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 cutting-edge 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 co-exists 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 \(\binom{n}{m} = \binom{n+1}{m-1}\)
• A. Kirillov -- On regular polygons, Euler's function, and Fermat numbers
• B. Bekker, S. Vostokov, and Yu. Ionin -- 2-adic 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