How to prepare for RMO?

"Let's wait for this exam to get over".. *Proceeds to wait for 2 whole fricking years! 

I always wanted to write a book recommendation list, because I have been asked so many times! But then I was always like "Let's wait for this exam to get over" and so on. Why? You see it's pretty embarrassing to write a "How to prepare for RMO/INMO" post and then proceed to "fail" i.e not qualifying. 

Okay okay, you might be thinking, "Sunaina you qualified like in 10th grade itself, you will obviously qualify in 11th and 12th grade." No. It's not that easy. Plus you are talking to a very underconfident girl. I have always underestimated myself. And I think that's the worst thing one can do itself. Am I confident about myself now? Definitely not but I am learning not to self-depreciate myself little by little.

Okay, I shall write more about it in the next post describing my experience in 3 different camps and 1 program. 

So, I got serious about the mathematical Olympiads from grade 9, when I heard about EGMO i.e European Girls' Mathematical Olympiad. EGMO is quite fascinating, being able to represent India is really everyone's dream. And the peer group is surely the best experience.. Solving problems with everyone and even playing games. Participating in group competitions ( Online Math Open and TrinMac, even Integirls was fun).

Anyways, what any beginner would ask a senior  is "THE PERFECT BOOK RECOMMENDATION LIST." And I think there's no perfect answer. The reason is this list differs from person to person.  Evan Chen's website actually has a great list here! So do surf through it once.

But here's a book recommendation list along with some FAQs from the Indian Math Olympiads perspective. (I was actually asked by a few people, so why not share here instead ). 

Note: I am surely not the best person to write this since I am not at all qualified. But here's the compilation, which I think everyone follows. 

Again, the level is PRMO/IOQM to RMO types. 

Here are a few books one must complete before trying other books. These books are to be done to make fundamentals clear and are almost enough theory for PRMO/IOQM level (The first round of the mathematical olympiad ). Additionally, please do see the Pythagoras theorem’s proof, intuitive one.

Basics:-

1. NCERT Class 8

2. NCERT Class 9

3. NCERT Class 10

4. NCERT Class 11 ( Sets, Relations and functions, principle of mathematical induction, Permutations and combinations, Binomial theorem, sequence and series, straight lines)

Note:- Many of the problems are very same, so feel free to skip them. Chapters like Statistics and SI, CI can be freely skipped.

And to get a taste of how Olympiad Mathematics is try Mathematical circles. (5)

Beginner ( Only the above-mentioned books are the pre-requisites)

1. Arihant- Indian National Mathematical Olympiad ( Rajeev Manocha) ( Theory of Numbers, Theory of equations, Combinatorics)

2. Challenges and thrill of Pre-college mathematics. ( Polynomials, Inequalities)

After these two refer to the following for more practice,

3. Pearson’s Pathfinder to Olympiad mathematics (Recursion (recommended by PC), Inequalities, Induction, Functional equation, Geometry)

 The pdfs of books at points 2 and 3 are easily available in libgen.

Miscellaneous Problems (PRMO/IOQM types):-

1. Past year papers

2. American Mathematical Competition 10 ( problem range 1- 18), AMC 12 (1-15) and AIME problem range (1-7)

Note: These were written from the perspective that one only just have to clear the stage and not prepare so hard, generally give like 2-month prep, and if you are from  low cutoff areas like Assam or Ne, 1 month is sufficient)

Miscellaneous Olympiad style problems (easy RMO level types):-

1. Old INMO/ RMO problems ( till 2005)

2. Old Canada Math olympiad problems (these can be found out at the art of problem-solving website, contest--> National contest--> Canada) ( till 1990)

Intermediate (olympiad i.e long answers problems):-

0. (MUST) Mathematical circles ( this develops the intuition required)

1. Geometry:- a. ABJTOG A beautiful journey through Olympiad geometry ( this book is open for all)

b. EGMO=Euclidean Geometry in mathematical olympiads (pdf available in libgen)

for RMO chapter 1,2,3,4 suffices from EGMO and ABJTOG (version 1.3) 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15.

for INMO whole book except chapters 6,7 from EGMO and ABJTOG whole book.

2. Number theory:– Theory: David burton( pdf in libgen)

Problems:- 104 Problems in Number theory – Titu Andreescu ( pdf in libgen)

3. Combinatorics:- Past year INMO problems suffice, but Pablo Seberon’s Problem-solving methods in Combinatorics ( available in libgen) is nice.

Also, Problem-solving strategies by  Aurther Engel ( springer) (available in libgen), refer to chapters first 3 chapters.

4. Algebra, I haven’t done much algebra, but I think the book’s I mentioned are sufficient.

Miscellaneous:- Also the problems are available on the art of problem-solving website.

1. Start trying out INMO/RMO problems

2. USAJMO P1,P4( USA junior math olympiad problems)

4. IMO P1s and easy problems ( old contests)

5. Shortlist problems of range 1 or sometimes 2.

More reading:- (just google search the names, and we can find the website.

