# Kvant Selecta: Algebra and Analysis, I

### About this Title

**Serge Tabachnikov**, *University of Arkansas at Fayetteville, Fayetteville, AR*, Editor

Publication: Mathematical World

Publication Year
1999: Volume 14

ISBN: 978-0-8218-1002-6 (print)

DOI: http://dx.doi.org/10.1090/mawrld/014

MathSciNet review: MR1730216

MSC: Primary 11-06

This volume is not part of this online collection, but can be
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Read more about this volume

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.

Readership

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

### Table of Contents

**Chapters**

- 1. The arithmetic of binomial coefficients
- 2. Do you like messing around with integers?
- 3. On Bertrand’s conjecture
- 4. On best approximations. I
- 5. On best approximations. II
- 6. On a certain property of binomial coefficients
- 7. On $n!$ and the number $e$ (Several approaches to a certain problem)
- 8. Rational approximations and transcendence
- 9. Close fractions
- 10. On the equation $\binom {n}{m} = \binom {n+1}{m-1}$
- 11. On regular polygons, Euler’s function, and Fermat numbers
- 12. 2-adic numbers
- 13. On the number $e$
- 14. Markov’s Diophantine equation
- 15. The arithmetic of Gaussian integers
- 16. Three formulas of Ramanujan
- 17. Amazing adventures in the land of repeating decimals