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.

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

"A complete course of instruction under one cover, Introduction to Abstract Algebra is a standard text that should be a part of every community and academic library mathematics reference collection in general, and algebraic studies supplemental reading in particular."—Reviewer’s Bookwatch, December 2015Smith’s update to the first edition (CH, Jul'09, 46-6260) is an alternative approach to the usual first semester in higher algebra. The author accomplishes this by including many topics often absent from a first course, such as quasigroups, Noetherian domains, and modules, which, theoretically, are developed alongside their mainstream analogues, like groups, rings, and vector spaces. It is essentially a first semester wink at universal algebra. Smith’s approach to axiomatic systems is few-too-many—he starts with structures with very few axioms, like semigroups and monoids, and continues adding axioms. He finishes with more complex axiomatic systems, like unique factorization domains and fields. The book is very well written and easy to read, flowing naturally from one topic to the next. Numerous supportive homework exercises are also included to help the reader explore further topics. This book will best serve readers with a background in abstract algebra who desire to strengthen their understanding and build bridges between various topics. Unfortunately, because many similar topics are handled in tandem, an inexperienced reader might become confused, especially as many clarifying examples are missing. This book is for readers who want an under the hood view of algebra.--A. Misseldine, Southern Utah University 2015