Modern Algebra

The author has written this book with two main goals in mind: to introduce the most important kinds of algebraic structures, and to help students improve their ability to understand and work with abstract ideas. The first six chapters present the core of the subject, the remainder are designed to be as flexible as possible. The book covers groups before rings, which is a matter of personal preference for instructors. The "Advice to Students" section gives suggestions to students on reading, writing and analyzing proofs and theorems. An expanded discussion of deductive reasoning and methods of proofs can be found in the appendix. Some traditional topics are presented earlier in the first six chapters for easier coverage of standard material. A new section has been added to expand the introduction of Galois theory for more thorough coverage. The discussion of Fermat's Last Theorem is updated to include Wiles' famous proof.