Algebra and analysis
著者
書誌事項
Algebra and analysis
（Mathematical world, v. 14-15 . Kvant selecta）
American Mathematical Society, c1999
- 1
- 2
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注記
Includes bibliographical references and index
"This volume is a collection of articles translated from Russian Editions of the journal "Kvant"" -- T.p. verso of v. 1 and v. 2
内容説明・目次
- 巻冊次
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1 ISBN 9780821810026
内容説明
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.
目次
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.
- 巻冊次
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2 ISBN 9780821819159
内容説明
This volume and ""Kvant Selecta: Algebra and Analysis, I"" (""MAWRLD/14"") 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.
目次
Binomial coefficients, polynomials, and sequences (Several approaches to a certain problem) by V. N. Vaguten Formulas for prime numbers by Yu. V. Matiyasevich Fermat's theorem for polynomials by B. Martynov Commuting polynomials by I. Yantarov On the removal of parentheses, on Euler, Gauss, and Macdonald, and on missed opportunities by D. B. Fuchs Chebyshev polynomials and recurrence relations by N. Vasil'ev and A. Zelevinskii Why resistance does not decrease by O. V. Lyashko Evolution processes and ordinary differential equations by V. I. Arnol'd Irrationality and irreducibility by V. A. Oleinikov Irreducibility and irrationality by V. A. Oleinikov The arithmetic of elliptic curves by Yu. P. Solov'ev Pascal's hexagrams and cubic curves by N. B. Vasil'ev Kepler's second law and the topology of abelian integrals (According to Newton) by V. I. Arnol'd Partitions of integers by F. V. Vainstein On the Denogardus great number and Hooke's law by V. Yu. Ovsienko Polynomials having least deviation from zero by S. Tabachnikov.
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