This book contains records of a one-year experimental special course in natural science content. It presents three topics: - analysis of the dimensions of physical quantities with examples of applications, including the Kolmogorov turbulence model; - functions of many variables and the phenomenon of concentration: nonlinear law of large numbers, geometric meaning of Gaussian and Maxwell distributions, the Kotelnikov-Shannon theorem; - classical thermodynamics and contact geometry: two principles of thermodynamics in the language of forms, distributions and the Frobenius theorem, the Carnot-Carathéodory metric.

The special course is intended primarily for mathematicians, but can also be useful for students and specialists of other specialties.

The appendix contains a publicly available article by the author “Mathematics as a language and method.”

M.: MTsNMO, 2018. - 155 p. — ISBN 978-5-4439-3225-5.

Literature on thermodynamics, physical and colloidal chemistry and related topics