This blog contains notes on IMO-type mathematics, targeted at SIMO students. By the way, SIMO stands for “Singapore International Mathematical Olympiad”. As time passes by, I may include notes on more advanced mathematics, but we’ll see how it goes.

The difficulty level of the notes is tagged roughly as follows:

**basic**: should be understandable with little to no background;**intermediate**: around Senior Team – National Team level;**hard**: beyond IMO-level (no guarantee that it’ll be useful to IMO-type mathematics);**expert**: pretty hardcore university stuff.

Note that *just because a set of notes is tagged basic doesn’t mean you’ll understand it with little effort.* Often, it introduces a new concept which requires a wholly different way of thinking. E.g. if you’ve never seen modular arithmetic before, it takes a while to get used to it.

Some generic advice to SIMO trainees / maths students in general:

- work on
*lots*of problems: when you first start out, most of them will be above your league, keep working anyway; - curb your expectations: no one can solve everything;
- learn as much as you can from a proof/article/post, even if you don’t understand everything;
- be persistent: even for a seasoned mathematician, such problems require one to think persistently;
- be persistent:
- if you try really really hard to solve a problem and win, you’ll remember the solution for a long time and get a level-up;
- if you try really really hard to solve a problem and lose, you’ll remember the solution for an even longer time and get a level-up;
- (on the other hand, if you don’t put in effort and just wait for the solution to be fed, it’s not going to stick and your XP remains the same);

- be persistent;
- be persistent.

Ultimately, you have to strike a balance between working too long on a problem and giving up too soon. Also between working out all details of a proof/article/post and glancing through everything too quickly.

To: SIMO ex-participants, trainers, and even trainees: if you have an interesting idea for a short post or two (or more), please do not hesitate to contact me! The students can only benefit if they’re exposed to more diverse ways of looking at mathematics. If you’d like an editor / author account, contact me also. 🙂

Feedback is also welcome. Have fun!

## Update on 23 Jan 2012

Some changes have been made:

- This blog no longer focuses on Olympiad-type of mathematics, but mathematics of various levels and forms.
- As such, the name has been changed too.
- This does
*not*preclude the possibility that I will be posting articles which are related to SIMO mathematics.

More details are posted here.

## Update on 29 Dec 2014

From this point on, many of the postings and articles will be rather disorganized. I’ve been doing a bit of reading up, and while I’d very much like to post some of my thoughts, there’s always the fear of appearing silly, or worse, misleading my readers. But life’s too short to worry about such things, so I’d urge my readers to *proceed with caution*.

Disclaimers and some details here. Also, things may get a bit difficult from here on.

Very useful information shared. Thanks for the suggestions on how to prepare for Mathematics Olympiad Exam. If it’s updated with the latest information then it will become more useful to the students and trainers.

Thank you so much for this blog. Such lucid notes on Topological Groups. Loved it ♥️. I referred a lot of books and they were giving complicated proofs. To be honest, you are a life saver. Love from India.

Thanks for the kind words. Really glad they were of help to you. 🙂