Math - Elements of Abstract and Linear Algebra

In 1965 I rst 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 about a dozen 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 a text. They
now appear (in modied form) as the rst ve chapters of this book. Here were some
of my motives at the time.

1) To have something as short and inexpensive as possible. In my experience, students like short books.
2) To avoid all innovation. To organize the material in the most simple-minded straightforward manner.
3) To order the material linearly. To the extent possible, each section should use the previous sections and be used in the following sections.