Abstract Algebra: For College Professors and Secondary Teachers by Richard Grassl

This textbook is designed to provide an adequate introduction to the essentials of abstract algebra and to some related number theory. A problem solving approach has been taken – there are over 150 problems – so be prepared for minimal text material to read. Very little background in abstract algebra is needed for a course based on this textbook. The content and methodology has been implemented successfully for well over a decade with in-service secondary teachers seeking licensure or an MA degree in teaching mathematics. The oft-quoted maxim - “You learn mathematics by doing mathematics” is embraced. A valuable by-product: A significant number of teachers who have experienced this material have incorporated a variety of the topics and problems into their secondary curriculum as they encounter topics like closure, binary operations, modular arithmetic, the structure of the integers (yes, gcd and lcm play a role), and the rational and real numbers.