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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 curriculae today. Others feature cutting-edge research from the 20th 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 articles in the first volume are mainly devoted to various topics in number theory, whereas the second volume treats diverse aspects of analysis and algebra.
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 curriculae today. Others feature cutting-edge research from the 20th 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 articles in the first volume are mainly devoted to various topics in number theory, whereas the second volume treats diverse aspects of analysis and algebra.
The arithmetic of binomial coefficients by D. B. Fuchs and M. B. Fuchs Do you like messing around with integers? by M. I. Bashmakov On Bertrand's conjecture by M. I. Bashmakov On best approximations. I by D. B. Fuchs and M. B. Fuchs On best approximations. II by D. B. Fuchs and M. B. Fuchs On a certain property of binomial coefficients by A. I. Shirshov On $n!$ and the number $e$ (Several approaches to a certain problem) by L. G. Limanov Rational approximations and transcendence by D. B. Fuchs and M. B. Fuchs Close fractions by V. N. Vaguten On the equation $binom{n}{m} = binom{n+1}{m-1}$ by A. I. Shirshov On regular polygons, Euler's function, and Fermat numbers by A. Kirillov 2-adic numbers by B. Bekker, S. Vostokov, and Yu. Ionin On the number $e$ by E. Kuzmin and A. Shirshov Markov's Diophantine equation by M. G. Krein The arithmetic of Gaussian integers by A. B. Goncharov Three formulas of Ramanujan by V. S. Shevelev Amazing adventures in the land of repeating decimals by V. G. Stolyar, E. A. Kuraev, Z. K. Silogadze, G. A. Galperin, and A. V. Korlyukov.
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