Mathematical World 1999; 155 pp; softcover Volume: 14 ISBN10: 0821810022 ISBN13: 9780821810026 List Price: US$27 Member Price: US$21.60 Order Code: MAWRLD/14
 This volume and Kvant Selecta: Algebra and Analysis, II (MAWRLD/15) are the first volumes of articles published from 1970 to 1990 in the Russian journal, Kvant. The influence of this magazine on mathematics and physics education in Russia is unmatched. This collection represents the Russian tradition of expository mathematical writing at its best. Articles selected for these two volumes are written by leading Russian mathematicians and expositors. Some articles contain classical mathematical gems still used in university curricula today. Others feature cuttingedge research from the twentieth century. The articles in these books are written so as to present genuine mathematics in a conceptual, entertaining, and accessible way. The volumes are designed to be used by students and teachers who love mathematics and want to study its various aspects, thus deepening and expanding the school curriculum. The first volume is mainly devoted to various topics in number theory, whereas the second volume treats diverse aspects of analysis and algebra. Cover art created by Sergei Ivanov. Used with permission. Readership Advanced high school and undergraduate students interested in mathematics; mathematics teachers in high schools and colleges. Reviews "The slate of the authors is most impressive ... It becomes even more impressive in view of the fact that these `serious' mathematicians went out of their way to make their sophisticated material understandable by a broad readership ... a welcome edition to mathematics literature where rigor coexists with fun and accessibility."  Zentralblatt MATH Table of Contents  D. B. Fuchs and M. B. Fuchs  The arithmetic of binomial coefficients
 M. I. Bashmakov  Do you like messing around with integers?
 M. I. Bashmakov  On Bertrand's conjecture
 D. B. Fuchs and M. B. Fuchs  On best approximations. I
 D. B. Fuchs and M. B. Fuchs  On best approximations. II
 A. I. Shirshov  On a certain property of binomial coefficients
 L. G. Limanov  On \(n!\) and the number \(e\) (Several approaches to a certain problem)
 D. B. Fuchs and M. B. Fuchs  Rational approximations and transcendence
 V. N. Vaguten  Close fractions
 A. I. Shirshov  On the equation \(\binom{n}{m} = \binom{n+1}{m1}\)
 A. Kirillov  On regular polygons, Euler's function, and Fermat numbers
 B. Bekker, S. Vostokov, and Yu. Ionin  2adic numbers
 E. Kuzmin and A. Shirshov  On the number \(e\)
 M. G. Krein  Markov's Diophantine equation
 A. B. Goncharov  The arithmetic of Gaussian integers
 V. S. Shevelev  Three formulas of Ramanujan
 V. G. Stolyar, E. A. Kuraev, Z. K. Silogadze, G. A. Galperin, and A. V. Korlyukov  Amazing adventures in the land of repeating decimals
