Olympiad Problem Solving:

THE USSROLYMPIAD PROBLEM BOOI(Selectecl Problems ancl Theorems of Elementary Mathematics D.O. Chen tzov, and l.M.Yaglom This book contains 320 unconventional problenrs in algebra, arithrnctic, clcrntntary. To solve each problem. The 400 Math Olympiad contest problems contained in this book are organised into 16 sets of five contests each. Every set represents one year’s competition. The first eight sets were created for Division J, for students in years 4-6, and the other eight for Division S, for students in years 7-8.

Problem-Solving and Selected Topics in Euclidean Geometry In the Spirit of the Mathematical Olympiads by Louridas, Rassias (2013).pdf Algebra: Equations and Trigonometry: It is assumed that you've completed and understand both Art of Problem Solving Introduction to Algebra and Art of Problem Solving Intermediate Algebra. Olympiad, Continued NOTE: Other FOLLOW-UP problems related to some of the above can be found in our two contest problem books and in “Creative Problem Solving in School Mathematics.” Visit www.moems.org for details and to order. METHOD 2: Strategy: List multiples of 8 and of 3 that are less than 20.

Problem solving and proofs at the Olympiad level are an entirely different skill from the AMC and AIME competitions.
There are a number of books both classical and modern the cover non-routine problem solving at the Olympiad level.
The classical resources on problem solving are mostly by the famous mathematician George Polya.
The famous general collections from Russia and Poland are classic and should be well studied.
The AopS books Art of Problem Solving volumes 1 and 2 are also well recommended.

Proof Techniques:

Geometry: Plane Geometry

It is assumed you've completed the Art of Problem Solving Introduction to Geometry.
In my view, the classical plane geometry resources are still the superior choices for study, even though they are very dense.
Start with #1 and #2 (CPIG and Geometry Revisited), however to do well on the Olympiad, you will need to study Altshiller-Court, Johnson, and Aref.
Altshiller-Court and Johnson are very light on problems, Aref is heavy on problems, so they all work together.
Everything you need for plane geometry success is right here.

Algebra: Equations and Trigonometry:

It is assumed that you've completed and understand both Art of Problem Solving Introduction to Algebra and Art of Problem Solving Intermediate Algebra.
In my view, the classical Algebra problem books are still the superior choices for study.

Algebra: Inequalities - (Geometric and Analytic)

The modern resources are far superior choices for study than the older books.
Start with the tutorials and then the modern and then if your really inspired take a look at the classical books, everything you will need is in the tutorials and modern books.
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.

Russian Math Olympiad Problems And Solutions Pdf

Algebra: (Functional Equations):

There are no classical books and resources on olympiad functional equations problems.
It was all hit or miss back then 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.

Math Olympiad Practice Problems Pdf

Discrete Mathematics (Combinatorics and Graph Theory):

It is assumed you've finished the Art of Problem Solving Counting and Probability book.
The modern treatments are far superior to the classical resources.
There are a number of good textbooks for background, but most include too much as they are oriented towards college courses.
The idea is to pick one and learn it well. I always liked the Tucker book, now in a 6th edition.
The Tucker and Vilenkin books have great coverage of generating functions.
The Art of Problem Solving Intermediate Counting is good also.

Number Theory:

It is assumed that you've covered the matieral in the Art of Problem Solving Introduction to Number Theory.
The necessary background for Olympiad level number theory can be found in any of dozens of books available that are usually titled 'Elementary Number Theory' or some variation.
The idea is to pick one and learn it well. Generally they don't cover diophantine equations that well, which is where the Olympiad problem books come in.
Note that at the olympiad level, you now must also know quadratic reciprocity. The ones I like are by Roberts, and by Dudley. Ther Roberts book is very unusual for style.
Once you know the basics it really is all about doing problems.

Math Olympiad Problems And Solutions Pdf 2018