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Algebra (2nd Edition) (Featured Titles for Abstract Algebra) 2nd Edition

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ISBN-13: 978-0132413770
ISBN-10: 0132413779
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Editorial Reviews

From the Back Cover

Algebra, Second Edition, by Michael Artin, discusses concrete topics of algebra in greater detail than most textbooks, preparing readers for the more abstract concepts. This book covers all of the topics that are important to the average mathematician, and are covered in the typical course. Linear algebra is tightly integrated throughout.


KEY TOPICS: Matrices, Groups, Vector Spaces, Linear Operators, Applications of Linear Operators, Symmetry, More Group Theory, Bilinear Forms, Linear Groups, Group Representations, Rings, Factoring, Quadratic Number Fields, Linear Algebra in a Ring, Fields, Galois Theory


MARKET: For all readers interested in algebra.

About the Author

Michael Artin received his A.B. from Princeton University in 1955, and his M.A. and Ph.D. from Harvard University in 1956 and 1960, respectively. He continued at Harvard as Benjamin Peirce Lecturer, 1960—63. He joined the MIT mathematics faculty in 1963, and was appointed Norbert Wiener Professor from 1988—93. Outside MIT, Artin served as President of the American Mathematical Society from 1990-92. He has received honorary doctorate degrees from the University of Antwerp and University of Hamburg.

Professor Artin is an algebraic geometer, concentrating on non-commutative algebra. He has received many awards throughout his distinguished career, including the Undergraduate Teaching Prize and the Educational and Graduate Advising Award. He received the Leroy P. Steele Prize for Lifetime Achievement from the AMS. In 2005 he was honored with the Harvard Graduate School of Arts & Sciences Centennial Medal, for being "an architect of the modern approach to algebraic geometry." Professor Artin is a Member of the National Academy of Sciences, Fellow of the American Academy of Arts & Sciences, Fellow of the American Association for the Advancement of Science, and Fellow of the Society of Industrial and Applied Mathematics. He is a Foreign Member of the Royal Holland Society of Sciences, and Honorary Member of the Moscow Mathematical Society.

Product Details

  • Series: Featured Titles for Abstract Algebra
  • Paperback: 560 pages
  • Publisher: Pearson; 2 edition (August 13, 2010)
  • Language: English
  • ISBN-10: 0132413779
  • ISBN-13: 978-0132413770
  • Product Dimensions: 7.2 x 0.9 x 9 inches
  • Shipping Weight: 2 pounds (View shipping rates and policies)
  • Average Customer Review: 3.7 out of 5 stars  See all reviews (10 customer reviews)
  • Amazon Best Sellers Rank: #109,972 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

60 of 60 people found the following review helpful By Reviewer #51413 on December 21, 2011
Format: Paperback
Since there is currently only one other review, which I find very inaccurate, I will throw in my 2 cents.

First of all, I disagree about the readability of Artin's book. I found the presentations crystal clear, and in particular the proofs are very readable. Artin avoids clever tricks when a straightforward approach is available and does a good job explaining the reasoning behind proofs. There are also enough examples to illustrate the concepts presented.

Second, the exercises in Artin are excellent. They provide a way to become familiar with the definitions and techniques in the chapter, as well as illustrate some interesting applications of the material. There are some easy exercises, and some very difficult ones. I'm not sure what more you could ask for.

As far as Dummit and Foote goes, I agree that it is an excellent text. However, I would prefer Artin as an introductory text, since it is a gentler introduction to all the abstraction. Dummit and Foote is a better for a course beyond an introduction, and also serves as a better reference. Anyway, Artin covers a different set of topics than more "standard" texts such as Dummit and Foote, such as plane symmetries and linear groups.

Overall, I think Artin's book is an excellent introduction to abstract algebra. In fact, the two semester course using Artin that I took (taught by the man himself), was one of the best academic experiences of my life.
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30 of 30 people found the following review helpful By book reviewer on December 25, 2011
Format: Paperback Verified Purchase
I used this book in an advanced algebra course in which the students learned on their own with minimal guidance from the professor and discussed the assigned readings and homework once a week. I found this book difficult for self-learning. Artin aims for concision in his proofs, making the reader prove some things on his own. This is not necessarily bad, and is often very helpful for the student's learning. But it can be tough and frustrating if you need a hint, or get lost in a proof. In other words, it's perfectly good to leave steps for the reader, provided that the reader can actually fill in the gaps. For that reason, I think this book is best used as a supplement to a professor's lectures, rather than for self-learning. This book does a good job of condensing the material, and the theorems are easy to find, so it is useful when reviewing. I like the topics in the book. One of the aims of this book is to introduce the reader to the various applications of algebra. To this end Artin includes not only the typical algebra material, but also symmetry and imaginary quadratic fields. Unfortunately I found the second edition worse than the first edition in its chapters on fields. Artin took out many examples in the first edition, for reasons I don't know. The chapter on fields is full of definitions and theorems, but in my mind it doesn't elucidate the main ideas and themes effectively. I think Dummit and Foote is much better at explaining basic Galois theory. The exercises, though, are very good. Overall, this is a challenging book; when used effectively in a well-taught course (for example, see Benedict Gross's excellent free online videos on algebra), it should prove to be very rewarding.
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Format: Paperback Verified Purchase
I don't think that there is any need for promoting this book. It is a must for every mathematics student. I had exposure to most of the materials of the 10 chapters of this book previously. However I was interested to review some of these materials from this book. I found it very clear both in proofs and in the presentation of topics. Therefore it is very well suited for self-study. The exercises are very pedagogical and are a main part of this book because very often new topics are introduced. I got the paperback edition. While the quality of the papers is acceptable (it is a little bit yellowish though), the cover can be damaged easily. Yet it is definitely worth the 100$ one can save over the original edition.
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4 of 7 people found the following review helpful By Carlos on December 11, 2014
Format: Paperback Verified Purchase
This book is great if you already know the material. If you don't know the material this book is horrible. About 40% of the Theorems are "obvious" or "clear" so he doesn't go through crucial proofs. Everything is obvious to a master but to a student this is not the case. Next, for certain.. well most material he goes through "simple" examples so he skips all the work and well the simpler the example the less of the theorem is being demonstrated. What I mean by this is how could you teach someone to factor out the GCF of terms which are relatively prime? The examples are simply poor and sparse. What Artin does in 500 pages most authors do in 700. I know it isn't about quality versus quantity but there isn't much quality in this book to find.
I recommend Dummit and Foote instead or wikipedia for that matter. The book is a bit higher level but much more well written and organized. If you can avoid this book, you should.
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0 of 2 people found the following review helpful By anonymus on May 9, 2015
Format: Kindle Edition
I am just posting some comments for now.

On p 137 the book notes that that SO3 is a group is not geometrically obvious. Can someone tell me what's wrong with the following seemingly obvious observation? :
if rho1 is applied to a point P, we can imagine it rotating on a cylinder of radius r1. But P's distance to the origin stays the same at r2, say by imagining a right triangle with r2 as hypo. Now if we apply rho2, the point will rotate on a different cylinder of r3 on a different axis, but the hypo of the new right triangle is still r2. Thus P will stay on the same sphere, and so rho2(rho1) is a new rotation.
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