Problems in Abstract Algebra
About this Title
A. R. Wadsworth, University of California, San Diego, CA
Publication: The Student Mathematical Library
Publication Year: 2017; Volume 82
ISBNs: 978-1-4704-3583-7 (print); 978-1-4704-4044-2 (online)
MathSciNet review: MR3643210
MSC: Primary 00A07; Secondary 12F10, 13-01, 20-01
This is a book of problems in abstract algebra for strong undergraduates or beginning graduate students. It can be used as a supplement to a course or for self-study. The book provides more variety and more challenging problems than are found in most algebra textbooks. It is intended for students wanting to enrich their learning of mathematics by tackling problems that take some thought and effort to solve. The book contains problems on groups (including the Sylow Theorems, solvable groups, presentation of groups by generators and relations, and structure and duality for finite abelian groups); rings (including basic ideal theory and factorization in integral domains and Gauss's Theorem); linear algebra (emphasizing linear transformations, including canonical forms); and fields (including Galois theory). Hints to many problems are also included.
Undergraduate and graduate students interested in teaching and learning undergraduate algebra.
Table of Contents
- Integers and integers mod $n$
- Linear algebra and canonical forms of linear transformations
- Fields and Galois theory
- Suggestions for further reading