Art of Problem Solving Books for British Mathematical Olympiad?

Hey guys,

I am a GCSE student who is preparing for the British Mathematical Olympiad later this year, and would like to do well, so I have started reading some UKMT-published books.

However, reading through the UKMT-published book Plane Euclidean Geometry, I found that my GCSE maths is not sufficient to understand it. For example, there is a page titled 'Elementary Trigonometry' that assumes knowledge of various basic trigonometric identities that I have never encountered, such as
sin(A+B) = sin A cos B + cos A sin B
To me, simply learning a formula like this does not mean that I will be able to use it in practice

I would also like to read books covering the whole syllabus of the BMO, such as combinatorics and number theory, which I haven't been taught at all.

I was wondering if you guys know of any maths books that explains these areas more thoroughly or from a simpler level?

I have heard of the Art of Problem Solving series of books (http://www.mathcomp.leeds.ac.uk/publications/index.php?type=Yearbook), which has received many positive reviews. Would you recommend getting this series?

Thanks so much for your help!
~LondonGamer

They are very good, but pricy. They have plenty of examples and are quite humorous sometimes. I'm looking forward to reading my few in the summer and then owning that thing in November!

How many of the Art of Problem Solving books do you own?
And do they explain everything from scratch or from a level that I, a GCSE student, can understand?

Thanks,
~LondonGamer

I own two with their answer booklets. The counting and probability one certainly looks accessible. The algebra one might be harder to get to grips with without buying the beginner one or whatever it's called as the intermediate one leaps in quite quickly.

These two books might also be worth a shout, the first being essential for practice questions with solutions provided:

The Mathematical Olympiad Handbook: An Introduction to Problem Solving based on the First 32 British Mathematical Olympiads 1965-1996

A Primer for Mathematics Competitions

I have a book called a Mathematical Olympiad Primer by Geoff Smith. However, I also find that there is not enough theory for me

How useful is the book titled 'A Primer for Mathematics Competitions'
Does it go through all the theory in detail? I saw that it is only 370 pages in total, so how can it go through all the BMO topics?

Which books would you recommend to a GCSE student who has no grasp at all on any further A-level knowledge, and needs to practice with new theories?

Thanks,
~LondonGamer

The Primer covers geometry really well from basics, and introduces topics such as inequalities and combinatorics. There is no real specific book I would recommend for GCSE students, only that they should be really good with their algrebra, but this will come by practicing maths.

I think what I need is a book that teaches everything from basics. For example, in geometry, I would need a book that explains trigonometric identities from basics and has plenty of examples and exercises for a beginner, e.g. for the sine rule. Which book do you feel does this best?

Definitely 'a primer for mathematics competitions' by Alexander Zawaira. The geometry part is fantastic and explains most topics from basics. However as much as it explains things from basics, you still have to ensure that you are confident with algebraic manipulations from GCSE. Looking up Partial Fractions may also be helpful.

Thanks, what I'm looking for is a definitive guide that will explain anything and everything I will need for the BMO. In my opinion, that book seems a bit short as it is only 368 pages long, and the UKMT books on just one subject, e.g. geomtry, seem to be at least 200 pages each.

Also, I don't know anything about partial fractions at all, is that needed for the BMO?

BMO1 in theory shouldn't require too much extra knowledge, it's just that extra knowledge can dig you out of a hole!

You don't need to know about partial fractions, but they are probably the only new algebraic technique taught at A-Level. Basically you use simulatenous equations to split a fraction into two or more. I'm sure there are some good web resources you can look at if you want to explore further.

The book I recommended gives a good grounding, and will teach you everything you *need* to know for BMO1 and a little more which will help you find better solutions etc.

Thanks, I'll look at the book. I hope I don't seem demanding or needy, but which books would you recommend for BMO2 and perhaps further?

You need to get a feel of what topics you like, or need improving by starting with BMO1 books first. Personally, I only realised about BMO1 in October so it was too late to do much preparation. For BMO2 you will want to get more subject specific books such as:

Geometry Revisited. There's a free copy online if you search in Google, but personally I'll purchase the book in the summer as it is much more convenient for me and the author deserves the money!

Thanks, I think that's the type of book I'm looking for. I'm trying to find books that will give me everything I need to potentially do every single question in BMO2. This includes geometry, combinatorics, number theory etc.

I was wondering whether the Art of Problem Solving series covers everything BMO2 related, or is there a better series?

Thanks so much for your help!
~LondonGamer

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Thanks, I think that's the type of book I'm looking for. I'm trying to find books that will give me everything I need to potentially do every single question in BMO2. This includes geometry, combinatorics, number theory etc.

I was wondering whether the Art of Problem Solving series covers everything BMO2 related, or is there a better series?

Thanks so much for your help!
~LondonGamer

Posted from TSR Mobile

You need to get a feel of what topics you like, or need improving by starting with BMO1 books first. Personally, I only realised about BMO1 in October so it was too late to do much preparation. For BMO2 you will want to get more subject specific books such as:

Geometry Revisited. There's a free copy online if you search in Google, but personally I'll purchase the book in the summer as it is much more convenient for me and the author deserves the money!

Oh wow, thanks! That book got amazing reviews on Amazon.com! So would that book cover everything geometry-related for BMO2?

What I was wondering was whether there was a particular series of books that covered the whole syllabus, as that means I would be studying the same level of mathematics across the topics, instead of jumping from one highly-advanced book to one simpler book?

Oh wow, thanks! That book got amazing reviews on Amazon.com! So would that book cover everything geometry-related for BMO2?

What I was wondering was whether there was a particular series of books that covered the whole syllabus, as that means I would be studying the same level of mathematics across the topics, instead of jumping from one highly-advanced book to one simpler book?

Just found this, it is from a conversation with another member of this forum after I asked what books he'd recommend for olympiad subjects.

GEOMETRY:
aops intro to geometry -> plane euclidean geometry (UKMT) -> geometry revisited -> prasolov problems in plane geometry -> challenging problems in geometry
COMBINATORICS:
aops intro to counting and probability -> aops intermediate counting and probability -> generating functionology -> 102 combinatorial problems ->mathematics of choice
ALGEBRA:
aops intermediate algebra -> algebra (by im gelfand) -> 101 problems in algebra (feng/andreescu) -> complex numbers from a to z
INEQUALITIES:
just look for articles on artofproblemsolving.com or use UKMT's inequalities handbook (not very user friendly if you're new to olympiad maths though)
Polynomials:
I personally learnt most things I know about olympiad polynomials from taking WOOT class on aops
NUMBER THEORY:
intro to NT (aops) -> intermediate NT seminar by aops -> 104 problems in number theory (zuming) -> number theory article by 'nsato' (abbreviation of his name) -> any other olympiad number theory articles
PROBLEM SOLVING BOOKS:
problem solving strategies (arthur engel)
maths olympiad handbook (not teh UKMT one!!)
Art and craft of problem solving (zeitz)

Thanks, so basically advocating art of problem solving series then?

And by the way how far did this person get in the mathematical olympiad?

Thanks,
~LondonGamer

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