Learning Modern Algebra : From Early Attempts to Prove Fermat's Last Theorem

Much of modern algebra arose from attempts to prove Fermat's Last Theorem, which in turn has its roots in Diophantus' classification of Pythagorean triples. This book, designed for prospective and practising mathematics teachers, makes explicit connections between the ideas of abstract algebra and the mathematics taught at high-school level. Algebraic concepts are presented in historical order, and the book also demonstrates how other important themes in algebra arose from questions related to teaching. The focus is on number theory, polynomials, and commutative rings. Group theory is introduced near the end of the text to explain why generalisations of the quadratic formula do not exist for polynomials of high degree, allowing the reader to appreciate the work of Galois and Abel. Results are motivated with specific examples, and applications range from the theory of repeating decimals to the use of imaginary quadratic fields to construct problems with rational solutions.

Al Cuoco is Distinguished Scholar and Director of the Center for Mathematics Education at Education Development Center, Inc., (EDC). He is lead author for the CME Project, a four-year NSF-funded high school curriculum, published by Pearson. He also co-directs Focus on Mathematics, a mathematics-science partnership that has established a mathematical community of mathematicians, teachers, and mathematics educators.

Joseph Rotman has been on the faculty of the mathematics department of the University of Illinois, Urbana-Champaign since 1959, and has been Professor Emeritus since 2004. Professor Rotman was an editor of Proceedings of the American Mathematical Society (1970, 1971) and managing editor (1972, 1973). Aside from writing research articles, mostly on algebra, he has written textbooks on group theory, homological algebra, algebraic topology, Galois theory, and abstract algebra.