Bibliography

I. N. Bronshtein and K. A. Semendyayev. Handbook of Mathematics for Engineers and Students of Higher Technical Institutions. 556 pp. (format 10 × 15 cm), OGIZ, State Publishing House of Technical and Theoretical Literature. Moscow—Leningrad, 1945. Price in binding 27 rubles.

In this “pocket-format” book the authors have very thoughtfully selected extensive reference material on mathematics. The book is divided into six sections. The first section: Tables and graphs. Here, in addition to 18 tables of elementary functions, 5 tables of special functions are given (gamma function, Bessel functions, Legendre polynomials, elliptic integrals, probability integral). In the chapter “Graphs,” along with graphs of elementary functions, curves of the third and fourth orders, cycloids, spirals (including Cornu’s spiral), and some other curves are given.

The second section: Elementary mathematics. Let us note the chapter “Approximate computations.” Very useful are tables 146 and 147 of errors in using “standard” approximate formulas such as $\sin x = x$ or $e^x = 1 + x$; the table indicates the ranges of the argument for which the error does not exceed 0.1%, 1%, and 10%. In the chapter “Trigonometry,” alongside plane trigonometry, material on spherical and hyperbolic trigonometry is given. The third section: Analytic and differential geometry. The fourth section: Fundamentals of mathematical analysis. Let us note here the fairly complete tables of indefinite and definite integrals, the most important series, and equations of mathematical physics. The fifth section: Supplementary chapters of analysis. Here are given: Complex numbers (including functions of a complex variable), vector analysis, Fourier series. The sixth section: Processing of observations, fundamentals of probability theory and the theory of errors, empirical formulas.

At the end of the book there is a bibliography and a detailed alphabetical index, which greatly facilitates use of the book.

The review just presented shows how rich in content this book is. Everything concerning the work of the authors and the publishing editor has been done in it with the utmost culture and expediency. Unfortunately, the same cannot be said of the typographical execution. It is simply unsatisfactory. The publication of books of this kind is a very responsible matter. This, apparently, was not at all appreciated by the printing house of Gospolitizdat, where the book was printed. For compactness, the book was printed in nonpareil; only thanks to this did the enormous amount of material fit into a book that can indeed be carried in one’s pocket. But in such a case the printing must be flawless; otherwise use of the book will be difficult. Meanwhile, in this case the pages are printed either pale and indistinct, or, on the contrary, flooded with ink; in the reviewer’s copy, in the table of the function $e^{-x}$ on p. 72, two lines did not come out at all (a white spot!); on p. 145 an example of abbreviated multiplication is almost impossible to make out, since some figures are barely visible and others have run together; the printing of pp. 450, 451, and a number of others is completely unsatisfactory.

It remains for us to wish that this very useful book, which will undoubtedly find wide circulation also beyond the circle of readers intended by the authors (in particular, among physicists), will soon appear in a second edition, in good form.

E. Shpolsky