Abstract Algebra: A Geometric Approach

by Theodore Shifrin

This book explores the essential theories and techniques of modern algebra, including its problem-solving skills, basic proof techniques, many applications, and the interplay between algebra and geometry. KEY TOPICS: It takes a concrete, example-oriented approach to the subject matter.

• Format: Paperback
• Language: English
• ISBN: 0133198316
• ISBN13: 9780133198317
• Release Date: August 1995
• Publisher: Pearson
• Length: 432 Pages
• Weight: 1.80 lbs.
• Dimensions: 0.9" x 6.9" x 9.2"

Customer Reviews

an excellent book for a student who will work hard

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.

A clear and well organized book.

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. [...]