Mathematics from Asia's Past
Victor Katz, Frank Swetz, Kim Plofer
June 10 - 15, 2007
Although much early mathematics developed in China, India, and the world of Islam, mathematical historians are just beginning to appreciate the many mathematical ideas that had their origins there. A great deal of this mathematics has now been translated into English; it is now possible for those teaching the history of mathematics, as well as other subjects in the undergraduate mathematics curriculum, to study this early mathematics and use it in their teaching. Further, the increasingly multicultural makeup of our student bodies makes it imperative that mathematics teachers be aware of the mathematical heritage of many of their students.
This workshop will present details of some of the mathematics of China, India, and Islam, and produce classroom materials based on these ideas that can be used in teaching various topics in the mathematics curriculum. To accomplish this goal, participants will
- Hear lectures on the mathematics of China, India, and Islam
- Participate in lecture/discussions on a few specific mathematical ideas from these cultures
- Read intensively selected original sources from Asian mathematics and take part in small- group discussions of these sources
- Prepare at least one classroom activity using the mathematics of Asia
An electronic network will be set up so participants can continue to work cooperatively on lesson materials in the next few months. We expect that some of these materials will make suitable articles for publication in Convergence, the MAA's online magazine in the history of mathematics and its use in teaching, as well as ideas for presentation at an MAA contributed paper session at the 2008 Annual Meeting.
Additional support provided by Princeton University Press
The Genius of Euler
June 18 - 22, 2007
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 approximations, 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.
For more information on these workshops, including costs and registration information, click here.