<p><img src="http://pic.pinggu.com/attachments/uploadfile_20082009/2008-3/200832317254076302.jpg" border="0" onload="if(this.width>document.body.clientWidth*0.5) {this.resized=true;this.width=document.body.clientWidth*0.5;this.style.cursor='pointer';} else {this.onclick=null}" alt="" /></p><p><br/>Introduction to Algebra<br/>By Peter J. Cameron</p><p>Publisher: Oxford University Press, USA <br/>Number Of Pages: 350 <br/>Publication Date: 2008-02-09 <br/>ISBN-10 / ASIN: 0198527934 <br/>ISBN-13 / EAN: 9780198527930 <br/>Binding: Paperback <br/>--------------------------------------------------------------------------------</p><p>Book Description: </p><p>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.<br/>--------------------------------------------------------------------------------</p><p>Summary: Excellent, concise introduction<br/>Rating: 5</p><p>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.</p><p>"Algebra" is divided into a 8 sections:<br/>1) Set Theory and Relation Theory<br/>2) Ring Theory<br/>3) Group Theory<br/>4) Vector Spaces<br/>5) Modules<br/>6) Numbers<br/>7) More Rings and Groups<br/>8) Galois theory and coding theory</p><p>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.</p><p>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.</p><p>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.<br/></p>