Comprehensiveness rating: 5 read less
This book is introductory, and covers the basic of groups, rings, fields, and vector spaces. In addition, it also includes material on some interesting applications (e.g., public key cryptography). In terms of covering a lot of topics, the book is certainly comprehensive, and contains enough material for at least a year-long course for undergraduate math majors. A "dependency chart" in the preface should be very useful when deciding on what path to take through the text.
One noteworthy feature of this book is that it incorporates the open-source algebra program Sage. While the .pdf copy I found through the OTN website only included a not-very-serious discussion of Sage at the end of most exercise sets, the online textbook found at
appears to contain a much more substantial discussion of how to use Sage to explore the ideas in this book. I admit that I didn't explore this feature very much.
Accuracy rating: 5
Though I have not checked every detail (the book is quite long!), there do not appear to be any major errors.
Relevance/Longevity rating: 5
The topics covered here are basic, and will therefore not require any real updates.
The book is also written in such a way that it should be easy to include new sections of applications.
Clarity rating: 5
I would say that this this book is well-written. The style is somewhat informal, and there are plenty of illustrative examples throughout the text. The first chapter also contains a brief discussion of what it means to write and read a mathematical proof, and gives many useful suggestions for beginners.
Through I didn't read every proof, in the ones I did look at, the arguments convey the key ideas without saying too much. The author also maintains the good habit of explicitly recalling what has been proved, and pointing out what remains to be done. In my experience, it is this sort of mid-proof "recap" is helpful for beginners.
Consistency rating: 5
The terminology in this text is standard, and appears to be consistent.
Modularity rating: 5
Each chapter is broken up into subsections, which makes it easy to for students to read, and for instructors to assign reading. In addition, this book covers modular arithmetic, which makes it even more "modular" in my opinion!
Organization/Structure/Flow rating: 4
It seems like there is no standard way to present this material. While the author's choices are perfectly fine, my personal bias would have been to discuss polynomial rings and fields earlier in the text.
Interface rating: 5
The link on page v to
appears to be broken.
My browser also had some issues when browsing the Sage-related material on the online version of this text, but this may be a personal problem.
Grammatical Errors rating: 5
I did not notice any major grammatical errors.
Cultural Relevance rating: 5
I'm not certain that this question is appropriate for a math textbook. On the other hand, I'll take this as an opportunity to note that the historical notes that appear throughout are a nice touch.
The problem sets appear to be substantial and appropriate for a strong undergraduate student. Also, many sections contain problems that are meant to be solved by writing a computer program, which might be of interest for students studying computer science.
I am also slightly concerned that the book is so long that students may find it overwhelming and hard to sift through.