Introduction to Algebra (Paperback)

by Peter J. Cameron (Author) "The purpose of this chapter is to introduce you to some of the notation and ideas that make up mathematics..." (more)
Key Phrases: rational canonical form, subgroup test, cycle notation, Proof Let, Definition Let, Proof Suppose (more...)

Editorial Reviews

Review
Review from previous edition This clearly written exposition is accompanied by well-chosen exercises. This book should be useful as a textbook for most undergraduates courses on algebra.

This is an extremely engaging introduction to abstract algebra by one of this country's most prolific and creative algebraists. Recognising that although the axiomatic method is unavoidable it is intially uncomfortable for many students, he adopts a relatively informal style which is constantly encouraging without ever lapsing into imprecision. Aided by a relaxed, friendly expository style, his expertise, sureness of touch and contagious enthusiasm for algebra shine through on every page this is a book to study, savour and enjoy

'Altogether this is a concise but solid introduction into algebra and linear algebra' Internationale mathematische Nachrichten

`'Altogether this is a concise but solid introduction into algebra and linear algebra'' Internationale mathematische Nachrichten

`Review from previous edition This clearly written exposition is accompanied by well-chosen exercises. This book should be useful as a textbook for most undergraduates courses on algebra.' EMS Newsletter

`Altogether this is a concise but solid introduction into algebra and linear algebra' Internationale mathematische Nachrichten

`(Cameron) forms an ideal basis for first and second units in abscract algebra, for second or third-level courses in group theory, and for supporting courses in Galois theory and coding theory. The exposition is clear, the prerequisites minimal and it covers a lot of ground.' The Times Higher Education Supplement

Product Description
Developed to meet the needs of modern students, this Second Edition of the classic algebra text by Peter Cameron covers all the abstract algebra an undergraduate student is likely to need. Starting with an introductory overview of numbers, sets and functions, matrices, polynomials, and modular arithmetic, the text then introduces the most important algebraic structures: groups, rings and fields, and their properties. This is followed by coverage of vector spaces and modules with applications to abelian groups and canonical forms before returning to the construction of the number systems, including the existence of transcendental numbers. The final chapters take the reader further into the theory of groups, rings and fields, coding theory, and Galois theory. With over 300 exercises, and web-based solutions, this is an ideal introductory text for Year 1 and 2 undergraduate students in mathematics.

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Product Details

• Paperback: 350 pages
• Publisher: Oxford University Press, USA; 2 edition (February 9, 2008)
• Language: English
• ISBN-10: 0198527934
• ISBN-13: 978-0198527930
• Product Dimensions: 9.1 x 6.1 x 0.9 inches
• Shipping Weight: 5.9 pounds (View shipping rates and policies)
• Average Customer Review: 4.3 out of 5 stars See all reviews (3 customer reviews)
• Amazon.com Sales Rank: #883,632 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

18 of 19 people found the following review helpful:

5.0 out of 5 stars Excellent, concise introduction, May 3, 2003

By	Geoffrey Zenger (Burnaby, BC) - See all my reviews

This review is from: Introduction to Algebra (Paperback)

Peter J. Cameron's "Introduction to Algebra" is exactly that, an introduction to algebra and a good one at that. I must confess that before reading this book had a very limited knowledge of abstract algebra however with a little bit of time and effort I am now quite comfertable with the subject thanks to this book.

"Algebra" is divided into a 8 sections:
1) Set Theory and Relation Theory
2) Ring Theory
3) Group Theory
4) Vector Spaces
5) Modules
6) Numbers
7) More Rings and Groups
8) Galois theory and coding theory

This book succeeds by having an interesting writing style, not being dry, and at the same time being very rigorous. The rigor is always present and all proofs are carefully developed however the "feel" of the subject is never lost as Cameron strives to help the reader grasp the "shape" of the algebraic structures that he introduces.

This book has a slightly wider scope than many introductory algebra books however it succeeds in covering all of its topics well although the sections on category theory and algebraic geometry are only a page or two long and thus are only present to whet the reader's interest. In addition, Cameron motivates the discussions by drawing the topics together in the end in the applications chapter. This chapter covers the basics of the commonly known Galois theory and the less covered Coding theory which is one of the backbones of the internet.

Final: Buy this book for a good introduction. I have borrowed a number of other introductory books from the university up the hill but this one was the clearest for me.

4 of 5 people found the following review helpful:

5.0 out of 5 stars 2nd Edition is Better, April 20, 2008

By	R. Matossian (Alhambra, CA USA) - See all my reviews (REAL NAME)

A nice thing about the new edition is the greatly expanded preliminary chapter which covers most of what a good advanced high school algebra course contains, plus a bit more. Depending on the reader's background, this may be very valuable. Also, this book is surprisingly lightweight (literally), which is good for those of us who carry around a lot of books in our backpacks.

3.0 out of 5 stars An average text:, November 21, 2008

By	Tom Margulies - See all my reviews (REAL NAME)

This is not a bad book but not more than an average text. The introduction is grafted on summary of high school algebra that isn't very cohesive or structured.

The presentations are rigorous but most modern math books are as well. The presentation is dry. I like math and math texts. Some add humor, some add history, and some add examples of applications to make things more interesting. This book could serve as the basis for a good course if the lecturer was dynamic but as a read it is only average.