Abstract Algebra: A First Course

by Dan Saracino

The simplicity of the language, the organization of the ideas, and the conciseness with completeness are this book's main strengths as it introduces abstract algebra. It plunges directly into algebraic structures and incorporates an unusually large number of examples to clarify abstract concepts as they arise. Theorem proofs do more than just prove the stated results, they are examined so readers can gain a better impression of where the proofs come from and why they proceed as they do. Most of the exercises range from easy to moderately difficult and ask for understanding of ideas rather than flashes of insight.

Genres: Mathematics, Nonfiction, Algebra, Textbooks, Reference

233 pages, Hardcover

First published April 1, 1992

Reviews

[Eli · Rating 4 out of 5]

A very good intro book for abstract algebra. It's short and sweet, but according to people who know more about the subject than I do, it has everything you should get in a first course. The style is conversational with lots of examples, but is not overly wordy. The theorems stand out visually from the page enough to find them, and a good amount of details are omitted as exercises. The problems are a good mix of difficulty. Comparing it to Lang I see now that they are a bit on the easy side, but still time-consuming and non-trivial, especially the later ones in the set. Almost all are proof-based.

[meg · Rating 5 out of 5]

I read this book while taking Professor Saracino’s Abstract Algebra course at Colgate University. I absolutely loved the class and the book. Concepts are explained clearly and precisely, examples and exercises are interesting, and Saracino’s passion for mathematics and friendly personality shine through the text.

[Babak · Rating 5 out of 5]

This was the first book I read about group theory many years ago. It is a basic book on Group, Ring and Field Theories. But I have to say I've never seen any other book explaining the abstract concepts this beautifully. After you read this book, you kind of wish that all the books in mathematics were written like this :]

[Timothy Mattnew · Rating 4 out of 5]

The book introduces a wide range of subjects: most of them in a perfectly structured manner. If your goal is to learn the theories of finite groups, rings, and fields, and to clearly comprehend the bases of these subjects, this is a great choice of a textbook. This book even attempts to introduce some more involved subjects, such as Sylow theorems, and applications of the theory of fields: constructions with straightedge and compass and, in the second edition, Galois theory. Therein lies its drawback: the chapters covering these latter topics feel rushed, and the theorems aren't sufficiently motivated, so they are significantly harder to read. The good news is, if you're okay with merely skimming over those chapters, and deciding whether or not you want to study them separately with the help of some other textbooks, that's a completely fine strategy. These topics are unnecessary for an introductory course. Neither are they necessary to rigorously understand all the other chapters and to get familiar with all the other theorems presented in the textbook (perhaps with some minor exceptions). These topics lie within the concluding chapters of the group theory part and the theory of fields part of the book, so they aren't used for any further developments of these subjects in it.

[Liquidlasagna · Rating 5 out of 5]

Waveland Press always seems to have great textbooks