft of Problem Solving — Paul Zeitz
  • PathFinder for Olympiad Mathematics

Proof Writing

CMI is heavily proof-based. This is not optional.

  • How to Prove It — Daniel Velleman
  • Mathematical Proofs: A Transition to Advanced Mathematics — Chartrand, Polimeni & Zhang

Algebra

  • Advanced Problems in Algebra — Vikas Gupta (Yellow Book)

Number Theory

CMI places significantly more emphasis on number theory than ISI.

  • An Introduction to the Theory of Numbers — Hardy & Wright
  • Number Theory — Niven, Zuckerman & Montgomery
  • Problem Solving Strategies — Arthur Engel (Number Theory chapters)

Calculus

  • Calculus — Vinay Kumar (bridges problem-solving intuition with rigour)
  • Problems in Calculus of One Variable — IA Maron
  • Calculus Vol. 1 — Apostol
  • Calculus — Michael Spivak

Combinatorics

Expect abstract, non-routine problems.

  • A Path to Combinatorics for Undergraduates — Titu Andreescu
  • Problem Solving Strategies — Arthur Engel (Combinatorics chapters)

Inequalities

  • Algebraic Inequalities — Zdravko Cvetkovski
  • Classical Inequalities — Jiri Herman

CMI rewards abstraction, clarity of thought, and independent mathematical reasoning. Past papers should run continuously throughout preparation — not attempted only at the end.