A rather interesting analysis problem that studies the Wallis function: \[ \begin{alignat*}{1} f:]-1,+\infty[&\to\mathbb{R}^{+*}\\ x&\mapsto \int_0^{\frac{\pi}{2}}(\sin t)^x \mathrm{d} t \end{alignat*} \] which is a generalization of the well-known integ…

A very long algebra problem set on polynomials and umbral calculus. At the heart of this formalism is the Pincherle derivation. We introduce the operator \(\mathbf{x}\) which is an endomorphism of polynomials: \[ \begin{alignat*}{1} \mathbf{x}:\math…

Quite an interesting, coherent problem, combining analysis and probability. There were some pretty tricky sections: Questions 22 to 25, which demonstrated the uniform convergence of a sequence of functions to the density of the normal distribution \(\…

The first part of the solutions for Maths 2 MP. Answers to the Maths 2 test on May 12 in the MP Centrale Supelec 2023 exam: Problem set: …

It's easy to get lost in the immensity of the world of matrices, the different types, their properties, the location of their eigenvalues, the different possible decompositions that apply to each category... This brilliant document, created by Kenji Hirana…