The Genius of Euler

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To honor the 300th birthday of Leonhard Euler (1707 - 1783), we will examine some of his many mathematical contributions. After a brief overview of his life and work, attendees will plunge into some of his "greatest hits". These results--presented in their original form--will include:

• The Basel problem - Euler's summation of the reciprocals of the squares
• Euler's calculus - his concept of "function" and "differential", his proof of L'Hospital's Rule, his approximation of pi, and some really neat integrals
• A taste of number theory - his discovery of dozens of "new" amicable pairs, the Euclid-Euler theorem on even perfect numbers, and the birth of analytic number theory
• Some of Euler's geometry - his proof of Heron's Formula and a quadrilateral theorem

Problem sets will accompany the daily sessions. These will include "modern" proofs of Eulerian theorems or subsequent developments suggested by his work. In addition, participants will have access to the first series of Euler's Opera Omnia - i.e., the 29 volumes of his collected works devoted to pure mathematics.

In keeping with the PREP philosophy, the week's final sessions will be devoted to participant presentations. Working in small groups and using either the Opera Omnia or other resources, participants will prepare lectures on topics of their choice, thereby helping to enrich our journey through Euler-land.

When all is said and done, each of us will understand why Euler is held in such high esteem by the mathematical community and why his tercentenary is an event to be celebrated.

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