5


I want to start learning olympiad mathematics more seriously, and I would like to have advice on some good books or pdfs to learn with.
I have background but not a big background. For example I know high school geometry (and in general high school mathematics) really well but in olympiad geometry (where creativity is really needed) I am not that good. I can solve a bit of the problems from the national math olympics in my home country but not problems from the IMO (though I can understand the solutions of the easier problems in the IMO, mostly easier geometry problems).

Right now I want to focus mainly on geometry and number theory, and maybe some combinatoris. Are there any books that are really recommended for a beginner (not a beginner who starts from absolute scratch, but still a beginner).

I heard about the book "Euclidean geometry in mathematical olympiads" written by Evan Chen but I understood that this book is advanced and a beginner should not start from that.
Any good books to begin with in geometry, number theory, and combinatorics (and if you have anything else to recommend on - for example a good Algebra book to begin with when I'll start learning algebra - of course I would like to hear it as well).
If you have any advice on math olympiad in general, or if you think I should learn something else first (for example if you think I should learn algebra before number theory) - please tell me.

Thanks!

Omer
  • 2,538
  • 5
    Refer to AOPS Books – user Sep 19 '18 at 15:03
  • @user170039 Hi, thank you for the comment. I will definitely check it. Is it recommended? I am looking for a book that is good to begin with, but a book that can still lead me to a level where I can solve some of the easy-medium leveled olympiad problems and understand some of the solutions to the hard ones. – Omer Sep 19 '18 at 15:08
  • 3
    Yes it is one of the main reference and you can also find a lot of material on line. Refer also to IMOMATH – user Sep 19 '18 at 15:11
  • @gimusi okay, thank you! do you think this is a good order of learning? maybe I should start learning algebra before geometry or number theory? what do you think will be the best order? thanks again! – Omer Sep 19 '18 at 15:21
  • 1
    There is a nice little book "solving mathematical problems - a personal perspective" by Terence Tao, which he first wrote before he was as famous as he is now. – Michal Adamaszek Sep 19 '18 at 15:24
  • 2
    There is not a fixed order in my opinion, often things are linked together therefore you can start simultaneously on all the topics starting from the basics. – user Sep 19 '18 at 15:25
  • @gimusi Got it, thanks. I found the following link in the same website: https://artofproblemsolving.com/wiki/index.php?title=Olympiad_books. Did you mean that I should read the "Introduction to ..." books? or in general books from this website? It is written in the link I sent that the "introduction to " books are only theory books, don't you think that I should read a theory + problem book? because the main target is to be able to solve olympiad problems at the end – Omer Sep 19 '18 at 15:29
  • EGMO is actually good for the basics, if you ignore the directed angles. They're a bit tough to understand. – DynamoBlaze Sep 19 '18 at 15:35
  • @Omer You should start from introductory theory and problems of course, start from the simpler and try to solve them looking also to the theory needed to understan and solve them. On the web you can find many sources for theory and problems. – user Sep 19 '18 at 15:39
  • You should simultaneously read all topics whenever your intuition says there must be a relation between them. From my experience those very great on a topic(not just math) try all whatever he can do to solve a problem, so I think order matter little, after all you will/should read them all. – linear_combinatori_probabi Sep 19 '18 at 15:57
  • @gimusi Hi, sorry for telling just now but I just saw the preview of intro to geometry/number theory and this seems really basic. I mean, for example in Intro to geometry the preview was an explanation about what similar triangles are and some exercises on proving similar triangles (which was simply AA). Why is it so basic? and could you please send me links to precise books that you think will be good, in number theory, algebra and geometry? sorry and thank you again... – Omer Sep 20 '18 at 20:39
  • @Omer For details in Combinatorics books see this https://math.stackexchange.com/questions/3781790/book-recommendation-olympiad-combinatorics-book/3782841#3782841 – James Moriarty Aug 09 '20 at 05:50
  • AoPS books are for the pre-olympiad level, not olympiad level. For the olympiad level, there are many books publised by Titu Andreescu through his XYZ Press. – Favst Dec 08 '20 at 14:36
  • I will suggest you to read the indian edition of the book, an excursion in mathematics. It is a great book and covers every aspect in detail. –  Jan 19 '19 at 13:47

0 Answers0