Abstract Algebra 3rd Edition by John A. Beachy (PDF)

Description

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.

User’s Reviews

Editorial Reviews: Review “I like the style of writing—formal and rigorous but not stuffy. It reads as an upper-level undergraduate text should. The exercises are the main reason I am interested in this book. They are a great mix of straightforward practice, some applications, and a healthy amount of theory that occasionally dives extra deep.” –Matt Keotz, Nazareth College”The book has a great selection of exercises. There are enough good ones to make it possible to use the book several semesters in a row without repeating too much. They come in a nice mix from easy computations to warm the students up to more difficult theoretical problems. A few have solutions, but most don’t. I like this balance very much.” –Will Murray, California State University, Long Beach”I like the gradual introduction to abstraction by starting with examples rather than abstract groups or rings. Many nice examples, as well as good theorems often omitted from undergraduate courses.” –William M. McGovern, University of Washington From the Publisher Titles of related interest from Waveland Press: Hillman-Alexanderson, Abstract Algebra: A First Undergraduate Course, Fifth Edition (ISBN 9781577660828) and Saracino, Abstract Algebra: A First Course, Second Edition (ISBN 9781577665366). From the Back Cover “The book has a great selection of exercises. There are enough good ones to make it possible to use the book several semesters in a row without repeating too much. They come in a nice mix from easy computations to warm the students up to more difficult theoretical problems. A few have solutions, but most don’t. I like this balance very much.” — Will Murray, California State University, Long Beach “I like the gradual introduction to abstraction by starting with examples rather than abstract groups or rings. Many nice examples, as well as good theorems often omitted from undergraduate courses.” — William M. McGovern, University of Washington “A well-written text with plenty of opportunity for students to get involved in the learning process.” — Francis T. Hannick, Minnesota State University, Mankato “This book moves from concreteness to abstraction more skillfully than any text I have ever seen. A completely convincing and student-oriented presentation of the `why’ of abstract algebra as well as the `how.'” — Vic Camillo, University of Iowa Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐When reviewing a math text, it is always important to separate one’s frustrations with the material from the shortcomings of the book. Face it, abstract algebra is a difficult subject for most math majors, and the first course is shockingly strange and different from the calculus or analysis that the student may have learned up to that time. Most introductory courses add stealth material, especially number theory, that comes as an unexpected surprise. It’s like learning flamenco after spending years dancing waltzes (oh, and did anybody mention that flamenco includes singing?). I like this text because it makes explicit distinctions between the various introductory micro-subjects (number theory, modular arithmetic) before using them in the larger context of group theory. Other reviewers mentioned Fraleigh, and this too is a fine book, but it blends everything together, and you have to learn everything at once. I much prefer Fraleigh as a reference now that I have completed some introductory courses. Another challenge with abstract algebra, and similarly with probability theory, is that you are learning about new and strange example domains while you are also learning the theory that applies to those domains. For example, beginners in probability learn some combinatorics (eg. how many ways can one draw an inside flush) , but that is just a sandbox for learning discrete probability. You need a lot of that in algebra too, like modular arithmetic, matrices and symmetry, before you can discuss actual algebra like group and ring theory. Here too, Beachy does a better job of concentrating on discrete topics before combining them into the larger discussion.

⭐I have read several introductory algebra books but it was not until I read this book that I really began to understand algebra at the level that I needed to. As the authors state, this book is meant for people who are 1. just beginning to learn to write proofs and 2. taking an algebra class for the first time. The organization of the book very clearly attempts (and in my opinion succeeds) to help a person who is new to proofs and taking algebra for the first time.To someone who has already taken algebra and is quite comfortable, you may be annoyed by some of the development. For example, in the chapter on polynomials, there is a proof that a particular set satisfies some random properties, only later do you find out that it was a proof that the ring of polynomials [over a field!] is a pid. Some people may object to this style of presentation, but it reflects the authors awareness of the mathematical maturity of their audience.That is a lot of blabber so here are the reasons this book gets 5 stars:1. The authors are EXTREMELY aware of their audience and know how to write to them.2. There is a lot of exposition which motivates the subject and puts it into a historical context.3. Examples are very well chosen and provide a lot of detail.

⭐I am using this book for a first course in Modern Algebra, so I have not read it all the way through, but according to my professor there are various errors in the book. Particularly, I think he said after Chapter 3 there were quite a few mistakes, typos, etc. The price for this book was relatively low, which was definitely a good thing.As far as recommendations go, I cannot say whether or not I would recommend this to someone until I read more. That being said, however, I would not recommend it as “leisure reading” unless you are a Math professor, or something, because if there are mistakes, they might not be apparent to someone first learning about the topic.

⭐This is as thorough an abstract algebra book as I have seen. It has lots of proofs to go along with definitions and goes into intense detail on the subject matter. I will be taking an advanced (level II) algebra course this semester and am glad I will have this book handy as a reference.

⭐Bought it for school so I don’t really have an opinion on it, but the book came in great condition. If you like math and proofs, this is the book for you

⭐Great book lot of exercises

⭐Very clear and a great supplement to the course.

⭐Perfect and new! Only a minor dent in the top but that can be expected from shipping.

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