An Euler Trifecta
Dr. William Dunham
Truman Koehler Professor of Mathematics, Muhlenberg College
The Department of Mathematics at the University of Dayton presents
The 8th Annual Kenneth C. Schraut Memorial Lecture
Saturday, November 3, 2007
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An Euler Trifecta Dr. William Dunham Truman Koehler Professor of Mathematics, Muhlenberg College
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Abstract:
To recognize Leonhard Euler’s 300th birthday, we
sketch his life and give a brief survey of some of his mathematical
achievements. Then we’ll consider three specific results from this great
mathematician. The first is his 1740 proof that there are as many ways to write
a whole number as the sum of distinct summands as there are ways to write it as
the sum of (not necessarily distinct) odd summands – the discovery that gave
birth to the study of number partitions. Next, we get a glimpse of his calculus
skills from 1775 as he evaluates a definite integral that no one would dare to
touch in Calc II. Finally, we examine Euler’s unorthodox proof of his famous
identity from 1749. Taken together, these examples remind us why it is so
fitting that we celebrate his birthday in 2007.
This talk should be accessible to undergraduate students with a bit of calculus
under their belts.
About the speaker:
William Dunham, who received his B.S. (1969) from the University of
Pittsburgh and his M.S. (1970) and Ph.D.(1974) from Ohio State, is the Truman
Koehler Professor of Mathematics at Muhlenberg College. Trained in general
topology, Dunham became interested in the history of mathematics. He has
directed NEH-funded seminars on math history at Ohio State and has spoken on
historical topics at national and regional meetings as well as at the
Smithsonian Institution, on NPR’s “Talk of the Nation: Science Friday,” and on
the BBC. In the 1990s, Dunham wrote three books – Journey Through Genius
(1990), The Mathematical Universe (1994), and Euler: The Master of Us All (1999)
– and in the present century he has written two more: The Calculus Gallery:
Masterpieces from Newton to Lebesgue (2005) and The Genius of Euler: Reflections
on His Life and Work (2007). Dunham’s expository writing has been
recognized by the MAA with the George Pólya Award in 1993, the Trevor Evans
Award in 1997, and the Lester Ford Award in 2006, and the Association of
American Publishers designated The Mathematical Universe as the Best Mathematics
Book of 1994.