IPhO & IMO Prep: Books & Tips for 3-4 Month Prep

[Shoku Z]

Hi!So,I am going to start my preparations for these olympiads.First round is in Nov-Dec,so I've like 3-4 months max.This is the first time I'm participating in both of these olympiads(And sadly,it's also the last).
Physics:I've An Introduction to Mechanics by Kleppner-Kolenkow,Problems in General Physics by I.E.Irodov,Resnick-Halliday-Krane,University Physics,H.C.Verma.Although I have all of these,I just KK and H.C.Verma.I just bought Irodov and I really like that book.What more do I need?For EM,I've heard Griffith is a good one.And what about QM?
Maths:I just have M.L.Khanna,A.D.Dasgupta and a book that contains previous olympiads' questions.As you can see,I don't have too many books specifically written for the olympiads.I need tough high-school level books and esp. Geometry.I'm weak in Geometry.Well,not that weak,but I'm kinda scared of Geometry.I couldn't solve even ONE from IMO.I want one really tough geometry book and one other book which explains theory really well.

Also,is Paul Zeitz's Art and Craft of Problem Solving a good book?I've heard a lot about it.But,is it worth 60$?Although,money isn't that big of a problem for me because I've got supportive parents.But is it as good as others say it is?Thank you!

 

[n1person]

For IPhO, don't use Griffiths Quantum Mechanics! You don't need calculus for anything on the test, and Griffiths uses multivariable calculus extensively!

For the IMO (and to an extent the IPhO), perhaps the most important thing you should be concerned about it passing whatever qualifying tests your country has. For the US, you have to do very well one the AMC (top 1% (10%?)) to go onto the AIME, which you have to do very well on to go onto the USAMO (about top 500 in the nation), and from that you have to do very well on to go onto to the MOSP (summer training program), and from that about half of the "black MOSP" goes on to the IMO. Although each of these levels is similar in that it requires problem solving math, it requires it at very very different levels (early AMC problems are mostly trivial, USAMO problems take literally hours and require long proofs!). And if you aren't from the US, most other countries have similar procedures (probably less intense since there are less people).

Seeing how you don't seem to have much experience with these sorts of competitive math/physics, first look at the qualifying tests (AMC and F=Ma in the US) and see how well you do! There is no need to study for the IMO/IPhO unless you are sure you can pass the "easy"/early tests.

EDIT: Art of Problem Solving books are VERY good for preparing you for the AMC/AIME/USAMO tests. (Disclaimer: I work for Art of Problem Solving :P)

 

[Shoku Z]

Thanks,I'm from India.And yeah,we too have qualifying tests and they are tough.And I was talking about Paul Zeitz's book.Is that any good?Does he own that Art of Problem Solving site?Thanks again

 

[rasmhop]

I only have experience with the IMO so I won't speak for physics, but I guess the situation is mostly similar. It's 2 years since I participated so some new instructional material that I'm unaware of may have come out in the meanwhile.

Unfortunately 3-4 months is not a lot of time to prepare for olympiad level math. Unless you are a very exceptional genius or have already studied a fair bit of extracurricular math you're unlikely to make the cut. In my experience a lot of Indians think highly of IMO and put in a lot of time to compete. In the end only 6 can represent each country and there are many smart Indian students who have likely prepared for years now.

That being said I will try to give a little guidance in case you want to give it a try anyway (whether for the experience, to challenge yourself, or just because you believe you can overcome the odds). Paul Zeitz' book The Art and Craft of Problem Solving is a great book and many participants at the IMO seem to have started out with this. Everything in it is relevant and it's a pretty good exposition (except for possibly the last chapter which is not that relevant). However on its own it's not enough for sufficient preparation to compete at IMO-level. If you can already solve some recent IMO problems (even if they are problems 1 and 4), then it may be too basic for your needs. You need to supplement with further instruction after Zeitz' book. Common choices are:
- The Art of Problem Solving series: very basic and moves really slowly, but gives good foundations if you have the patience and time to go through them. Given your short timeframe this is likely not that useful for you.
- Problem-Solving Strategies by Arthur Engel: Great book with many excellent problems and good techniques. Fairly advanced, but this is the type of book you need for actual IMO problems. Not really meant to be read from cover to cover, but you should read about specific topics.
- Geometry Revisited by Coxeter: Pretty universally regarded as "the" geometry book for olympiads. At least most participants at IMO seemed to at some point have been in possession of this book and most liked it.
- Books by Titu Andresscu (and co-authors). In particular I recall 104 number theory problems, 102 combinatorial problems, 103 trigonometry problems, mathematical olympiad challenges, complex numbers for A to ..Z. These all have fairly modest prerequisites but quickly moves onto pretty interesting problems and techniques. They all have older IMO problems.

