Diane Cass, Math Librarian, Carlson Library
dcass@library.rochester.edu

Thanks, Diane. Here's the list:

Euler : the master of us all / William Dunham. 

Mathematical Association of America, c1999. 
Carlson Library Circulating Books 3rd Floor 
Call Number: QA29.E8 D86 1999


The Hilbert challenge / Jeremy J. Gray. 
Oxford ; New York : Oxford University Press, 2000.
Carlson Library Circulating Books 3rd Floor 
Call Number: QA29.H5 G739 2000 


Hilbert / Constance Reid. 
New York : Copernicus, c1996. 
Carlson Library Circulating Books 3rd Floor 
Call Number: QA29.H5 R4 1996

Date: Wednesday November 6, 2002 Place: Hylan 901 (Undergraduate Math Lounge) Time: 8:00pm

Speaker: Dr. Mark McKinzie Monroe Community College

co- winner of the 2002 Allendoerfer award for his article with Curtis Tuckey on "Higher Trigonometry, Hyperreal Numbers, and Euler's Analysis of Infinities" in Math Magazine (December 2001)

Title: Precalculus circa 1748: Euler's Introduction to the Analysis of Infinities

Abstract: Leonhard Euler's "Introductio in analysin infinitorum" (1748) was explicitly written as a precalculus text. Euler writes: "Although analysis does not require an exhaustive knowledge of algebra, ... still there are topics which prepare a student for a deeper understanding. However, in the ordinary treatise on the elements of algebra, these topics are either completely omitted or are treated carelessly. For this reason, I am certain that the material I have gathered in this book is quite sufficient to remedy that defect." The contents of Euler's text, including derivations of the power series for the exponential, logarithmic and trigonometric functions, the factorizations of the sine and cosine functions, and the consequent evaluation of the sum of the reciprocal squares, bear scant resemblance to what we currently teach in our own precalculus classes. In this talk, we will examine Euler's arguments for the above results, and give an overview of recent interpretations of Euler's "Introductio in analysin infinitorum" in light of modern developments in nonstandard mathematics.

Hope you can make it! -Inga

Comments: In Euler's time there didn't seem to be a lot of concern about whether infinitesimals existed or whether series converged -- that came later, with Cauchy and Weierstrass who were more rigorous -- or were they? Maybe Euler knew what he was doing. About 40 years ago Abraham Robinson showed that in fact it was possible to reason logically with infinitesimals, founding the subject frequently known as Non-standard Analysis. If the timing had worked out a bit differently would we be doing calculus with infinitesimals now instead of limits? And would that be an improvement?

-- Mike

(see also Euler, The Master of Us All)
Posted by Michael Gage on 10/28/02; 3:27:59 AM
from the dept.
Discuss