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Rings, Fields and Groups: Introduction to Abstract Algebra (Modular Mathematics Series) [Paperback]

R. B. Allenby , Allenby , Reg Allenby
4.5 out of 5 stars  See all reviews (4 customer reviews)
RRP: 43.99
Price: 40.99 & FREE Delivery in the UK. Details
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Book Description

15 Aug 1991 0340544406 978-0340544402 2
'Rings, Fields and Groups' gives a stimulating and unusual introduction to the results, methods and ideas now commonly studied on abstract algebra courses at undergraduate level. The author provides a mixture of informal and formal material which help to stimulate the enthusiasm of the student, whilst still providing the essential theoretical concepts necessary for serious study. Retaining the highly readable style of its predecessor, this second edition has also been thoroughly revised to include a new chapter on Galois theory plus hints and solutions to many of the 800 exercises featured.

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Rings, Fields and Groups: Introduction to Abstract Algebra (Modular Mathematics Series) + Introduction to Complex Analysis
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Product details

  • Paperback: 412 pages
  • Publisher: Elsevier Limited; 2 edition (15 Aug 1991)
  • Language: English
  • ISBN-10: 0340544406
  • ISBN-13: 978-0340544402
  • Product Dimensions: 24.5 x 17.1 x 2.1 cm
  • Average Customer Review: 4.5 out of 5 stars  See all reviews (4 customer reviews)
  • Amazon Bestsellers Rank: 386,360 in Books (See Top 100 in Books)
  • See Complete Table of Contents

Product Description

Review

" ... here is no dry-as-dust textbook ... it will pay rich dividends to those who give time and effort to delve into its pages" Mathematical Spectrum

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Most Helpful Customer Reviews
12 of 12 people found the following review helpful
4.0 out of 5 stars Not bad 9 July 2007
For the most part, this book is a clear and concise introduction to abstract algebra. The prose is lucid and the author's notes and remarks give some intuitive rationale behind several of the results. The exercises are well-thought out, and in some cases they expound on an idea touched on earlier in the chapter.

On the other hand, a few of the chapters went over my head. The Prologue, for example, cites the major contributions of the key figures in the historical development of algebra. Since I was still an algebra novice when I read the Prologue, I found it hard to follow. Moreover, Chapter 5 on Group Theory begins with an introduction that summarizes two methods of solving the cubic. I had a lot of trouble following this section as well. In his description of Tchirnhaus' method, he brings up a simultaneous equation involving a cubic and quadratic but skips over some calculations. I spent 2 days trying to fill in the gaps, only to throw my 20 pages of scribble into the wastebasket in frustration. If you are not as obsessive as I am, then you might be ok with skipping over topics or exercises that are too advanced.

Having done every single exercise up to Chapter 5, I've found about 3-4 typos in the print, which is decent for a math text.
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3 of 3 people found the following review helpful
5.0 out of 5 stars An math student must have! 14 Jun 2012
Verified Purchase
This book is very clear and easy to use. The author is clearly well informed in the area, and his years in lecturing reflect his ability to communicate effectively. I used this book as a companion to my lectures at uni and was very useful in providing alternative definitions and extra examples. A must have for an undergrad student in maths.
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17 of 27 people found the following review helpful
4.0 out of 5 stars A Must for any Undergrad Maths Student...!! 18 Nov 2000
The book is intended for extensive use of undergradurate Maths students. It is recommended by University Professors as the Core texts and introduction of anything that is related to Abstract Algebra courses. Good use of examples, with fairly clearly laid out definitions.
!The material used in this book will be useful for any undergrad students throughout the whole three year course!
(This is the recommended course text in my Uni, you can't go wrong with it!)
Anyway,(enough said!) a MUST buy not only because it covers a good understanding of the course, but by far the most important reason - it is a one of the very few grumpy Maths books that a student can afford, cheap enough to get it without the hassle of getting it out from the library!
PS. Put it that way, I am forced to buy it NOT because I am a nerd. I want to pass my exams too, but when the Professor was too intelligent for ordinary humanoids like myself and the rest of my classmates it would be mission impossible. So don't come emailing me with Maths questions unless you are studying at the primary level!!
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2 of 4 people found the following review helpful
5.0 out of 5 stars Does what it says on the tin.... 5 Mar 2011
Verified Purchase
This book is really useful for the module that I have been doing. Not only describes abstract algebra, but goes into a lot of detail, giving another angle to look at things. There is also alot of interesting information on the players and the history of abstract algebra. All in all very helpful to anyone studying this.
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Most Helpful Customer Reviews on Amazon.com (beta)
Amazon.com: 4.0 out of 5 stars  2 reviews
15 of 17 people found the following review helpful
4.0 out of 5 stars Algebra for advanced beginners 13 Sep 2000
By Janus Mens - Published on Amazon.com
I used this book as a supplement to a course in algebra at master level. Allenby uses a simple step by step approach to the subject supplied with simple examples and some exercises (not that simple).
What I realy like with this book is the historical tour of algebra and the brief presentation of many of the worlds famoust mathematicians.
I think the simple approach and the historical elements is main reason for still using this book when I am plying with the math.
5 of 5 people found the following review helpful
4.0 out of 5 stars Good for self-study 22 Sep 2009
By Brian Jo - Published on Amazon.com
For the most part, this book is a clear and concise introduction to abstract algebra. The prose is lucid and the author's notes and remarks give some intuitive rationale behind several of the results. The exercises are well-thought out, and in some cases they expound on an idea touched on earlier in the chapter.

On the other hand, a few of the chapters went over my head. The Prologue, for example, cites the major contributions of the key figures in the historical development of algebra. Since I was still an algebra novice when I read the Prologue, I found it hard to follow. Moreover, Chapter 5 on Group Theory begins with an introduction that summarizes two methods of solving the cubic. I had a lot of trouble following this section as well. In his description of Tchirnhaus' method, he brings up a simultaneous equation involving a cubic and quadratic but skips over some calculations. I spent 2 days trying to fill in the gaps, only to throw my 20 pages of scribble into the wastebasket in frustration. If you are not as obsessive as I am, then you might be ok with skipping over topics or exercises that are too advanced.

Having done every exercise up to Chapter 5, I've found about 5-6 typos in the print, which is decent for a math text. Brief solutions for most problems are in the back, which makes this book ideal for self-study.
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