Master's studies

Preparations for Master's examinations left almost no time for research: the theoretical courses which were to be studied for the examinations were quite extensive, and the examination requirements were extremely challenging. In July 1911, in the letter in which Friedmann informed his professor about his forthcoming marriage, he also gave a brief “graduate student's” report: “Our studies with Yak. Dav. seem to be going quite well. They have naturally been confined to reading the courses you recommended and articles for the Master's examinations. We are through with hydrodynamics and are going on to study the theory of electricity.” Therefore, during his Master's studies Friedmann published relatively few papers. In one article – ‘On finding particular solutions of the Laplace equation”, which appeared in 1911 in the Bulletin of the Kharkov Mathematical Society – he solved, as any Master's degree student was supposed to do, the problem set in his teacher's doctoral thesis: find all orthogonal coordinates in which Laplace's three-dimensional equation admits of partial separation of the variables. In solving this problem, according to V. A. Steklov's testimonial, Friedmann ‘displayed the required ingenuity and a good knowledge of analysis.” Another paper on the theory of partial differential equations, “On finding isodynamic surfaces,” came out in 1912. Friedmann learned about the problem of isodynamic surfaces from A. E. H. Love's textbook on the theory of elasticity. In Lamé's definition, isodynamic surfaces are surfaces in an elastic body, on which there are no oblique tensions, and each normal tension depends on only one coordinate.