A problem about normal law, Student's and \(\chi^2\)'s.

An original problem which studies different models of ferromagnetism.

A proof of the irrationality of \(\zeta(2)=\sum_{n=1}^{+\infty} \frac{1}{n^2}\).

The main topic of this problem set is the optimization of multivariable functions.

The first part of the problem is about polynomial osculation. The second is linear algebra in \(\mathbb{R}_n[X]\) fitted with an inner product. The third is about the power series development of \(r\mapsto (1-2rx+r^2)^{-\lambda}\).In the last part, we introduce positive-type functions in dimension \(N\).