Olympiad Training Materials

Preparation material

Olympiad level

• Arithmetics in extensions of \( \mathbb Q \) (Dušan Djukić)

• Combinatorics (Ivan Matić and Milan Novaković)

• Equations in polynomials (Dušan Djukić)

• Functional equations (Marko Radovanović)

• Geometric inequalities (Ivan Matić)

• Inequalities (Ivan Matić)

• Inversion (Dušan Djukić)

• Pell’s equation (Dušan Djukić)

• Polynomials (Dušan Djukić)

• Projective geometry (Milivoje Lukić)

• Quadratic congruencies (Dušan Djukić)

College level

• Calculus

• Putnam preparation

Other

• Math puzzles

Recommended Books

Follow this link for the list of useful books about math competitions.

Practice tests

Multiple choice tests

The following link will generate a test from a database of problems similar to those that appear on multiple choice mathematical competitions (e.g. AMC).

Generate test

Other tests

These tests are similar to AIME. Each problem has a solution that is a non-negative integer, and you need to enter the solution in the box provided. You may want to try these tests more than once because once the program has determined that you solved the problems, you will be offered a new problem set.

• Algebra
• Combinatorics
• Geometry
• Number Theory
• Mixture of problems

Problems from Journals

Many mathematical journals have a problem section publishing various problems. We try to gather such problems. If you have anything of this kind, we will appreciate receiving it. For now we offer two problem sets with 1878 problems in total.

• Mathscope - a collection of problems selected from Vietnamese math journals (particularly Mathematics and the Youth from the last 10 years), compiled by Phạm Vǎn Thuận. At this moment it contains 424 problems. (Updated: February 12, 2007)
• Collection of Inequalities - a collection of inequalities published in various math journals (a majority in Crux Mathematicorum) and books, compiled by Eckard Specht. At this moment it contains 1454±ε problems. (Updated: October 22, 2006)