In 1965 I first taught an undergraduate course in abstract algebra. It was fun to teach because the material was interesting, and the class was outstanding. Five of those students later earned a Ph.D. in mathematics.
Since then, I have taught the course several times from various texts. Over the years, I developed a set of lecture notes, and in 1985 I had them typed so they could be used as text. They now appear as the first five chapters of this book.
This book is a survey of abstract algebra emphasizing linear algebra and is intended for mathematics, computer science, and physical sciences students. The first three or four chapters can stand alone as a one-semester course in abstract algebra. However, they are structured to provide the background for the chapter on linear algebra.
Linear algebra has top priority. It is better to go forward and do more linear algebra than to stop and do more group and ring theory. It is more important that students learn to organize and write proofs themselves than to cover more subject matter. Algebra is a perfect place to start because there are many “easy” theorems to prove. Many routine theorems are stated here without proof, and they may be considered exercises for the students.