Quantum mechanics:

Quantum state evolution with the use of path integrals (polish)
Solution to Schroedinger equation for an electron in uniform electric field (polish)
Transmission coefficient for a scattering on a potential well and potential barrier (polish)

Statistics/Probability theory:

Derivation of the distribution of arcs length on a sphere (polish)
Derivation of estimator of Maxwell distribution parameter using maximum likelihood method (polish)
Probability in a tennis tournament (polish)

Mathematics:

Calculation of $\int_{0}^{+\infty}\frac{x^{3}}{e^{x}-1}$ (appears e.g. in derivation of Stefan-Boltzmann law) (polish)