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Here I have published a few unsorted documents about "olympiad-like" maths. All of these are in Italian. E-mails which point out errors and typoes and/or contain useful comments will be appreciated: my current addresses are fphthirtyseven@ngi.it or f.polonithirtyseven@sns.it. Please remove the number 37 to get the real addresses, I prefer not to publish them on the internet as they are to avoid spam. Anyway, I hope at least one of them is still active when you read this :) .
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Please note that there are a few restrictions upon the usage of the following documents:


ps pdf An incomplete and unofficial "syllabus", i.e. a programme which lists all the knowledge and theory you will need to know at the Italian Math Olympiads
ps pdf INCOMPLETE. A short essay on "pratical" problem-solving, titled "Barbatrucchi per il problem-solving". If you find it interesting, write me: if I get many enthusiastic and cheerful e-mails about it, I could even find the time/strength/will to finish it :)
pdf INCOMPLETE Some quick pratical notes and tricks in Number Theory (pre-IMO level). I have tried to write it in the same spirit as the previous "barbatrucchi". Please read the introduction for more information.
ps pdf My own (commented) solutions to problems 1,2,4 and 5 of IMO 2003 (I was not able to solve the others :) ) Hope you will like my style. :)
ps pdf "Arnesi per risolvere le equazioni funzionali" : a 20-pages paper on functional equations. It is the most complete work I have written up to now, it covers the subject quite fully.
ps pdf A short essay on Newton's and MacLaurin's inequalities. Short introduction and (analytic) proof. It uses some "quinta liceo" analysis.
ps pdf This is my high-school "tesina", titled "Una dimostrazione elementare dell'ellitticitą delle orbite". It contains an original proof that orbits (in the classical two-body gravitational problem) are conics. Hope you'll find it interesting. It has never been reviewed since I wrote it (at the age of 18/19), so there could be lots of errors. Moreover, I think the introduction and the whole textual part would need a complete rewriting. Anyway, I think the proof itself works. Someone told me I could try to have it published on a "didactic-of-physics" journal, but I never cared to do it.
ps pdf A proof of Napoleon's theorem (given a triangle, erect equilateral triangles on its sides: then their centroids form another equilateral triangle) using complex numbers. It includes as well a short introduction on the use of complex numbers in geometry and their relationship with plane isometries. Read this only if you are already familiar with exponential form and complex roots of unity.
ps pdf This is my high-school "tesina", titled "Una dimostrazione elementare dell'ellitticitą delle orbite". It contains an original proof that orbits (in the classical two-body gravitational problem) are conics. Hope you'll find it interesting. It has never been reviewed since I wrote it (at the age of 18/19), so there could be lots of errors. Moreover, I think the introduction and the whole textual part would need a complete rewriting. Anyway, I think the proof itself works. Someone told me I could try to have it published on a "didactic-of-physics" journal, but I never cared to do it.
ps pdf A short seminar paper about "covering and partitioning problems", which I had to do for the last univerisity term (it was my "Ricerca Operativa" oral exam). This is not, strictly speaking, elementary and olympic maths, but I think it might be interesting for someone, so I published it with the other docs. Moreover, all you need to know to read the paper is how to multiply vectors and matrices (plus understanding some tricky nonation on "breaking" matrices and vectors into parts).
pdf My Bachelor (laurea triennale) thesis. Disclaimer about non-olimpicity as above. Since I currently have no non-olimpic math zone to publish it, I have simply put it here. Enjoy.

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