Associativity of the Secant Method

by Sam Northshield

Year of Award: 2003

Publication Information: The American Mathematical Monthly, vol. 109, no. , 2002, pp. 246-257

Summary: This paper defines an algebraic operation based on the secant method for finding a root of a fixed function $f$ and shows this operation is associative.  The applications of this fact include interesting results spanning many branches of mathematics.

About the Author: (from The American Mathematical Monthly, Vol. 109, (2002))

Sam Northshield a product of the free-school movement in the U.S., was groomed to be an as- trologer/farmer. After a brief career as an artist and unable to find a real job, he enrolled at Marlboro College where he fell in love with mathematics (thanks to Joe Mazur.) He went on to get a Ph.D. at the University of Rochester (thanks to Carl Mueller) in 1989. His first, and possibly last, real job (interrupted by visiting positions at the University of Minnesota, Gustavus Adolphus College, and Carleton College) is at Plattsburgh SUNY, where he is now Professor of Mathematics. He is very happy to have a job so closely related to his favorite hobby. His preferred research areas are probability, discrete mathematics, and number theory.

Subject classification(s): Algebra and Number Theory
Publication Date:
Tuesday, September 23, 2008