Also, I want to make it clear: Beginner.
I'm getting really frustrated trying to study for math competitions:
On the one hand, there are books teaching the high school curriculum, but that's it. I don't need these, I know (almost) everything on your regular high school curriculum.
On the other hand, there are books for the IMO. But they assume you have a really strong olympiad mathematics background, and they are only there to prepare you for the IMO. They're basically composed of one or two lines of theory per chapter, and then a huge list of hard exercises and problems. I don't need these either: I'm not even near the IMO calliber, and the solutions to the problem seems to rely on theorems and techniques that aren't taught in high school.
What I am really looking is for a bridge between these two extrema: A book that makes a connection between high school basic math and IMO advanced math.
A book that covers this list of topics is what I am trying to find. I've never heard about any of these topics, though they seem to be essential for math competitions. Also, I've never found any book that covers them.
I'm not sure whether a single book will contain such a broad range of topics, so I believe that I'll need a book for Algebra, a book for Number Theory, a book for Combinatorics, etc.
But if that's the case, I also want to make it clear that I'm not looking for a book that teaches you college Algebra, college Number Theory, etc. I want something that covers topics that appear on a math competition, but doesn't assume anything other than high school maths.
Thank you in advance.