Sol Lederman of Wild About Math interviewed Al Cuoco on his latest book Learning Modern Algebra: From Early Attempts to Prove Fermat's Last Theorem (co-author Joseph Rotman).
Listen to the interview here.
Learning Modern Algebra: From Early Attempts to Prove Fermat's Last Theorem
by Al Cuoco and Joseph Rotman
book is designed for prospective and practicing high school mathematics
teachers, but it can serve as a text for standard abstract algebra
courses as well. The presentation is organized historically: the
Babylonians introduced Pythagorean triples to teach the Pythagorean
theorem; these were classified by Diophantus, and eventually this led
Fermat to conjecture his Last Theorem. The text shows how much of modern
algebra arose in attempts to prove this; it also shows how other
important themes in algebra arose from questions related to teaching.
Indeed, modern algebra is a very useful tool for teachers, with deep
connections to the actual content of high school mathematics, as well as
to the mathematics teachers use in their profession that doesn't
necessarily "end up on the blackboard."