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 John Scherk - Chapman & Hall
The book emphasizes the computational aspects of modern abstract algebra. Author integrated the software Mathematica into the discussions -- especially in the group theory sections -- but is careful not to make any logical reliance on this software.
by Anthony W. Knapp
Contents: Preliminaries about the Integers, Polynomials, and Matrices; Vector Spaces over Q, R, and C; Inner-Product Spaces; Groups and Group Actions; Theory of a Single Linear Transformation; Multilinear Algebra; Advanced Group Theory; etc.
by Peter J. Cameron - Queen Mary, University of London
These notes are intended for an introduction to algebra. The text is intended as a first introduction to the ideas of proof and abstraction in mathematics, as well as to the concepts of abstract algebra (groups and rings).
by F. Oggier - Nanyang Technological University
Contents: Group Theory (Groups and subgroups, The isomorphism theorems); Ring Theory (Rings, ideals and homomorphisms); Field Theory (Field extension and minimal polynomial); Galois Theory (Galois group and fixed fields).