0. You can check out my Olympiads page for some handouts and problem sets. 

1. Evan Chen’s Handouts

2. Alex Remerov’s Handouts

3. Yufei Zhao’s Handouts ( I did almost all of his handouts)

4. Rohan Goyal's Handouts ( Rg's handouts can be found here ) 

5. Modern Olympiad Number Theory by Aditya Khurmi

A few FAQs:-

1. Is it necessary to complete all the chapters?

Ans: No. Not at all. I am pretty sure completing all these books, and papers will take you a lot of time. Feel free to skip problems. Also if you feel a problem is ugly, just skip it. 

2. Is it okay to skip problems?

Ans: Yes. At least I think. See, the whole essence of Olympiad math ( at least Intermediate Olympiad math) is to make you love math and not force you to do the math. And doing problems, which don't seem ugly, is completely fine. 

3. How do you define ugly?

Ans: Self-explanatory. It's from person to person. I feel ugly problems are geometry ineqs, weird graph theory problems using high fi stuff, bashes. But this is my PoV, for you, it might differ. I know people who love to just bash a geo problem. So you see it varies.

4. You said to do both EGMO and ABTJOG.. How exactly should we do?
Ans: I posted this answer, quite long time ago in STEM-Horizons. 

I will repost it here.

Disclaimer:- I am really a bad person to suggest, so take me lightly. So I personally think one should get a like a full base ready.. so imo if you are quite new to geos then start from ABJTOG. And do like the first 17 chapters and chapter 24 . 

I know it sounds big but each chapter is quite small in theory, yet really cute. Do the exercises problems too side on side. And by exercise problems, try like at least half of them ( not full if u don't want to). 

After these 17 chapters, You would have already completed the theory need in the first 4 chapters! So then start the first egmo chapters, and "theory" won't feel new. 

Why am I even saying to try both? This is because egmo assumes that you know some geometry, but in case of ABJTOG, it really teaches you from what we say the actual base of geometry(euclidean). Plus idk about others but EGMO was a bit too fast for me to digest. 

Now after this, skip the bash chapters from egmo( Just skip them :P). And choose any one of projective /inversion, doesn't matter which one you choose. Both are quite cute and both are quite helpful tools. But for either of them, refer EGMO. A special note for inversion is that do refer it from ABJTOG after u completed egmo inversion. It has \sqrt{BC} and \sqrt{BC/2} inversion, which egmo hasn't talked much.

 But on the side, I am telling you to do after egmo since ABJTOG hasn't gone to the dept of inversion, so quite hard to digest. Projective/harmonic is really nice in egmo, I haven't even touched it from ABJTOG. But I think pole/ polars chapter is nice too in ABJTOG. Now for chapter 10 i.e complete quads from egmo. I would personally say that egmo thing is enough, but if you want really dept then, really u must do chapter 18 and chapter 19 first and then do egmo. Then u are left with bashing chapters in egmo and Feuerbach’s Theorem in ABJTOG. Now complete ur choice, do whatever u want!!

 I haven't the Feuerbach’s Theorem in ABJTOG, but i heard there's a simple complex bash solution, so I would read that instead! 

Yeah, that's it :P. Sorry. Woah lol it turned out to be pretty big 

5. How many hours should I study?

Ans: I never ever recommend this question to be asked. I used to ask too, but it is sometimes annoying. Here's the thing it differs from person to person. Some of my friends just study for 3 hrs and clear INMO. But some study hrs and hrs. I read somewhere that on average people spend 48 hrs a week.
   Not to fix any time; just do it whenever you want to do it-- Anand

6. Should we prefer Handouts or Books?
Ans: Handouts are nice. I think both. For handouts, ask your peers what you should try.

7. I just started out Oly but I am doing X too ( where X is NTSE, JEE, KVPY,etc). Is it okay?
Ans: No in my opinion. Some people are able to manage, but most can't. I couldn't even manage my boards, now I am going to be kicked out soon of the house once the results are announced.

JEE is very hard. I tried to manage both and I am failing miserably. So one has to choose one (luckily I am now retired so it's fine).

8. Any olympiad similar to RMO/INMO?

Ans: For RMO, Try NMTC, Pakistan MOs, Bangladesh National MOs, Canada old MOs, Peru MOs, British MO round 1, etc.

For INMO, I am not at the level to suggest people. I think Evan's Website is the best.

9. Should I refer to some YT channels?

Ans: Yes. Sure! I don't watch YT or very rarely, so maybe ask someone else.

10. Should I make notes?

Ans: I make. But I am very careless, so I always misplace my notes or delete the pdf.  

11. Sometimes I don't feel like studying, what should I do?

Ans: Take a break and have a Kit-Kat. (Sorry lame tha)

Just take a break, your brain is saying you to take a break, that's it.

12. Are teachers helpful?

Ans: Generally your parents and coaching teachers help but tbh it's your own hard work. My Father helped me till class 8. But it's mostly self-study. If you get doubts, post them on AoPS or Math Stack Exchange.

 

Anyways, I hope this blog post would help you in some way. I hope you share this post to all the beginners. I think this post will benefit them a lot!

Image credit: Pinterest

Have a nice day

Sunaina💜