文档介绍：Tutorials in Elementary Mathematics for Math Olympiad Students
Resources for mathematically gifted students
Tutorials in Algebra, Number Theory, Combinatorics and
Geometry
The aim of this section is, in the series of tutorials, to cover the material of the unwritten
syllabus of the IMO, more precisely that part of it which is not in the school curriculum of
most participating countries.
Algebra
● Rearrangement Inequality This article by K. Wu, Andy Liu was first published in
"petitions" Vol. 8, (1995), pp. 53--60. This journal is
published by Australian Mathematics Trust. The article is reproduced here thanks
to the kind permission of the authors and the Editor of "Mathematics
Competitions" Warren Atkins.
Combinatorics
● Interactive Graph Theory Tutorials By Chris K. Caldwell from the University of
Tenessee at Martin.
● Permutations.
● Friendship Theorem.
Numbers
● Divisibility and primes
● Euclidean algorithm
● Euler's theorem
● Representation of numbers
● Bertrand's postulate.
Geometry
● Ptolemy's inequality
● Euler's theorem
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Tutorials in Elementary Mathematics for Math Olympiad Students
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Syllabus of the IMO
Resources for mathematically gifted students
Unwritten Syllabus of the IMO
These thoughts were written in 1997, when I was working on the Problem Selection
Committee of the 38th IMO in Argentina and when my impressions about the problems,
which were submitted, and the attitude of mittee to these problems were still
fresh. I edited them very little since.
The syllabus of IMO is, of course, unwritten but there are several tendencies which can
be clearly observed. It is all ruled by tradition, there is no logic in all this whatsoever.
Some topics are included, alhtough they are not in the school curricula for most
countries,