Math Olympiads resources

Use and redistribution

  • all documents are © Federico Poloni.
  • the author grants license to use the following documents for the personal study of single students and scholars.
  • permission to use the following documents as training material in any course, to sell, redistribute, or publish them, is not granted. All uses apart from personal study must be explicitly authorised by the author.
  • the author is quite likely to authorise anyone asking him politely, he added the above clauses only to keep track of how his works are used.
  • the author’s name and all the relevant copyright information must be distributed along with the documents.
  • please inform me if you see an unauthorised version of these documents (printed or published in electronic form).


  • 2018-10-22 added slides on Sagemath
  • 2014-10-06 updated syllabus
  • 2009-03-08 migrated to the new site


All this material is in Italian, since we aim to kick the other nations’ asses at the IMO. Most of this stuff was written many years ago, so it is rough and maybe unfinished. As there is very little teaching material on mathematical problem-solving available in Italian, I prefer writing new notes to cleaning up the existing ones. Moreover, I have started doing university and research work, so my thinking time is now mostly devoted to numerical linear algebra.


  • (pdf) (italian) “Come barare alla gara a squadre con Python / Sagemath” Brief tutorial on using Sagemath to check numerical results (‘cheat’, tongue-in-cheek).
  • (pdf) (italian) unofficial syllabus: a list of everything you need to know to take part in the Italian Mathematical Olympiad. Aimed mainly at the district (gara provinciale, Febbraio) and national (Cesenatico) stages. Now hosted on a public github repository.
  • (pdf) (italian) A short essay on functional equations. It started as a transcript of some of my lesson notes, then evolved to be a decent and self-contained work.
  • (pdf) (italian) known as Barbatrucchi: unfinished short essay on some practical problem-solving tricks. This part is about algebra.
  • (pdf) (italian) similar to the above, but covers number theory.
  • (pdf) (italian) commented solution to problem 1,2,4,5 of IMO 2003. That’s all I could manage to solve in a decent amount of time :)
  • (pdf) (italian) Newton’s and Mac Laurin’s inequalities. Introduction and short proof using basic calculus.
  • (pdf) (italian) A proof of Napoleon’s theorem using complex numbers