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Rating: 
Summary: A Fine Intro to Modern Algebra
Review: A very readable first text on modern algebra! This book does a great job to ease the reader into the subject. Durbin keeps it in mind that students often struggle with reading and writing proofs at this level, and accomadates starting off with detailed proofs in the beginning and backs off as he moves on through the text. Those who want a more rigorous treatment may want to read Herstein. Over all, it's a fine introductory text.
Rating:
Summary: A comprehensive and concise introduction to Algebra.
Review: 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.
Rating: 
Summary: Too vague with many errors in later chapters/sections
Review: 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.
Rating: 
Summary: Good Exposition, Poor Problems
Review: 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.
Rating:
Summary: Good Exposition, Poor Problems
Review: 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.
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