International math olympiad

Introduction

Laymen explanation

The International Mathematics Olympiad (IMO, also known as the International Mathematical Olympiad) is an annual mathematics competition for high school students [IMO Article in Wikipedia]. It is one - in fact, the oldest - of theInternational Science Olympiads. The first IMO was held in Romania in 1959.

Technical explanation

For this olympiad, the problems come from various areas of mathematics, such as are included in math curricula at secondary schools. Finding the solutions of these problems, however, requires exceptional mathematical ability and excellent mathematical knowledge on the part of the contestants.

Selection process

The selection process for the IMO varies greatly by country. In some countries, especially those in east Asia, the selection process involves several difficult tests of a difficulty comparable to the IMO itself.

Award

The participants are ranked based on their individual scores. Medals are awarded to the highest ranked participants, such that slightly less than half of them receive a medal. Subsequently the cutoffs (minimum scores required to receive a gold, silver or bronze medal respectively) are chosen such that the ratio of gold to silver to bronze medals awarded approximates 1:2:3. Participants who do not win a medal but who score seven points on at least one problem receive an honorable mention

Syllabus

• • Number Theory, including

    • • Fundamental Theorems on Arithmetic

      • Linear and quadratic Diophantine equations, including Pell's equation

      • Arithmetic of residues modulo n, Fermat's and Euler's theorems

  • Algebra, including

    • • Fundamental Theorems on Algebra, e.g. inequalities, factorization of a polynomial into a product of irreducible polynomials

      • Symmetric polynomials of several variables, Vieta's theorem

  • Combinatorics, including

    • • Graph theory

  • Geometry, including

    • • Properties of the orthocentre, Euler's line, nine-point-circle, Simson line, Ptolemy's inequality, Ceva and Menelaus etc.

Reference

https://en.wikipedia.org/wiki/International_Mathematical_Olympiad

http://olympiads.win.tue.nl/imo/

http://www.sofworld.org/