Subject: [HM] Fundamental Theorem of Algebra
From: John Dawson (jwd7@psu.edu)
Date: Fri Apr 07 2000 - 14:50:53 EDT
Is there a proof of the fundamental theorem of algebra that can be
understood by students with only a calculus background? I seem to recall,
years ago, that one of the older calculus texts included a proof involving
no concepts beyond partial derivatives. As I recall it was not well
motivated -- the result fell out as a result of some precise numerical
estimates with inequalities -- but did accomplish its purpose. I've
examined the text by Fine and Rosenberger, which includes many proofs of
the theorem and could serve as the basis for a wonderful survey course
integrating topolgy, Galois theory, complex analysis etc., but none of the
proofs there seem low-level enough to present to calculus students.
Thanks in advance for any advice/references.
Dr. John W. Dawson, Jr.
Professor of Mathematics
Penn State York
1031 Edgecomb Avenue
York, PA 17403 U.S.A.
Tel.: 717-771-4131 (work)
717-846-1225 (home)
FAX: 717-771-8404
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