Rings, Fields and Groups, An Introduction to Abstract Algebra 2nd Edition by Reg Allenby (PDF)

Description

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.

User’s Reviews

Editorial Reviews: 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 From the Publisher 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. About the Author R. B. Allenby, Senior Lecturer, School of Mathematics, University of Leeds. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I’m a PhD student in physics. I was always good at math since I was a kid but I chose physics for profession. In college, pure math were only taught during the first two years, and after that, it was always “mathematics for physicists.” It continues in grad school and I expect it will be like that even after.I decided to learn pure math on my own to make sense of what are just given to us. After browsing online discussions, this book was the best choice for my level. And yes, it answers a lot of ignored questions I had in undergrad and early grad.I recommend not to rush following this book because it is straight to the point, so if you just skim through one page, it will not be repeated later on that you’ll have to go back. Also try to do all the exercises even if you feel like you understood all the concepts in the chapter, the exercises prove to be very valuable knowledge when you compare yourself to other mates.Like all books, sometimes you wish there would be answer keys available. In this book, the exercises are kind of classic that you might find the solutions online.

⭐A solid and comprehensive introduction to abstract algebra.

⭐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 read every word and done every exercise up to Chapter 5, I have only noticed about 5-6 typos in the print, which is pretty outstanding for a math text. Brief solutions for most problems are in the back, which makes this book ideal for self-study.

⭐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.

⭐* PhysicalThe book is printed on very good paper, with a good size of the font for those who need specs.* Target audience, H.N.D, Undergrad, Post Grad?In my opinion, this great book is the first, and second-year degree of a Math topic.* Prerequisites?In my humble opinion, the following books are great help primers, but the price for this first book is too high, but you can get the first in a digital Kindle download format for a snip.International Edition, A First Course in Abstract Algebra, John B. Fraleigh, seventh edition.AND ORFields and Galois Theory (Springer Undergraduate Mathematics Series) Paperback – 2 Jun 2010 John M. HowieI reread both of these books as they have been on my shelf for years after a less than successful initial reading for study, but it’s better second-time around.* Topics covered?In 383 pages this great book covers, 0 Elemental set theory and methods of proof, 1 Number and Polynomials, 2 Binary Relations and binary Operations, 3 Introduction to rings, 4 Factor rings and fields, 5 Basic group theory, 6 Structured theorems of groups theory, 7 A brief excursion into Galois theory, Practical solutions* CommentsThis book is great with this line of attack. The key is to commit to memory the axioms and other elements and it just clicks together in a coherent way. This time around it’s just clear to me what’s been going on and how important this line of studies in math.* SummaryIt’s clearly brought into focus this introduction of Abstract Algebra and this supports for example Calculus. The set theory vernacular is a skill into its self too. This is a good book the second time around and I humbly recommend it to those learning in this area.

⭐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.

⭐Basic introductory stuff that anyone can print from the web for free.

⭐Fantastic! Easy to read and exercises really helped clearing up sticky points.

⭐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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