Students' Mathematical Society of the University of Silesia conquered the holiday resort of US in Szczyrk again and ignoring the not-so-pleasant aura indulged itself in social and mathematical activities.
We were not too strict about sticking to the original topic and so
- Agnieszka Klama and Grzegorz Goldyszewicz gave us a little talk from the mathematical economy, talking about utility and demand functions. Along the way we got to know about applications of the theorem of a non-empty intersection of a centred family of subsets of a compact space or the implicit function theorem. Rafał Kucharski showed us terrible formulas which told us that sometimes demand for goods rises even though their prices also rise (we call them Giffen goods).
- Radek Smogura told us about game theory (which has applications in solving economical problems)
- Włodek Fechner showed us an interesting problems along with three different solutions of it.
- dr Tomasz Szostok, who gave us a visit as our new tutor, presented the problem of generalising the sinus functions to arbitrary normed spaces.
- Renatka Kawa and Tomek Kochanek introduced us to the astonishing (and soporific to some) world of the p-adic numbers. Rafał Kucharski put forward some technical results concerning the Hilbert symbol and Kuba Byszewski applied all of this to classify the quadratic sorms on Q (the Hasse-Minkowski theorem) and show some corollaries (e.g. when is a natural number a sum of two, three or four squares).
last update: 23.01.2011