Introduction to Abstract Algebra

Jonathan Smith is a Professor at Iowa State University. He earned his Ph.D., from Cambridge (England). His research focuses on combinatorics, algebra, and information theory; applications in computer science, physics, and biology.

... The author goes the extra mile to build algebraic concepts by confronting the pedagogic and logical sequence groups-first or rings-first dilemma ... a perfect pure math precursor to Grillet and Knapp's works. ... The book's well-thought out sequence supports a set of useful statements on how to use its 11 chapters in a course ... The book is also outstanding for self-study. ... I recommend this book as second to none on abstract algebra for its content, style, and expository efficiency. -Computing Reviews, January 2011 ... a careful treatment of the principal topics of abstract algebra ... This is an attractive book which could be read by everybody because the author supposes not so much knowledge from the reader and gives all the necessary information to continue the reading from [one] chapter to the next. The approach used by the author to introduce modules and group actions is new and innovative. The book is well written ... students and even experienced researchers may benefit strongly from this book. ... -IACR Book Reviews, October 2010 ... This compact book covers topics one would expect to find in an abstract algebra text. ... Smith's approach is carefully implemented, and topics flow logically from one chapter to the next. The writing is careful and rigorous, yet accessible to hardworking students. The problems are collected at the end of each chapter in two sets, with one set made up of shorter exercises. ... This is an ideal text for an abstract algebra course comprised of mathematics students or CS students who have either a strong minor or second major in mathematics. ... -Computing Reviews, December 2009 One can trace the author's research interests to the border between algebra and category theory, which gives the textbook its unique flavour. -EMS Newsletter, March 2009 The book is well written and flows well. Readers looking for an alternative approach to abstract algebra should consider this volume. -J.R. Burke, Gonzaga University, CHOICE, July 2009, Vol. 46, No. 11 This book is well written, interesting to read, and the proofs and examples are clear and clean. -David F. Anderson, Mathematical Reviews, 2009e

• Numbers. Functions. Equivalence. Groups And Monoids. Homomorphisms. Rings. Fields. Factorization. Modules. Group Actions. Quasigroups.