This book is for the honors undergraduate or introductory graduate course. Linear algebra is tightly integrated into the text.
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This introduction to modern algebra emphasizes concrete mathematics and features a strong linear algebra approach.
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94 of 103 people found the following review helpful
By Ellipsic
Format:Hardcover
Artin's book is probably one of the better books, more because of the way you have to read it to learn it. Artin's book is extremely nonstandard, in the sense that it isn't so "encyclopedic" as you usually encounter with the whole theorem, corollary, proof, proof, proof, example, example sequence. What I think a lot of readers miss is that Artin's book makes you fill in the details he leaves out by using the hints he mentions in words within the text. For example, I was able to expand the two pages of notes on Ch 2, section 5, in Artin into about 8 pages of original notes and theorems, just by digging for the main points. If you want a sample of my notes, please email me and I'll email you a brief PDF sample for you to compare. That being said, assume that you will have to dig a lot in this book, and should you choose to study from it, I suggest the following:
How to read it:
With a cup of coffee, or tea, and a notepad of paper for you to make comments on. Do not take notes; anyone knows that simply rewriting things doesn't do anything for learning. You should do the proofs in different ways, if you can see how, and try to make some of the aside remarks he makes into theorems or more precise ideas (this is not to say that Artin lacks rigor; this is just talking about the general commentary. When he makes commentary, it always seems to be enough to actually dig out exactly what to do after a little scratching). He also leaves a lot of easier proofs to the reader, so do them.
Is non-standard a less-rigorous approach?
No. Artin is definitely doing his own thing here, but I think it works really well. Getting through that book FORCES you to take responsibility for your math education by making you get your hands dirty while also developing an intuitive understanding of algebra.
What about his personal flavor of algebra?
Well, it's fairly clear to all of us that texts seem to have different flavors (being a function of the author's research area, and what was fashionable during the time the book was authored). Artin's book is algebra with light strong hints of geometry throughout, as he is in algebraic geometry. You will find that unlike most authors, Artin loves structures made of matrices when working with examples, as opposed to permutation groups or the ``symmetries of the square group,'' known also as the ``octic group.'' While these things have their place in his book, he changes the emphasis here. That's why I suggest using a companion book so as to have two sharply contrasting flavors of presentation, and Herstein seems to write in such a way that would do this. Artin covers a lot of material extremely quickly, but focuses on the bigger picture in several key areas. For example, the sections 7 and 8 in chapter 2 deal almost exclusively with how one would go about investigating a particular group structure to learn about it, teaching a student how to dig into something they might barely understand.
Advice to make a wondeful course:
Use another book which IS encyclopedic as a reference, since Artin doesn't label theorems and definitions so explicitly. I suggest Lang's Algebra or Undergraduate Algebra.
Personal Charracterization:
This book helps you learn how to fight with algebra problems--in a course that can be taught in a very dry way, M. Artin has been able to supply a text with a large scope, borrowing ideas from topology, analysis, etc. The book has a very broad scope, and the exercises and problems Artin has chosen are great for teaching you to dig into ideas.
* EDIT * This book is based on lecture notes, and so is great to learn from, but not so great as a reference text. Things you might like to look up (i.e., correspondence theorem for subgroups containing a normal subgroup) are left as exercises, so it's tough to track down some things.
How to read it:
With a cup of coffee, or tea, and a notepad of paper for you to make comments on. Do not take notes; anyone knows that simply rewriting things doesn't do anything for learning. You should do the proofs in different ways, if you can see how, and try to make some of the aside remarks he makes into theorems or more precise ideas (this is not to say that Artin lacks rigor; this is just talking about the general commentary. When he makes commentary, it always seems to be enough to actually dig out exactly what to do after a little scratching). He also leaves a lot of easier proofs to the reader, so do them.
Is non-standard a less-rigorous approach?
No. Artin is definitely doing his own thing here, but I think it works really well. Getting through that book FORCES you to take responsibility for your math education by making you get your hands dirty while also developing an intuitive understanding of algebra.
What about his personal flavor of algebra?
Well, it's fairly clear to all of us that texts seem to have different flavors (being a function of the author's research area, and what was fashionable during the time the book was authored). Artin's book is algebra with light strong hints of geometry throughout, as he is in algebraic geometry. You will find that unlike most authors, Artin loves structures made of matrices when working with examples, as opposed to permutation groups or the ``symmetries of the square group,'' known also as the ``octic group.'' While these things have their place in his book, he changes the emphasis here. That's why I suggest using a companion book so as to have two sharply contrasting flavors of presentation, and Herstein seems to write in such a way that would do this. Artin covers a lot of material extremely quickly, but focuses on the bigger picture in several key areas. For example, the sections 7 and 8 in chapter 2 deal almost exclusively with how one would go about investigating a particular group structure to learn about it, teaching a student how to dig into something they might barely understand.
Advice to make a wondeful course:
Use another book which IS encyclopedic as a reference, since Artin doesn't label theorems and definitions so explicitly. I suggest Lang's Algebra or Undergraduate Algebra.
Personal Charracterization:
This book helps you learn how to fight with algebra problems--in a course that can be taught in a very dry way, M. Artin has been able to supply a text with a large scope, borrowing ideas from topology, analysis, etc. The book has a very broad scope, and the exercises and problems Artin has chosen are great for teaching you to dig into ideas.
* EDIT * This book is based on lecture notes, and so is great to learn from, but not so great as a reference text. Things you might like to look up (i.e., correspondence theorem for subgroups containing a normal subgroup) are left as exercises, so it's tough to track down some things.
