Gunter and Kuzmin: Collection of Problems in Higher Mathematics: A complete English edition of the classical Russian problem collection (Russian Math Classics — English Editions)

The most complete problem book the Russian mathematical school produced — in English for the first time.

For most of the twentieth century, a student of higher mathematics in Russia worked from one collection. 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, reached 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."

6,314 problems. 814 pages. Every main division of higher mathematics:

- Analytic geometry in the plane and in space
- Differential calculus and its applications, including differential geometry
- Higher algebra
- Indefinite and definite integration
- Multiple, curvilinear and surface integrals; field and potential theory
- Ordinary and partial differential equations
- Improper integrals, special functions, Fourier integrals
- Series and Fourier series
- Approximate computation
- Functions of a complex variable
- Mathematical physics — partial differential equations
- Calculus of variations
- Probability theory

The theoretical interludes that make the problems usable sit exactly where a working student needs them, not in an appendix. The complete answer key is translated in full, with its figures.

The authors were research mathematicians, and the book has the shape it has because of it. Nikolai Günter (1871–1941) was taught by Korkin, Markov and Possé — the direct line of Chebyshev's school — took his doctorate in 1915 on the characteristics of systems of partial differential equations, and was elected a corresponding member of the USSR Academy of Sciences in 1924; his treatise on potential theory appeared in Paris in 1934 in Borel's collection. Rodion Kuzmin (1891–1949) settled in 1928 a question Gauss had raised and left unanswered — the limiting distribution of the partial quotients of a continued fraction — and the result carries both their names. In 1930 he proved that 2^√2 is transcendental, a case of Hilbert's seventh problem, four years before Gelfond and Schneider settled it in general.

A faithful translation, not an adaptation. No problem has been resequenced, renumbered, added or quietly repaired. The numbering runs continuously from 1 to 6314 exactly as in the original, so a reference in the Russian literature to "Günter and Kuzmin, problem 3872" resolves here to the same problem. The Russian-school notation is preserved. Where the original contains a genuine misprint it is corrected only when the correction is the sole reading its own printed answer allows — and every correction is listed at the back with the original reading, so any reader can restore it.

Part of Russian Math Classics — English Editions. Translated by Valery Manokhin, PhD (Royal Holloway, University of London). Published by Northern Star Academic Press. Full catalogue at russianmathbooks.com.