Learning Modern Algebra aligns with the CBMS Mathematical Education of Teachers–II recommendations, in both content and practice. It emphasizes rings and fields over groups, and it makes explicit connections between the ideas of abstract algebra and the mathematics used by high school teachers. It provides opportunities for prospective and practicing teachers to experience mathematics for themselves, before the formalities are developed, and it is explicit about the mathematical habits of mind that lie beneath the definitions and theorems.
Learning Modern Algebra is designed for college students who want to teach mathematics in high school, but it can serve as a text for standard abstract algebra courses as well. First courses in abstract algebra usually cover number theory, groups, and commutative rings. This book focuses on number theory, polynomials, and commutative rings. Groups are introduced in the last chapter, for the earlier discussion of commutative rings allows an explanation of how groups are used to prove Abel’s Theorem: there is no generalization of the quadratic, cubic, and quartic formulas giving the roots of the general quintic polynomial.
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 from 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.
* As a textbook, Learning Modern Algebra does have DRM. Our DRM protected PDFs can be downloaded to three computers. iOS tablets can open secure PDFs using the AWReader app (available in the App Store). The iOS app uses the native iPad PDF reader so it is a very basic reader, no frills. Linux is not supported at this time for our secure PDFs.
Electronic ISBN: 9781614446125