Algebra: Abstract and Concrete
by Frederick M. Goodman
Publisher: Semisimple Press 2015
Number of pages: 587
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 required background for using this text is a standard first course in linear algebra. Also included is a brief summary of linear algebra in an appendix to help students review. There are also 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.
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by Edwin H. Connell
Covers abstract algebra in general, with the focus on linear algebra, intended for students in mathematics, physical sciences, and computer science. The presentation is compact, but still somewhat informal. The proofs of many theorems are omitted.
by Peter J. Cameron - Queen Mary, University of London
After a short introductory chapter consisting mainly of reminders about such topics as functions, equivalence relations, matrices, polynomials and permutations, the notes fall into two chapters, dealing with rings and groups respectively.
by Donu Arapura - Purdue University
This book covers basic abstract algebra. Rather than spending a lot of time on axiomatics and serious theorem proving, the author wanted to spend more time with examples, simple applications and with making scenic detours.
by Anthony W. Knapp - Birkhäuser
This book includes chapters on modern algebra which treat various topics in commutative and noncommutative algebra and provide introductions to the theory of associative algebras, homological algebras, algebraic number theory, and algebraic geometry.