Introduction to Algebra [Paperback]

Peter J. Cameron (Author)

Book Description

Publication Date: February 9, 2008 | ISBN-10: 0198527934 | ISBN-13: 978-0198527930 | Edition: 2

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.

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

About the Author

Peter Cameron has taught mathematics at Oxford University and Queen Mary, University of London, with shorter spells at other institutions. He has received the Junior Whitehead Prize of the London Mathematical Society, and the Euler Medal of the Institute of Combinatorics and its Applications, and is currently chair of the British Combinatorial Committee.

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 0.8 inches
• Shipping Weight: 1.2 pounds (View shipping rates and policies)
• Average Customer Review: 4.3 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #1,270,095 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

21 of 22 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.

2 of 3 people found the following review helpful:

5.0 out of 5 stars Best Abstract Algebra book for undergrads, August 12, 2009

By 

Wu Bing "Cornelius" (Singapore) - See all my reviews

This review is from: Introduction to Algebra (Hardcover)

Cameron's 2nd Edition is the first book I have seen in the market which is remarkably better than other similar "Intro" to Abstract Algebra for teaching undergrads who have never been exposed to New Math:

1) He places Rings (chap 2) before Groups (chap 3)- this is a very bold idea and I think very logical. Rings (like Z) are very familiar to normal high school students, so easier to understand than the more abstract Group theory.
Starting from Ring to learn factor ring, ideals, Laws of Isomorphism and other concepts, then revisit them later in Group will help to reinforce understanding.

2) He uses simple layman languages to explain complex concepts. For example: Homomorphism vs Isomorphism is akin to seeing things by short-sighted person without glasses (look similar) vs with glasses (exact image 1:1).

4 of 7 people found the following review helpful:

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

By 

Tom Margulies - See all my reviews
(REAL NAME)   

Amazon Verified Purchase

This review is from: Introduction to Algebra (Paperback)

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.