Customer Reviews

Modern Algebra: An Introduction

5 star:		(0)
4 star:		(2)
3 star:		(3)
2 star:		(1)
1 star:		(0)

 

 

First off, I want to say that this book isn't the worst I've read. It's well organized and written fairly clear. The main problem I have with it is the cost!

I originally thought this book was an OK introduction until I read Abstract Algebra by Beachy and Blair and Abstract Algebra by Herstein. I recommend the first for those who need to work on proof writing, and the second for those who have a solid foundation in abstract mathematics and aren't afraid of a little rigor. Both of them are cheaper, and do a much better job exposing the material.

The only reason I'm keeping the text is because chapters XIV, XV and XVI seem like they have interesting applications (crystallography, cryptography, etc.)

As a first year student studying maths at Trinity College Dublin I have found this book very helpful. Our lecturer in Algebra sticks closely to the format of the book and almost uses it as his lecture notes. The book is very student friendly and gives a lot of good examples along the way. As with any good maths book no point is trivialised and the wording is all important. Modern Algebra can be a challenging subject but it is also immensely rewarding when things begin to fall together.

This book covers many of foundations of abstract algebra including groups, rings, homomorphisms, isomorphisms, Sylow's theorem, Galois theory, etc. While most of the sections are fairly well-worded, most of the text is vague and the more challenging problems are given without too much training on them in the section's text.
Also, I found the algebraic coding chapter very difficult to read and understand. Durbin does a lackluster job at clearly explaining the concept of coding theory. There are also many errors in the answer key which definitely lead to confusion especially for newcomers.
On a positive note, I found the section on frieze and crystallographic groups an icebreaker in the seemingly endless blurb of unclear information.

This is a nice book overall. Clear exposition, good examples, and not too thick. I personally found the problems lacking in motivation and scandalously simple, which made it difficult for me to complete my homework sets (if you ain't learning nothin', it ain't worth doin').

Another good point is that it contains a number of sections introducing more advanced topics (galois theory, algebraic coding, finite fields and field extensions, symmetry and crystallographic groups, and more).

So this book probably is great for an introduction to the subject, just don't look for anything exciting.

This book is acceptable as an introduction to abstract algebra, but once one has learned the material and looked at a few other books, it will be clear that there are many books that are far superior. First off, the book seems to fall apart towards the chapters on field extensions and Galois theory; many of the more technical proofs of theorems become rushed or even incomplete, while many of the earlier, easier proofs are given much more care. I used this book for a two semester course in algebra, and the beginning went very well; but towards the second half of the second semester my professor was a bit frustrated with the text and was forced to provide a good amount of supplementary notes.

The majority of the exercises were computational or routine verifications. Also, many standard topics were omitted. For example, classifying finite groups up to order 15 or would be instructive and wouldn't consume too much time, while they fail to even mention dihedral groups until the end; also, there was absolutely NO content about modules, which seem to be one of the most important algebraic structures, right up there with groups, vector spaces, and so on.

In summation, I would've given this book 3.5/5 if possible; the first few chapters are good. But they aren't anything that you won't find in every other book. The reason I rated as I did is because there are other books out there that are not as expensive, more complete, and contain a better exposition of this amazing subject.

With the exception of material such as encoding that requires a computer for the most complex problems; the area called modern algebra has not changed in decades. In fact, this is an area where the inclusion of a computer in the early work is detrimental rather than beneficial. Modern algebra is also known as abstract algebra for good reason, to understand it you have to be able to process symbols abstractly. Therefore, I tend to score modern algebra books lower if there is significant dependence on a computer.
That is not an issue with this book; computer involvement is kept to a minimum. First courses in modern algebra are now fairly fixed in terms of coverage and this one is in no way a deviant. Proofs of the most important basic concepts are present but not in overwhelming numbers. The style of presentation is to introduce one concept, illustrate it with examples and then have a series of exercises, some of which are answered in an appendix. The final three chapters cover:

*) Symmetry
*) Cryptography and algebraic coding
*) Lattices and Boolean algebras

Effectively usable is a phrase that describes this book, nothing in it that will make you consider it outstanding and nothing that would cause you to reject it.