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Review
"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 Nachricheten
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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Most Helpful Customer Reviews
4 of 4 people found the following review helpful
Format:Paperback
From the first chapter it is clear that the author of this book has been teaching algebra for the whole of his professional career. By the end of the book the reader will certainly have a solid knowledge of groups, rings, fields and vector spaces. A thirst for the applications of these algebraic structures is inspired by Cameron in the later chapters. Although Cameron starts from the basics, the repetition of the background mathematics in the first chapter allows the reader to concentrate on the "meat" of the later chapters. The book is an essential read for anybody taking a course in abstract algebra and will be of especial benefit to students because it takes a wider view than most undergraduate textbooks.
2 of 2 people found the following review helpful
Format:Paperback
This is a very pleasant book to read, which could be read by someone starting a degree in maths, and which goes on to explain about rings, groups, vector spaces, and modules. There is very little prior knowledge required. The author even explains basic set theory in chapter 1. In chapter 7, the author dives into the deeper waters of group, ring and field theories, and in the last chapter outlines the basics of Galois theory and coding theory, proving the Abel-Ruffini theorem: it is impossible to solve the general quintic using radicals. Another beautiful moment is where the author shows that the 3 classic ruler-and-compass constructions of Euclidean geometry are impossible, using notions from field theory. There is a list of further reading, covering books which enter into even more advanced aspects of Abstract Algebra. All in all, a very pleasant, enjoyable, educational book!
2 of 2 people found the following review helpful
Format:Paperback
This book is the best I've seen on the enjoyable subject of algebra. The writing style is perfect. Not too dry, symbolic and condensed to make it unreadable. Not too slow and detailed to make it patronising. It leaves the important bits in and the unimportant bits to be 'filled in as an excersise'. The style is jovial and makes both quick reading and more intensive study enjoyable. The few basic errors which come from being not well enough checked or edited, like others in the same Oxford series, are annoying - like a zero instead of a one, changing an entire proof, or other obviously false statements caused by ommisions, mistakes or misprints. Luckily, these errors only occur a couple of times per chapter and, if taken with the right attitude, make the book all the more fun to read (you get to correct an obviously very experienced algebraist).
Overall this is a fantastic book covering most parts of first and second year undergraduate algebra. You might need a different book for the very basic bits, or for the very advanced bits, but this one has the bulk of the middle ground covered superbly.
Overall this is a fantastic book covering most parts of first and second year undergraduate algebra. You might need a different book for the very basic bits, or for the very advanced bits, but this one has the bulk of the middle ground covered superbly.
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Most Recent Customer Reviews
Algebraic Wonder
Introduction to Algebra is a beautifully crafted text, that encourages you to keep on reading. It has a light touch without loosing any rigor. Read more
Published 4 months ago by Nickabit
When should you judge a book by its cover?
Other reviewers, the Product Description, and Amazon's 'LookInside' feature all contribute to a good precis. So I'll avoid repetition, and just say that I concur. Read more
Published 9 months ago by SJGT
exploring concepts of algebra
Introduction (I. m. h. o)
The book wants to build upon the fundamental principles, so jumps 'feet-first' by introducing fundamental concepts of algebra. Read more
The book wants to build upon the fundamental principles, so jumps 'feet-first' by introducing fundamental concepts of algebra. Read more
Published on 6 Mar 2006 by ab..c
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