Customer Reviews

Abstract Algebra: A Geometric Approach

5 star:		(2)
4 star:		(0)
3 star:		(1)
2 star:		(1)
1 star:		(1)

 

 

This is a very intelligent book, by a gifted expositor and teacher. The organization is based on thoughtful pedagogy rather than imitating other standard texts. E.g. it makes sense to begin with integers and polynomials and fields, instead of groups as most books do, because these are simpler and more familiar objects, and most people will find them more useful.

The abstract ideas that will occur in studying groups (and general rings) come up here in a more familiar setting. The author is always mindful of the interest of the material and gives significant applications as soon as they are feasible.

A particularly strong feature is the excellent sets of problems. Students should try all of them. The use of algebra to do some interesting projective geometry offers a fine glimpse of the more advanced use of the topic usually denied beginning students.

The book is written in a style suitable to a reader who has some mathematical sophistication, clear but not spoonfed. Shifrin never talks down to the student, and tends to present proofs in an articulate, but somewhat succint, rigorous, elegant style. A student with no experience at proofs will be challenged to understand some arguments, where parts are left for the student to fill in.

Thus reading this book is intended to be an active endeavor, pencil in hand, as it should always be.

I took Ted Shifrin's Abstract Algebra course at UGA using the lecture notes that eventually became this book. Shifrin is one of the most decorated mathematics teachers around; his skill at presentation and his concern for student understanding come through in this book.

A course taught from this book will, of course, reflect its instructors abilities and compatibility with the text. As a book to read yourself this is an outstanding text. The geometric flavor of the book works extremely well for the geometrically inclined. Because of its focus on clear instruction, its weakest role is as a reference book.

If they'd only release a second edition fixing the books typos this would be more solid five star text. [...]

Only on chapter 2, but I can see that the text jumps several steps in the equations. Need to fill them in for yourself. If you're a career changer like myself who is coming back to this level math after several years, search the internet for math examples or look up other texts that fill in the holes.

This is the worst math book I have ever encountered. It is counterintuitative moving backwards compared to other text books teaching the same content. This book could have been so much more informative, however, there are little theorems that are missing. It could have had more pictures illustating the bigger ideas! There is no solutions to odd numbered exercises. I struggled to find other books to help me through this one, but no other book I found approaches the material in the same manner.

I took a course which used this text, and I must say that that class was the least interesting class I have taken in my life. I think that looking at algebra from a geometric standpoint (and vice versa, an equivalent statement) ruins both algebra and geometry. Algebra is beautiful. Geometry is beautiful, but for a different reason. The intersection of their beauty (also, the beauty of their intersection) is the null set.