Concrete Approach to Abstract Algebra

by W.W. Sawyer

A Concrete Approach To Abstract Algebra (Dover Books On Advanced Mathematics)

Genres: Mathematics, Reference

234 pages, Paperback

First published June 1, 1978

About the author

Walter Warwick Sawyer (or W.W. Sawyer) was a mathematician, mathematics educator and author, who taught on several continents.
https://en.wikipedia.org/wiki/Walter_...

Reviews

[Savino Longo · Rating 5 out of 5]

This book is wonderful. At first glance it may seem too elementary, especially for those who have already studied some mathematics, but don't be fooled by the central part where the fundamentals of vector spaces are exposed. You can safely skip these two chapters if you have studied engineering or mathematics or physics. The important thing is to understand that in a book of this type the vector spaces are then used as a tool for the theory of the extensions of algebraic fields! In reality, this book wonderfully explains, with a practical approach, the theory of the extensions of algebraic fields, and then crowns the whole treatment arriving stupendously at the demonstration of the impossibility of constructing some angles with ruler and compass. That's all it takes to have a first coherent and contained exposure to the way impossibility theorems are proved in abstract algebra! I suggest reading this book and then moving on to a manual that talks about Galois groups and isomorphisms.

[Kyle · Rating 5 out of 5]

This is another excellent mathematics textbook written by WW Sawyer. If you would like to learn what Modern Algebra (or "Abstract Algebra") is about, this book starts from simple examples and builds up your intuition excellently. You understand why some axioms or properties are chosen for study, and how they can be used to enrich our understanding of number systems. I also thought the exercises were well crafted. The only complaint I have is that the the degree of a field extension was covered too quickly, and so was not clear to me until I consulted a different abstract algebra book. Other than that, I thought Sawyer clearly presented concepts, motivated them, and gave useful examples. He goes through the steps of examples, as well, which I often find as useful as the surrounding explanations.

The book is really an introduction to the subject, however, so if you want a full treatment of modern algebra, you will need to consult other texts.

[Jerry Balzano · Rating 5 out of 5]

See my review of Mathematician's Delight. Basically, anything written by W. W. Sawyer is pure gold, and worth reading. This book shows that Sawyer is just as adept with advanced as with elementary material.

[George · Rating 5 out of 5]

If you are a practical mathematician/physicist/engineer, then this is a great book for you! (Assuming you want to know something about fields).

This book was outside my usual reading area - I am a physicist and find pure maths topics and style hard to follow, and hard to apply to useful things. However, Sawyer is an excellent teacher, and the 'concrete approach' was perfect for my practical way of thinking. There are lots of concrete examples, also worked examples, and exercises with the answers (and some working also :) at the back of the book. I wish other authors were this good.

I often brush up against mathematicians' style in papers and books, and often the terminology and style is hard to follow - 'why on earth would they do it like that?' - this book has helped me to understand some of the things that mathematicians 'bang on about'. Now some of their writings seem less strange.

[Calvin · Rating 4 out of 5]

Nice and short book, I would say it is a good introduction to some topics of abstract algebra and probably a good first book into the field, before more serious ones.