TheInternational 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. 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.
Linear and quadratic Diophantine equations, including Pell's equation
Arithmetic of residues modulon, Fermat's and Euler's theorems
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
Properties of the orthocentre, Euler's line, nine-point-circle, Simson line, Ptolemy's inequality, Ceva and Menelaus etc.
Complex numbers (though present in the past)
Inversion in geometry
Solid geometry (though present in the past; may return)
The usual size of an official delegation to an IMO is (a maximum of) six student competitors and (a maximum of) two leaders. There is no official ``team''. The student competitors write two papers, on consecutive days, each paper consisting of three questions. Each question is worth seven marks. (The preceding information is taken from anOverview of the IMOprovided by the IMO'95 host country, Canada; also see below.) A total score of 42 points is possible. Awards are determined as follows:
GOLD MEDAL: the top 1/12 of scores receive gold medals
SILVER MEDAL: the next 2/12 of scores receive silver medals
BRONZE MEDAL: the next 3/12 of scores receive bronze medals
HONORABLE MENTION: any competitor who receives a perfect score of 7 on any one question, but who does not receive a medal, is awarded an honorable mention
The 37th IMO was hosted by India in Mumbai (Bombay) on July 5-17, 1996. Contact information: Professor A.M. Vaidya IMO-Cell, School of Mathematics, Tata Institute of Fundamental Research Homi Bhabha Road, Mumbai (Bombay) -400005 India
This site has some statistics about scores at IMO 1993 an on (except 1994). Maintained byJoseph Myers.
KöMaL- Mathematical and Physical Journal for Secondary Schools
More than one hundred years ago, Dániel Arany, a high school teacher from the city of Gyõr, decided to found a mathematical journal for high school students. His goal was "to give a wealth of examples to students and teachers". The journal's first edition appeared on January 1, 1894.
Created in 1977 by Dr. George Lenchner, an internationally known math educator, the Math Olympiads went public in 1979. In the year 2000, over 120,000 students from 5,000 teams worldwide participated in the Olympiads, representing 26 countries.
TheBay Area Mathematical Olympiad(BAMO) is a contest for high school students sponsored jointly by the Mathematical Sciences Research Institute (MSRI), the American Institute of Mathematics (AIM), the University of California at Berkeley (UCB), and the University of San Francisco (USF).
Information and problem sets (in Spanish) for the math olympiads in which Spanish high school students participate, including the Spanish Mathematics Olympiad (Olimpiada Matemática Española = OME). Maintained by Cristobal Sánchez Rubio (firstname.lastname@example.org).
TheUSA Mathematical Talent Search(USAMTS) is a free mathematics competition open to any US middle or high school student. It is a great contest for students aspiring to Olympiad problem solving, since many of the problems require proof-based solutions.
Here you will find a large collection of olympiad problems from all over the world. You will also find all the information regardingThe IMO Compendium, the most complete collection of problems proposed to the International Mathematical Olympiads.
TheArt of Problem Solvingcontains a variety of resources for avid students of mathematics in middle and high school. There are many free resources (in addition to a Forum) such as articles, a LaTeX tutorial, and online Math Jam sessions. Olympiad problem solvers from all over the world participate in problem discussions. The site also sells a set of problem solving textbooks and has an online school.
A collection of puzzles ranging over geometry, probability, number theory, algebra, calculus, and logic. Hints are provided, along with answers, fully worked solutions, and links to related mathematical topics. Many of the puzzles are elementary in their statement, yet challenging. New puzzles are added on a regular basis.
A key feature of the site is the detailed exposition, from first principles, of the puzzle solutions. Some of the puzzles are used to showcase particular mathematical concepts. See, for example, puzzle 56, which introduces a partition identity, and puzzle 63, where Ptolemy's Theorem permits a surprisingly simple solution. Further references are provided with many of the solutions.
Inverse Symbolic CalculatorWhen you give this program an approximation to a real number, it will do its best to decide what that number `really' is. In essence, this is a greatly expanded online version of theDictionary of Real Numbersby Borwein & Borwein (1990).