**Mathematical World**

Volume: 14;
1999;
155 pp;
Softcover

MSC: Primary 00;

**Print ISBN: 978-0-8218-1002-6
Product Code: MAWRLD/14**

List Price: $31.00

AMS Member Price: $24.80

MAA Member Price: $27.90

**Electronic ISBN: 978-1-4704-6826-2
Product Code: MAWRLD/14.E**

List Price: $31.00

AMS Member Price: $24.80

MAA Member Price: $27.90

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# Kvant Selecta: Algebra and Analysis, I

Share this page *Edited by *
*Serge Tabachnikov*

This volume and

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.

#### Readership

Advanced high school and undergraduate students interested in mathematics; mathematics teachers in high schools and colleges.

#### Reviews & Endorsements

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

# Table of Contents

## Kvant Selecta: Algebra and Analysis, I

- Front Cover 11
- Title 66
- Copyright 77
- Contents 88
- Preface 1010
- The Arithmetic of Binomial Coefficients 1414
- Do You Like Messing Around with Integers? 2626
- On Bertrand's Conjecture 3434
- On Best Approximations. I 4040
- On Best Approximations. II 5050
- On a Certain Property of Binomial Coefficients 6262
- On n! and the Number e (Several Approaches to a Certain Problem) 7070
- Rational Approximations and Transcendence 7878
- Close Fractions 8484
- On the Equation ([sup(n)][sub(m)]) = ([sup(n+1)][sub(m–1)]) 9696
- On Regular Polygons, Euler's Function, and Fermat Numbers 100100
- 2-adic numbers 112112
- On the Number e 124124
- Markov's Diophantine Equation 134134
- The Arithmetic of Gaussian Integers 140140
- Three Formulas of Ramanujan 152152
- Amazing Adventures in the Land of Repeating Decimals 158158
- Back Cover 169169