Algebra: Abstract and Concrete

This text provides a thorough introduction to “modern” or “abstract” algebra at a level suitable for upper-level undergraduates and beginning graduate students.
The book addresses the conventional topics: groups, rings, fields, and
linear algebra, with symmetry as a unifying theme. This subject matter is
central and ubiquitous in modern mathematics and in applications ranging
from quantum physics to digital communications.
The most important goal of this book is to engage students in the active practice of mathematics. Students are given the opportunity to participate and investigate, starting on the first page. Exercises are plentiful, and
working exercises should be the heart of the course.
The required background for using this text is a standard first course
in linear algebra. I have included a brief summary of linear algebra in an
appendix to help students review. I have also provided appendices on sets,
logic, mathematical induction, and complex numbers. It might also be
useful to recommend a short supplementary text on set theory, logic, and
proofs to be used as a reference and aid; several such texts are currently
available.