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Olympiad General Preparation:

Geometry: Plane Geometry
The classical geometry resources are still the superior choices for study, even though they are very dense. Start with 1 and 2 (CPIG and Greitzer), but everything you will need can be found in Altshiller-Court,Johnson, or Aref.

Classical Olympiad Study:
Modern Olympiad Level Presentations:
Algebra: Inequalities – (Geometric and Analytic)
The modern resources are far superior choices for study. Start with the tutorials and then the books, everything you will need is there. The classical resources include large amounts of material that is not relevant for high school olympiad contests and though interesting, can eat up your time.
Introductions:
Modern Olympiad Level Presentations:
Classical Olympiad Level Study:
Additional Inequalities Problem Books and Reference:
Algebra: (Functional Equations)
There are no classical resources on olympiad functional equations problems. It was all hit or miss from various magazine problem sections. Start with the tutorials, then on to the books, then it’s just a matter of doing problems. Treat each one as a puzzle.
Discrete Mathematics (Combinatorics, Graph Theory):
The modern treatments are far superior to the classical resources. There are a number of good textbooks for background, but often include too much. The Art of Problem Solving Intermediate Counting is a good book to start with.
Number Theory:
The background for number theory can be found in any of dozens books that are usually titled “elementary number theory” or some variation. Once you know the basics it really is all about doing problems.

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