Algebra, Second Edition, by Michael Artin, is ideal for the honors undergraduate or introductory graduate course. The second edition of this classic text incorporates twenty years of feedback and the author's own teaching experience. The text discusses concrete topics of algebra in greater detail than most texts, preparing students for the more abstract concepts linear algebra is tightly integrated throughout.
Salient Features
High emphasis on concrete topics, such as symmetry, linear groups, quadratic number fields, and lattices, prepares students to learn more abstract concepts. The focus on these special topics also allows some abstractions to be treated more concisely, devoting more space to the areas students are the most interested in.
• Thechapter organization emphasizes the connections between algebra and geometry at the start, with the beginning chapters containing the content most important for students in other fields. To counter the fact that arithmetic receives less initial emphasis, the later chapters have a strong arithmetic slant.
• Treatment beyond the basics sets this book apart from others. Students with a reasonably mature mathematical background will benefit from the relatively informal treatments the author gives to the more advanced topics.
• Content notes in the preface include teaching tips from the author's own classroom experience.
• Challenging exercises are indicated with an asterisk, allowing instructors to easily create the right assignments for their class.
Table of Content
1. Matrices
2. Groups
3. Vector Spaces
4. Linear Operators
5. Applications of Linear Operators
6. Symmetry
7. More Group Theory
8. Bilinear Forms
9. Linear Groups
10. Group Representations
11. Rings
12. Factoring
13. Quadratic Number Fields
14. Linear Algebra in a Ring
15. Fields