Product Description

This book is an informal and readable introduction to higher algebra at the post-calculus level. The concepts of ring and field are introduced through study of the familiar examples of the integers and polynomials. A strong emphasis on congruence classes leads in a natural way to finite groups and finite fields. The new examples and theory are built in a well-motivated fashion and made relevant by many applications--to cryptography, coding, integration, history of mathematics, and especially to elementary and computational number theory. The later chapters include expositions of Rabiin's probabilistic primality test, quadratic reciprocity, and the classification of finite fields. Over 900 exercises, ranging from routine examples to extensions of theory, are found throughout the book; hints and answers for many of them are included in an appendix.

Product Details

• Amazon Sales Rank: #575456 in Books
• Published on: 2000-02-01
• Original language: English
• Number of items: 1
• Binding: Hardcover
• 536 pages

Review
From the reviews:

"The user-friendly exposition is appropriate for the intended audience. Exercises often appear in the text at the point they are relevant, as well as at the end of the section or chapter. Hints for selected exercises are given at the end of the book. There is sufficient material for a two-semester course and various suggestions for one-semester courses are provided. Although the overall organization remains the same in the second editionAChanges include the following: greater emphasis on finite groups, more explicit use of homomorphisms, increased use of the Chinese remainder theorem, coverage of cubic and quartic polynomial equations, and applications which use the discrete Fourier transform." MATHEMATICAL REVIEWS

Customer Reviews

A pleasure to read
Let it be proclaimed as the first axiom of mathematics writing: Difficulty should never be multiplied without necessity. The informal prose is the one feature that stands out prominently throughout this book.

The misty road towards a true understanding of the abstract and sometimes difficult concepts in modern algebra (group, ring, field, homomorphism etc) is paved with concrete examples and applications from number theory. This approach not only parallels the very historical development of the subject, but also has the pedagogical advantage that it does not divorce the theory from the practice. Laid to rest is the mythical belief that the whole edifice of modern algebra rests precariously on a theoretical foundation of purely axiomatic constructs separate from everyday reality: any student who can tell time on an analog clock or values the security of her credit card will appreciate the practical contribution of the field.

My only complaint is that the book is rife with errors, of which some can be checked against the errata available on the author's website. Other than that, I lavish only praise upon it.