Abstract Algebra

by John A. Beachy, William D. Blair

Highly regarded by instructors in past editions for its sequencing of topics as well as its concrete approach, slightly slower beginning pace, and extensive set of exercises, the latest edition of Abstract Algebra extends the thrust of the widely used earlier editions as it introduces modern abstract concepts only after a careful study of important examples. Beachy and Blair’s clear narrative presentation responds to the needs of inexperienced students who stumble over proof writing, who understand definitions and theorems but cannot do the problems, and who want more examples that tie into their previous experience. The authors introduce chapters by indicating why the material is important and, at the same time, relating the new material to things from the student’s background and linking the subject matter of the chapter to the broader picture. Instructors will find the latest edition pitched at a suitable level of difficulty and will appreciate its gradual increase in the level of sophistication as the student progresses through the book. Rather than inserting superficial applications at the expense of important mathematical concepts, the Beachy and Blair solid, well-organized treatment motivates the subject with concrete problems from areas that students have previously encountered, namely, the integers and polynomials over the real numbers.

Genres: Mathematics, Algebra, Textbooks

484 pages, Hardcover

First published February 1, 1990

Reviews

[Hannes Salin · Rating 4 out of 5]

As a graduate student I had Fraleigh's "A first course in abstract algebra" which I back then found a bit hard to digest, and now a few years later when reading Beachy's "Abstract algebra" it is often quite clear (except some proofs and abstract concepts) and easy to follow. My point is that I'm not sure if this is due to mathematical maturity or if Abstract algebra is a better book, i.e. more clear and better examples? I know for sure that this book will be my first reference book in abstract algebra (unless I find something better of course).

[Guy · Rating 2 out of 5]

Prof sucked.

[Mike · Rating 1 out of 5]

I would first like to point out that this is a slow pace subject. On john Beachy's website his syllabus for Algebra I is Chapters 1.1 to 3.5 and Algebra II is 3.6 to 6.3. I didn't see one for Algebra III because that still leaves 6.4 to 6.7 and chapters 7, 8 and 9. So he doesn't even teach Galois theory, which is chapter 8. I would say you have over a year worth of material in this book. Now on to my review on why this book isn't suitable for an introduction or learning of abstract algebra. In my course We covered chapters 3 to 5. Chapters 1 and 2 were done in intro to proofs. First thing, this book was not meant to learn from. It was made to fit the general style of abstract algebra textbooks of here are your theorems with proofs. Now lets throw in some examples and on the the problems. The writers of the book went out and got every book on Abstract Algebra. Put the same theorems and proofs you can find in any other book and then started rewriting them ever so slightly, so it becomes their theorem and not one just copy and pasted out of another book. The Definitions, theorems and proof are encyclopedic so it can't really to be used for self study. The examples are mostly trivial and in no way help to fully understand the theorems and proofs. The problems in the book are impossible from using this book alone. Many of the problems are made up of smaller problems not offered and have to be solved first. complete understanding of the reading material presented is required to solve the questions, which no first time student will have. The authors did not care where the problems came from, as long as they had their 20-30 per section. The more I analyze this book the more I see how they tried to up sell the book by making it look intriguing with it charts and tables. Also with The free 600 problems with solutions to around 300 on Beachy's website. But I guarantee you'll be Youtubing how to make those tables and charts yourself and again The Problems here are also can't be solved by students. They are only there to entice you to buy this book over a book without extra problems with solutions. The problems fooled me, but once I stared looking at the problems for chapter 3 and beyond I became disappointed. Go on John Beachy's website yourself and look at his problems with solutions. You will not understand what the problems are asking you to do so you are dependent on the solutions which aren't very detailed and easy to get lost in . You'll see things like "It's obvious the function is one to one" Well of course it is to the teachers, but not for the first time student who needs details explanations. You will need solutions for the solutions. In the text only a few problems per chapter have answers in the back of the book. Compared to the usual answers for all odd problems. People who give the book good review most likely only read chapters 1, 2. They most likely have already seen that material on integers and functions in books like "Mathematical Proofs: A Transition to Advanced Mathematics" by Chartrand. But wait till you get to chapter 3 on groups, which is worse that chapter 4 on polynomials and chapter 5 on commutative rings. I've noticed this with books like Howard Anton's "Elementary Linear Algebra" Where the book starts off good, everything is explained well, the problems seem well selected. This is most likely because the first chapter is what everybody reads to decide if the book is worth buying or not. But once you get to chapter 3 and beyond everything is done poorly. So do I recommend other books? Well this is the book I've used the most, I've glanced at Hungerford, Fraleigh, and Gallian and their all about the same. Again it's the style of writing these books that is used which goes back decades. I did find some of the writing in Hungerford 2nd edition of "Abstract Algebra: An Introduction" slightly easier to follow. In my opinion this material is not that hard. The books make it hard. When I was given clear explanations during teacher office hours and given clear examples and appropriate problems, The material became understandable. My teacher was telling me how Abstract Algebra logic is important for computer science majors. With the demand of people with computer degrees going up, don't be surprised if they add this to the list of degree requirements.

[Thomas · Rating 1 out of 5]

I had to read it for my first algebra course, and I hated it. The author tries to provide specific instances of groups and rings, and at times his explanations accompanying the examples are so verbose that it makes it harder to read the book. Several paragraphs can be shortened to a sentence, without affecting the clarity. Herstein's treatment is much more elegant, and the problems in Topics in Algebra is far better than this one.