**Mathematical World**

Volume: 15;
1999;
165 pp;
Softcover

MSC: Primary 00;

**Print ISBN: 978-0-8218-1915-9
Product Code: MAWRLD/15**

List Price: $31.00

AMS Member Price: $24.80

MAA Member Price: $27.90

**Electronic ISBN: 978-1-4704-6880-4
Product Code: MAWRLD/15.E**

List Price: $31.00

AMS Member Price: $24.80

MAA Member Price: $27.90

# Kvant Selecta: Algebra and Analysis, II

Share this page *Edited by *
*Serge Tabachnikov*

#### Readership

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

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.

Published in the very popular and relatively basic-level Mathematical World series. Features a low price and a colorful cover. This is kind of a “What's Happening in Russian Mathematics” (Russian mathematics are still considered to be among the best in the world). Second of two volumes on the topic.

`MAWRLD/14`

#### Table of Contents

# Table of Contents

## Kvant Selecta: Algebra and Analysis, II

- Cover 11
- Title 66
- Copyright 77
- Contents 88
- Preface 1010
- Binomial Coefficients, Polynomials, and Sequences (Several Approaches to a Certain Problem) 1212
- Formulas for Prime Numbers 2424
- Fermat's Theorem for Polynomials 3636
- Commuting Polynomials 4242
- On the Removal of Parentheses, on Euler, Gauss, and MacDonald, and on Missed Opportunities 5050
- Chebyshev Polynomials and Recurrence Relations 6262
- Why Resistance Does Not Decrease 7474
- Evolution Processes and Ordinary Differential Equations 8484
- Irrationality and Irreducibility 9898
- Irreducibility and Irrationality 106106
- The Arithmetic of Elliptic Curves 116116
- Pascal's Hexagrams and Cubic Curves 128128
- Kepler's Second Law and the Topology of Abelian Integrals (According toNewton) 142142
- Partitions of Integers 152152
- On the Denogardus Great Number and Hook's Law 164164
- Polynomials Having Least Deviation from Zero 172172
- Back Cover 177177