Apart from these books most teams hand out material to people passing the first couple of national tests as part of the training for international competitions. In particular inequalities are usually taught from notes combined possibly with Engel's book. For the very basic techniques like basic application of the AM-GM or Cauchy-Schwarz inequality the art of problem solving books and Paul Zeitz' book are useful, but approaching the IMO this is assumed as known as it was likely used on the national test. Some of these notes are published online. For instance Kiran Kedlaya's article on inqualities:
http://www.artofproblemsolving.com/Resources/Papers/KedlayaInequalities.pdf
was very useful in my preparation for IMO. The only useful actual book on inequalities I encountered was the excellent book "The Cauchy-Schwarz Master Class" by Steele, but for the purposes of the IMO it is likely mostly overkill (except perhaps if you're looking for those last 1 or 2 points on a problem 6).

Geometry is usually also either taught from notes, Coxeter, or just straight classroom instruction + problem solving. Most geometry at IMO is fairly basic Euclidean stuff, but usually quite tricky so the main form of instruction is usually in the form of problem solving. You need to solve a lot of geometry problems. When you know basic stuff like facts about parallel lines, exterior/interior angles, similar triangles, inscribed circles, medians, etc. you are usually set to go. The only advanced theory used in IMO problems I can think of is the operation of inversion which can be quite useful, but if I recall correctly is not in the curriculum for the IMO so all accepted IMO problems have an official solution that does not use inversion.

Number theory may also be taught from notes, but books such as 104 number theory problems also make for a great introduction of precisely the techniques and theory used at the IMO. I have heard the book "the theory of numbers" by niven be recommended to advanced students, but this is way overkill for IMO-level stuff and more useful as a preparation for more advanced college courses if that is what you want.

If you have any specific questions on the IMO feel free to ask. I participated twice for a fairly weak team (compared to India at least) so national qualifiers were not as grueling for me.

 

[Shoku Z]

Thanks a lot,Rasmhop!Why did you say 3 months is really less for IMO unless I'm a genius?And there is one more thing I've always wanted to ask!I've this book which has old IMO problems.I can't even solve one problem!Is this the case with everyone else who have not yet started their preparations?I mean those who qualify for IMO,can they solve 2-3 problems from IMO without any preparation?And what about you?Were you able to solve some before you started your preparations?And thanks a lot,again!

 

[rasmhop]

Thanks a lot,Rasmhop!Why did you say 3 months is really less for IMO unless I'm a genius?And there is one more thing I've always wanted to ask!I've this book which has old IMO problems.I can't even solve one problem!Is this the case with everyone else who have not yet started their preparations?I mean those who qualify for IMO,can they solve 2-3 problems from IMO without any preparation?And what about you?Were you able to solve some before you started your preparations?And thanks a lot,again!

It's uncommon to be able to solve olympiad level problems with no preparation. Personally I prepared for 5 months for our national qualifiers and at that point I might have had a shot at problems 1 and 4 on IMO (the easiest problems), but usually couldn't even solve these. After a total of about 10 months of preparation I was able to usually give problems 1,2,4,5 a shot on most tests, but 3,6 were out of my reach and in the end I didn't score high enough for a medal. I'm pretty sure I wouldn't have qualified for a team as strong as India's because at the time of the national tests I couldn't solve IMO problems (except for old ones which are much easier).

I say 3 months is little because you are judged relative to your peers who have likely had more. I suspect there are at least 100 students (likely more) in India who have studied quite seriously for olympiad level problems for the last year. You are to somehow score better than them in national qualifying tests. For most people this is impossible, but people learn at different rates and if you learn 10 times as fast as any other Indian student, then you are in with a shot. I'm not trying to discourage you, but you need to realize that it's hard and you should not be disappointed if you do not manage to qualify.

I started preparing with about the same advance notice as you (5 months before first national qualifiers). I ended up getting a perfect score along with 3 other previous IMO-participants. I continued preparing. When the time came for the IMO (about 10 months after my start of preparation) I had a decent shot at problems 1,2,4,5, but 3,6 were totally out of my reach and in the end I didn't score high enough for a medal (which was to be expected). Before I started preparation I knew little to no Euclidean geometry, had no knowledge of the idea of divisibility, congruence relations, binomial coefficients, induction, etc. which are all vital to solving even easy olympiad problems.

As n1person said your first aim should be to score well on India's first national test. So improve on any weak points you may have and try to solve older problems.

 

[Shoku Z]

Ok,thanks!Thanks for informing about Coxeter Geometry book.I just checked reviews on Amazon and it's a 5/5.Let's see what happens!Thank you n1person and rasmhop!

 

[yielder]

I also learn a lot .Thank you

 

[heliogracie]

Competitive Geometry (2011) by Liubomir Chiriac is a new book on the market containing a wealthy collection of problems from recent mathematical Olympiads and treating a series of topics, which are not generally covered in usual sources on the subject (eg Casey's Theorem, Butterfly theorem, Geometric transformations,etc). Most problems in this book are of the IMO level, so it's an excellent working tool for students preparing for USAMO or IMO. It seems that you can only find it on Ebay for now.