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 Maya Mohsin Ahmed
The focus of this book is applications of Abstract Algebra to polynomial systems. It explores basic problems like polynomial division, solving systems of polynomials, formulas for roots of polynomials, counting integral roots of equations, etc.
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).
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 W. Edwin Clark - University of South Florida
This book is written as a one semester introduction to abstract algebra. Applications of abstract algebra are not discussed. A certain amount of mathematical maturity, some familiarity with basic set theory, calculus, and linear algebra, is assumed.