As per the request of many, I am writing this post about how I prepared for the Note on how to prepare for isi/cmi is little different and will be added later.
I did not started much earlier (which sometimes I regret). I was in class 9 when a boy of our class came with a notice, about the MTRP contest. I did not even know the name of isi that time. (I even asked him, “ISI? Where is it?”) And that was the first contest I participated and which was, I would say, a stepping stone in my life.
I loved geometry and it was the only olympiad stuff I could do at that time. I used to read the book ‘Challenging Problems in Geometry’ and also practised some problems from one website that my teacher recommended.
(Somehow now I can’t recall the name of the website, only thing that I remember is, the founder is Antonio Guiterrez.) *Edit: The site is named ‘GoGeometry.com’.* Near the end of class 10, I started reading the book ‘Elementary Number Theory’ by Burton. I participated in that year’s RMO(2014) and I could finish some 3-4 problems but could not qualify the mcq round by 2-3 marks. (In that year, mcq and subjective rounds were held together)
After passing class 10, (madhymik) I got admitted to RSM. (This is another thing I regret, for not coming to RSM before that. My teacher said I could have joined in class 9 or 10)
The first thing we were taught at RSM is combinatorics. I did problems from Excursion (An excursion in mathematics), CTOPM (challenges and Thrills of precollege mathematics) and after finishing the basics, a book named ‘A Path to Combinatorics’ was referred. (Rarely any of us read it but its actually a very nice book). And then we were taught Number Theory. As you know possibly, that a bunch of books and notes are written on number theory and it is not possible to read them all in such short time. So Excursion was the only book I followed regularly (I also read Burton but not regularly). (And of course, we did problems from various sources.)
Actually I would say now that if you have little time to prepare, just follow excursion, nothing else. It has what you need to know even upto inmo level.
Thereafter, we were taught polynomials and inequalities and the next Rmo came. Oh that year there was a pre-Rmo before Rmo. Fortunately, this time I qualified. We had a one-week long training camp at ISI. We also had some ‘Inmo classes’ at RSM. (Inmo in that year happened earlier than before, so everyone was in a hurry!) That was the time I enjoyed the most. Everyday we received bunch of good problems as well as learned some nice stuffs from the teachers.
Then I appeared at inmo 2016. But I couldn’t go beyond it. I got a score of 53 and that merely fetched a merit-certificate.
Ok, so what is above, is just the story of mine. This post still seems incomplete because I didn’t added much information like names of books or notes, right? But it is exactly how it happened. You need to know only some standard tools which you can study from Excursion. (and some reference if you want, that’s your own choice) Intution is the key in olympiads, nothing else. And, I would say, if a student doesn’t know basic stuffs like inclusion-exclusion principle, he/she better not go for stuffs like Zsigmondy’s theorem. Just learn the standard tools, and jump on to problems wherever you get.
And one note for students passing Rmo: It seems nowadays that geometry problems in inmo are kind of bashy. So besides learning homothety and inversions, do learn some complex bashing, vector methods too. Not only geom, also do some bashing problems in algebra. Like, doing manipulation with identities, factorisation techniques, case chasing etc.
For reference of books or notes, here is what I recommend :
(1) Finish the book excursion. (Yes, the term ‘finish’ includes the past year problems at the end of the book. This is very helpful.)
(2) For combinatorics, beginners can follow CTOPM. Then you can follow Arthur Engel’s Problem solving strategies.
(3) Do problems (specially geometry and number theory problems) from everywhere, but be sure about the authenticity of the problem. It is better not to waste time on incorrect problems as well as superhard unsolved problems.
(4) Functional equations don’t usually come before Inmo. For this topic, the book by BJV is best, in my opinion.
Good luck to every participant!