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Abstract Algebra: An Introduction with Applications

Derek J. S. Robinson
Publisher: 
De Gruyter
Publication Date: 
2022
Number of Pages: 
400
Format: 
Paperback
Edition: 
3rd
Price: 
51.99
ISBN: 
978-3110686104
Category: 
Textbook
[Reviewed by
Benjamin Linowitz
, on
05/24/2022
]
See Mark Hunacek's review of the second edition.
 
Robinson's textbook Abstract Algebra: an introduction with applications is an abstract algebra textbook written for advanced undergraduates and beginning graduate students. The book covers all of the standard topics that one expects such a book to cover (groups, rings, modules, tensor products, fields, Galois theory), as well as a number of interesting applications (the Polya enumeration theorem, latin squares, error correcting codes, as well as an interesting and far less standard application to algebraic models of accounting systems).
 
The largest changes made for the third edition are:
 
  • A new chapter on the representation theory of finite groups (ending with a proof of Burnside's p-q theorem)
  • A new chapter on category theory
  • A new chapter introducing presentations of groups, generators and relations, and free products
  • The section on Zorn's lemma, which had previously appeared in the final chapter, now appears at the end of the first chapter. This raises the level of abstraction in parts of the book, though the text's overall level of accessibility has been maintained.

Benjamin Linowitz ([email protected]) is an Assistant Professor of Mathematics at Oberlin College.