Modern Algebra: An Introduction, 4th Edition

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.


Better introductory algebra books available   June 8, 2007
Stephen Shank (Philadelphia, PA)
2 out of 2 found this review helpful

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; not many had me totally stumped or thinking hard (which is something a serious math student should want to do). 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.


Too vague with many errors in later chapters/sections   April 8, 2003
Sweetcheeks McMuffin (Ohio, USA)
10 out of 12 found this review helpful

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.