Written for the mathematically literate reader, this book provides a glimpse of Euler in action. Following an introductory biographical sketch are chapters describing his contributions to eight different topics—number theory, logarithms, infinite series, analytic number theory, complex variables, algebra, geometry, and combinatorics.
Table of Contents
Euler and Number Theory
Euler and Logarithms
Euler and Infinite Series
Euler and Analytic Number Theory
Euler and Complex Variables
Euler and Algebra
Euler and Geometry
Euler and Combinatorics
Appendix: Euler’s Opera Omnia
About the Author
William Dunham is the Truman Koehler Professor of Mathematics at Muhlenberg College in Allentown, Pennsylvania. He has won two awards for excellence in expository writing from the Mathematical Association of America: the 1993 George Pólya Award, and in 1997, the Trevor Evans Award. His books Journey Through Genius: The Great Theorems of Mathematics, and The Mathematical Universe have both been selections of the Book-of-the-Month Club and the History Book Club. He has also been the recipient of several grants from the National Endowment for the Humanities to fund seminars on the great theorems of mathematics in historical context.
Who are the ten best baseball players of all time? Or the ten best pieces of music? With so many excellent choices, who could ever agree on the answers?
Bill Dunham faced similar questions when he picked Euler's best work from over 35,000 pages, over 800 works. He had experience, though. When he wrote his excellent book, Journey through Genius, he narrowed the field to just twelve great theorems in mathematics, and won awards for his efforts.
In Euler: The Master of Us All, Bill Dunham describes some of Euler's most important contributions in eight mathematical fields, Number Theory, Logarithms, Infinite Series, Analytic Number Theory, Complex Variables, Algebra, Geometry and Combinatorics. These eight chapters, sandwiched between a Biographical Sketch at the beginning, and a few pages of Conclusions, make this a short book and leave the reader hungry for more. Dunham anticipated this in his Preface, where he confesses "I have omitted virtually ALL of Euler's work." He also admits that "Fifty different authors would come up with fifty different books (and I'd be interested in the other forty-nine)." Continued...