Mathematical Olympiads are international competitions for high school students. They are the oldest and by far the largest of the olympiads on school subjects (which today comprise physics, programming, latin, phylosophy, ...) reaching over one hundred nations worldwide.
In my youth I competed myself. I won the Italian Mathematical Olympiad in 1994 and I was a contestant at the IMO in 1993 and 1994, with a bronze medal award in 1993.
Today I help with the activities in Italy, as a member of the Italian Mathematical Olympiad Committee.
Italy usually sends a team to four competitions:
To prepare our pupils to become strong contestants, we have a training program with three one-week stages held in Pisa:
The traditional subjects are algebra, combinatorics, geometry and number theory.
I am in charge of the training in algebra. The other subjects are entrusted to Ludovico Pernazza, Samuele Mongodi and Roberto Dvornicich, who is also the historic team leader of Italy at IMO. Massimo Gobbino is generally considered the head coach: he organizes our work and takes care of all the tests.
To prepare the algebra sessions of all the recent meetings I relied on the work of a group of very special people, who found the best problems, gave precious advice and shared with me the teaching:
During these years I have been collecting all the problems selected by our group in a unique document which is free to download:
Algebra problems collection (not completely up-to-date).
The final competition of the Italian Mathematical Olympiad is held every year in Cesenatico at the beginning of May.
This is a four days event whose organization is based on the work of many people. The core is the one-day individual competition, which is four and a half hours long and involves 300 students, but the most anticipated event is probably the two-rounds team competition, which involves one hundred schools, 700 contestants and hundreds of spectators.
The selection of the 300 contestants of the individual competition is quite complex. The previous step is a test held in February in about one hundred different places. It would be impossible to enforce the same level of security and exaclty the same conditions of work in all the locations, so we settled not to merge the scores of the different districts, but to give to each one of them a determined number of places or shares ("quote").
The shares of each district are computed with a complex algorithm which takes into account the results of the district's contestants in Cesenatico during the previous three years and the number of schools in the district which took part to the first local test of the Olympiads.
I am in charge of the management of the algorithm and of the database of the individual results (available since 1997). Some materials can be found below.
Silvia Galfrè (my wife) is the designer of the t-shirts that we give and sell in Cesenatico every year. Eleonora Iotti, Luigi Corvacchola and myself help the management of the over one thousand t-shirts.
Members of the committee and strong ex-contestants are frequently invited to give training sessions of different levels all around Italy.
Many materials can be found here.
From May 2017 I am starting a list (or database) of problems from Italian Olympiads, starting with the somewhat intermediate level of gara provinciale. This is intended as a collaborative work and anyone who wants to help can email me. The list is in the form of a Google spreadsheet and can be viewed and downloaded by anyone here. This activity was presented and explained a little in this talk
In February 2017 I gave some lessons in Macomer, Sardinia at the level of the second individual selection. Materials can be downloaded here.