For most of the twentieth century, if you studied higher mathematics in Russia, you worked from one problem book. This is its first English edition. Günter and Kuzmin's Collection of Problems in Higher Mathematics began in 1912 as a working set of problems compiled by the mathematics department of the Institute of Engineers of Ways of Communication in St Petersburg. It grew to three volumes, ran to a thirteenth edition, and became the standard problem book of the Soviet universities and the higher technical institutes alike. Russian biographical accounts record that its problems supplied the mathematics of the entrance examination Lev Landau set his prospective students — the celebrated "theoretical minimum." Here is the part most people don't know. The two men who assembled it were not textbook compilers. They were working research mathematicians, and it shows on every page. RODION KUZMIN (1891–1949) left two permanent results. In 1928 he settled a question Gauss had raised and left unanswered — the limiting distribution of the partial quotients of a continued fraction — and was the first to prove it with an estimate of the rate of convergence. The theorem and the distribution now carry Gauss's name and his. In 1930 he proved that a^b is transcendental whenever a is a positive algebraic number other than 1 and b is a real quadratic irrational. So 2^√2 is transcendental. That is a case of Hilbert's seventh problem, and he got there four years before Gelfond and Schneider settled it in general. He was expelled from Petersburg University for student politics, finished his degree at Petrograd in 1916, and held the chair of general mathematics at Leningrad University from 1945 until his death. NIKOLAI GÜNTER (1871–1941) was taught by Korkin, Markov and Possé — the direct line of Chebyshev's school. Doctorate in 1915 on the characteristics of systems of partial differential equations. Professor from 1916 until his death. Corresponding member of the USSR Academy of Sciences from 1924. His treatise on potential theory was published in Paris in 1934, in Borel's collection at Gauthier-Villars, and reviewed in the English mathematical press on publication. He led the higher mathematics department at the Institute of Engineers of Ways of Communication from 1906, and for long stretches taught at four institutions at once, across some four decades. Günter died in 1941. Kuzmin finished the last revision alone and signed its preface from Biysk, in 1944, a long way from Leningrad. WHAT IS IN THE BOOK 6,314 problems, numbered continuously from 1 to 6,314, running from analytic geometry in the plane through to the calculus of variations and the theory of probability. Higher algebra, integration, multiple and surface integrals, ordinary and partial differential equations, special functions, series, approximate computation, complex variables, mathematical physics. The theoretical interludes that make the problems usable sit exactly where a working student needs them — not in an appendix. a.co/d/07jMUsK1

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I came to realize people liked the french #slopcore without having the lyrics 😅 sorry! So here is a version with english subtitles!