37 of 40 people found the following review helpful
Format:Hardcover
By treating the concrete before the abstract, Artin has produced the clearest and easiest to understand expositon I have seen. He delves quite deeply into groups, rings, field theory and Galois theory. It is NOT true, as one reviewer claims, that Artin does not treat fields: an entire chapter is devoted to the topic.
If Bourbaki is your god and you believe axiomatization is the only way to present this material, then you won't like this book. But remember that this work is written by the son of the great Emil Artin, and Michael is a first-rate mathematician as well.
The ordering of topics and the approach are non-standard but this emphasis on the concrete before the abstract and the use of a function motivated development make this book stand apart from the competition. It is not only the best undergraduate abstract algebra text that I have seen but it can be very useful for graduate students. My undergraduate major was not in math, I HAD NO UNDERGRADUATE COURSE IN ABSTRACT ALGEBRA but I jumped into a really heavy-duty graduate level abstract algebra course with Hungerford as the text. Now, I feel that Dummit and Foote is much better than Hungerford and Artin is even better than the aforementioned and much better - and more thoughtful -than Gallian. I wish I had Artin to give me enlightenment and perspective when I was struggling with this material having had no prior exposure to it.
If Bourbaki is your god and you believe axiomatization is the only way to present this material, then you won't like this book. But remember that this work is written by the son of the great Emil Artin, and Michael is a first-rate mathematician as well.
The ordering of topics and the approach are non-standard but this emphasis on the concrete before the abstract and the use of a function motivated development make this book stand apart from the competition. It is not only the best undergraduate abstract algebra text that I have seen but it can be very useful for graduate students. My undergraduate major was not in math, I HAD NO UNDERGRADUATE COURSE IN ABSTRACT ALGEBRA but I jumped into a really heavy-duty graduate level abstract algebra course with Hungerford as the text. Now, I feel that Dummit and Foote is much better than Hungerford and Artin is even better than the aforementioned and much better - and more thoughtful -than Gallian. I wish I had Artin to give me enlightenment and perspective when I was struggling with this material having had no prior exposure to it.
43 of 49 people found the following review helpful
By "mikeu3"
Format:Hardcover
Pretty much any introductory abstract algebra book on the market does a perfectly competent job of introducing the basic definitions and proving the basic theorems that any math student has to know. Artin's book is no exception, and I find his writing style to be very appropriate for this purpose. What sets this book apart is its treatment of topics beyond the basics--things like matrix groups and group representations. I suppose many introductory books shy away from much of the material on matrix groups in Artin's book because it involves a little analysis (and likewise for the section on Riemann surfaces in the chapter on field theory). However, Artin correctly realizes that a reasonably mathematically mature student--even one who doesn't know much analysis--will be able to profit from and enjoy the relatively informal treatments he gives these slightly more advanced topics. Of course these topics can also be found in graduate-level texts, but I for one would much rather be introduced to them via an example-based approach such as that in Artin than through the diagram-chasing obscurantism in more advanced books. I happened upon this book a little late--in fact, only after I'd taken a semester of graduate-level algebra and already felt like analysis was the path I wanted to take--but I'm beginning to think I would have been more keen on going into algebra if I'd first learned it from a book like this one.
Most Recent Customer Reviews
5.0 out of 5 stars
The classic text
Many excellent texts on abstract algebra exist. I would recommend Artin to an absolute beginner however along with Pinter, or Saracino, or Fraleigh or Herstein's Abstract Algebra... Read more
Published 1 month ago by Stuart Leviton
4.0 out of 5 stars
Good but needs a different organization
This book has an approach that is not intuitive. One commenter suggests to change how the chapters are organized. I heartily agree.
Published 12 months ago by Lulu Cerne
4.0 out of 5 stars
fine
Book is in good shape as advertised. Don't particularly like the big USED sticker right across the middle of the front cover but the rest is fine. Read more
Published 15 months ago by Thomas Cleary
5.0 out of 5 stars
An elegant and concise text
This text provides a very nice treatment of abstract algebra; most proofs are in the book and the ones that aren't are straightforward. Read more
Published 20 months ago by Anonymous
2.0 out of 5 stars
Paradoxically useless
This book is useless for students enrolled in a college or university. As others mention, this book mimics lecture notes and doesn't follow the theorem-proof-example-excercise... Read more
Published on November 25, 2010 by Chris
5.0 out of 5 stars
Excellent undergraduate algebra
Excellent undergraduate algebra, with emphasis on examples and interaction with other areas of mathematics, a mixture of simplicity and sophistication. Read more
Published on December 20, 2009 by Ioan Pit
5.0 out of 5 stars
Teaches instead of expounds
Not having the experience of listening to Artin lecture, one can only surmise that this man has to be a great teacher. Read more
Published on August 26, 2009 by Gnugs
5.0 out of 5 stars
Why You Should Get This Book Instead of Dummite & Foote
Artin's Algebra is a great book. It covers a good deal of introductory Algebra, leaving out some stuff, but ultimately covering everything you need to be able to move on to the... Read more
Published on May 31, 2009 by A. Foster
2.0 out of 5 stars
Incredibly insightful, deliberately disorganized text
I wish to first point out that several positive reviewers argue that the strength of the book is what it forces you to look for and that if you cannot find the missing puzzle... Read more
Published on May 7, 2009 by Mitchell C. Amiano
1.0 out of 5 stars
A totally useless textbook.
The book by Artin was the most useless math textbook I have ever used. His proofs are impossible to understand, the exercises are frequently useless (either trivial results or... Read more
Published on January 21, 2008 by J. Williamson
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