This paperback book is in excellent condition. The cover is almost as new except for a slight indentation across the front and a small crease at the back of the top of the spine. Internally the pages are in excellent condition - clean, tight and unmarked - almost as new.
Mathematics is often regarded as the study of calculation, but in fact, mathematics is much more. It combines creativity and logic in order to arrive at abstract truths. This book is intended to illustrate how calculation, creativity, and logic can be combined to solve a range of problems in algebra. Originally conceived as a text for a course for future secondary-school mathematics teachers, this book has developed into one that could serve well in an undergraduate course in abstract algebra or a course designed as an introduction to higher mathematics. Not all topics ina traditional algebra course are covered. Rather, the author focuses on integers, polynomials, their ring structure, and fields, with the aim that students master a small number of serious mathematical ideas. The topics studied should be of interest to all mathematics students and are especially appropriate for future teachers.
One nonstandard feature of the book is the small number of theorems for which full proofs are given. Many proofs are left as exercises, and for almost every such exercise, a detailed hint or outline of the proof is provided. These exercises form the heart of the text. Unwinding the meaning of a hint or outline can be a significant challenge, and the unwinding process serves as a catalyst for learning.
This book began life as a set of notes that I developed for a course at the University of Washington entitled Introduction to Modern Algebra for Teachers. Originally conceived as a text for future secondary-school mathematics teachers, it has developed into a book that could serve well as a text in an undergraduate course in abstract algebra or a course designed as an introduction to higher mathematics. This book differs from many undergraduate algebra texts in fundamental ways; the reasons lie in the book's origin and the goals I set for the course. The course is a two-quarter sequence required of students intending to fulfil the requirements of the teacher preparation option for our B.A. degree in mathematics, or of the teacher preparation minor. It is required as well of those intending to matriculate in our university's Master's in Teaching program for secondary mathematics teachers. This is the principal course they take involving abstraction and proof, and they come to it with perhaps as little background as a year of calculus and a quarter of linear algebra. The mathematical ability of the students varies widely, as does their level of mathematical interest.