**Dolciani Mathematical Expositions**

Volume: 22;
1999;
185 pp;
Softcover

**Print ISBN: 978-0-88385-328-3
Product Code: DOL/22**

List Price: $43.00

AMS Member Price: $32.25

MAA Member Price: $32.25

**Electronic ISBN: 978-1-4704-5841-6
Product Code: DOL/22.E**

List Price: $43.00

AMS Member Price: $32.25

MAA Member Price: $32.25

# Euler: The Master of Us All

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*William Dunham*

MAA Press: An Imprint of the American Mathematical Society

Recipient of the Mathematical Association of America's
Beckenbach Book Prize in 2008!

Leonhard Euler was one of the most prolific
mathematicians that have ever lived. This book examines the huge scope
of mathematical areas explored and developed by Euler, which includes
number theory, combinatorics, geometry, complex variables and many
more. The information known to Euler over 300 years ago is discussed,
and many of his advances are reconstructed. Readers will be left in no
doubt about the brilliance and pervasive influence of Euler's
work.

#### Reviews & Endorsements

An ideal book for enlivening undergraduate mathematics … he [Dunham] has Euler dazzling us with cleverness, page after page.

-- Choice

Mathematician William Dunham has written a superb book about the life and amazing achievements of one of the greatest mathematicians of all time. Unlike earlier writings about Euler, Professor Dunham gives crystal clear accounts of how Euler ingeniously proved his most significant results, and how later experts have stood on Euler's broad shoulders. Such a book has long been overdue. It will not need to be done again for a long long time.

-- Martin Gardner

William Dunham has done it again! In "Euler: the Master of Us All", he has produced a masterful portrait of one of the most fertile mathematicians of all time. With Dunham's beautiful clarity and wit, we can follow with amazement Euler's strokes of genius which laid the groundwork for most of the mathematics we have today.

-- Ron Graham, Chief Scientist, AT & T

# Table of Contents

## Euler: The Master of Us All

- Cover Cover11
- Copyright ii3
- Title iii4
- Contents ix10
- Acknowledgments xi12
- Preface xv16
- Biographical Sketch xix20
- 1. Euler and Number Theory 130
- 2. Euler and Logarithms 1746
- 3. Euler and Infinite Series 3968
- 4. Euler and Analytic Number Theory 6190
- 5. Euler and Complex Variables 81110
- 6. Euler and Algebra 103132
- 7. Euler and Geometry 125154
- 8. Euler and Combinatorics 149178
- Conclusion 171200
- Appendix: Euler's Opera Omnia 175204
- Index 181210