Gunter and Kuzmin: Collection of Problems in Higher Mathematics: Part I of two — the classic Russian university problem book, first English edition (Russian Math Classics — English Editions)

Part I of 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.”

This is Part I of two. 3,827 problems, numbered 1 to 3827 exactly as in the original. Chapters 1 to 9 carry a reader from the straight line in the plane to multiple, curvilinear and surface integrals: the whole of the geometry, the differential calculus and the integration.

• Analytic geometry in the plane
• Analytic geometry in space
• Differential calculus
• Applications of the differential calculus
• Geometric applications of the differential calculus (differential geometry)
• Higher algebra
• Indefinite integration
• Definite integrals and their plane-geometric applications
• Multiple, curvilinear and surface integrals

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

Which book to buy. The complete work is published in one 814-page volume (ISBN 978-1-919012-45-2), and also in two parts for readers who want a book that opens flat and a binding that survives use. This is Part I; Part II carries differential equations, series, complex variables and probability. A reader who owns only Part I has a complete course in analytic geometry, differential calculus and integration. The numbering never restarts, so the three editions are interchangeable as references: a citation to “Günter and Kuzmin, problem 3872” resolves to the same problem in all of them.

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 silently altered. 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.