This course is for those students who are passionate about Mathematics. Firstly analyze whether you qualify yourself fit to study in ISI or CMI. By being fit to study, I mean to say if you love math. If your target is just to get a brand name or just qualify the exam for “a” college, please don’t take the exams.

Now that you are sure that you are a math lover, you can proceed to take the course.

The course is for high school students who want to give the ISI & CMI entrance exam after their 10+2.

Recommended Books:

- Problem Solving Strategies (pdf available) (which I’ll refer to as PSS),
- Test of mathematics at the 10+2 level (published by ISI) (which I’ll refer as TOMATO),
- An excursion in mathematics (which I’ll refer to as Excursion).
- Challenges and Thrill of pre-college Mathematics.
- Also refer to some standard textbooks for calculus definitions (like I.A. Maron, Bartle-Sherbert or Apostol).

The syllabus is just high school math. I’d broadly classify the syllabus into the following topics:

- Number Theory: My personal favorite. Questions seem to attack the common sense (after all, they’re beautiful numbers, which are close to one’s conscience). Read Excursion for basics. Solve a few exercise problems. Try out the problems on TOMATO. If comfortable, do PSS exercises (examples are hard).
- Combinatorics: You can expect beautiful problems from here. CMI lives up to this expectation. In ISI, the combi problem(s) will certainly be tricky. Know very well when to add and when to multiply. Know P&C of 11th grade like the back of your hand. Read Excursion for basics. The only mantra to master this topic is to practice lots and lots of problems. Again, Excursion for basics. Read through PSS as well (easy questions from chapters 1,3,4,5 are very very important). Do all questions from TOMATO without help (if you stumble, think later, but solve on your own).
- Algebra: Know your high school algebra very well. Besides this, you might want to know (and understand) the triangle inequality, the AM-GM-HM inequality, and the Cauchy-Schwartz inequality. It’ll be your added advantage if you some further tricks in solving problems for algebra. But it’s pretty fun to analyze algebraic structures and draw analogies from other fields (which makes the topic super interesting). Polynomial is an important subtopic. Theory from Excursion and practicing problems from TOMATO is enough.
- Geometry: Yet another treasure (Coordinate geometry must be your last option). Even if you love Euclidean geometry, nobody can assure you that you can answer a question in the paper. Revise all the geometry theorems and lemmas that you had done in your 9th and 10th grade. Ask your coaching institute guide to help you out with topics and problems. Nothing much to read from Excursion. But practice from TOMATO and the easier problems from Excursion.
- Calculus: Very much weighted for ISI paper. Know everything very precisely. Before applying a theorem or a lemma, make sure you can prove it. Requirements: Definition of sequence, limit (of sequence and function), continuity, differentiability. Extreme value theorem (proof not needed), Intermediate value theorem(proof not needed), sandwich theorem, mean value theorems (Rolle, Lagrange’s MVT, Cauchy’s MVT), MVT for integral, Darboux theorem, one-one-ness of a continuous monotone function etc. Please ask your coaching teacher to guide you, or ask help from someone experienced. Read Apostol or Bartle-Sherbert for theorem statements snd definition. For practice, try out TOMATO.

After knowing the basics of these topics, you might want to try out many A1 and A2 problems from Putnam contest. It’s okay if you can’t solve all by yourself. See the solutions and learn. You might face many questions which will cover concepts from multiple topics. These test your actual ability to think. But if you can’t solve a problem, don’t get discouraged.

For MCQ in ISI, practice mathematics papers of JEE mains (avoid solving too many questions from coordinate geometry and indefinite integration). CMI questions have an added Olympiad flavour to them. So practicing Excursion and PSS helps.

Before sitting for the exams, make sure that you complete TOMATO (each and every question, with or without help) and all the past year questions of ISI and CMI. Keep away a few MCQ papers (of ISI) as unseen ones so that you can use them for time-bound practice a couple of weeks before the D-day.

If you think you’re pretty comfortable with a topic, please go for PSS (Don’t start with the mentality that you’ll complete it, save for a few exceptional ones). Even solving the first 15 problems (in each exercise) by yourself is good enough.

Overall, TOMATO is very important and must be solved completely. Excursion is for reference. PSS is for further problem-solving practice to gain experience.

The interview in ISI is very important. The interview panel will sit with your subjective copy and they’ll ask abt any conceptual errors that you made in your paper. Be prepared to face that. Not even God can help if your concepts aren’t crystal clear. It’s okay if they ask you to solve a problem and you solve it with the hints they provided (or don’t solve it completely). I repeat they don’t tolerate basic mistakes. But don’t worry, even if you make such errors that may not appeal to your eye, they’ll point it out and you’ll get a chance to correct yourself. Please think aloud. They want to know your thought process (it won’t matter even if you don’t solve a problem fully).

Another very important point is to find yourself a math community. This keeps your zeal intact. One way is to (mathematically) socialize with your friends at the coaching center. If there aren’t enough enthusiastic candidates, you can always find an online community. The best one that I know so far is Art of Problem Solving (aops.com). Every year, an ISI/CMI preparation group is created. You can keep yourself updated with math everyday on such a forum, besides discussing “other” beautiful ways to approach a particular sum. There are pr0 people (like IMO medalists) there to help you too.

2 years should be enough to prepare for ISI and CMI, provided you are sincere enough. There’s no need to sacrifice sleep. Proper sleep enhances your performance. Just remember to brush up your concepts and practice problems regularly.