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Book Reviews

Review of Algebra

Reviewed by gh-bigfoot, from Oregon, USA
My first taste of algebra came from Lang's book (big mistake). I then read Gallian's undergrad. book and tried Lang again, it was still very difficult. I finally found Grove. This is a great book. Very easy to read and understand. Although it doesn't cover everything in Lang, it covers everything that commonly comes up in a first year graduate class. The book's only drawback is it's difficulty to find. If you're looking for a good intro. to algebra text (and if you can find it) buy it!

Reviewed by Todd Ebert, from Irvine, Ca United States
This is one of my favorite beginning graduate texts. Although it follows a very terse definition-example-theorem-proof style, the proofs and examples seem very enlightening. Each Chapter comeswith numerous exercises interleaved with the material, as well asexercises at the end of the chapter. Groups, rings, fields, and modules are covered in depth.

Review of Tae Algebra I

Editorial review
An abridged edition of the author's previous two-volume work, Ring theory, which concentrates on essential material for a general ring theory course while omitting much of the material intended for ring theory specialists. Annotation copyright Book News, Inc. Portland, Or.

Review of Algebra

Editorial review
This introduction to modern algebra emphasizes concrete mathematics and features a strong linear algebra approach.

Reviewed by mikeu3, from Berkeley, CA, USA
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.

Reviewed by a reader, from Cambridge, MA
This is the best undergraduate algebra text I've encountered. It is written for students who are already fairly mathematically mature. Artin's proofs contain just the right amount of detail and the book rewards careful and attentive reading. Many people are put off by the emphasis on linear groups and linear algebra. But I think Artin's choice is the correct one. Students get to use the tools of algebra on nontrivial groups from the very beginning (for instance, the orbit-stabilizer theorem on SL_2(F_p)). The exposition is beautiful and the exercises are both challenging and interesting. Special points include Artin's inclusion of a chapter on the classical linear groups and a brief introduction to both Lie groups and a smattering of algebraic geometry.

Reviewed by wang@math.sc.edu, from COLUMBIA, SC United States
I believe that the guys who favor this text book are those who read group theorems only. As one of the best student, I have to say, I believe you will encounter unbearable difficulties if you read Ring and Field parts. I must read everything from any other text book to understand clearly what Artin is saying in his book. can you believe it? Few definition is described clearly, few theorem is proved in a logic-clear, easy-to-undersatnd way. The most important is that many useful properties of Ring , field are not included in his book, but in the problems you have to find all these totally by yourself in order to solve the problems. Also, the textbook is NOT well- orginized. A typical exmaple, Artin has not yet tell the reader basic informations and properties of Ring Of Polynomial in one variable , but he starts to describe the structure of Ring Of Polynomial in 2 or more variables. The reader's minds would be completely mixed up if he doesn't not have an extremely high IQ. I believe , your knowlege of Ring and Filed will be very limited and very unclear if you use Artin's book only. Abstract Algebra is a hard topic. You should not use a book which is definitely not a help for you but rather a trouble for you!!!. I hate this book!!. Artin may be a famous mathematician, but he is not a good educator. He doesn't not know to teach students in a good manner.

Reviewed by nootropic@hotmail.com, from a beautiful island
I don't like this book because it doesn't follow a clear definition/theorem/proof format, like Rudin's Principles of Mathematical Analysis. In Artin's efforts to clarify he actually ends up confusing. The definitions and even some important concepts are haphazardly introduced in a "conversational" style, in the middle of long paragraphs (what are paragraphs doing in a math book?). These "explanatory" paragraphs are meant to clarify and add meaning, but although this style might sound helpful it actually gets in your way and makes learning much, much harder and more confusing. On the other hand, Rudin gets right to the point, he formalizes and crystallizes everything, he presents no pictures (and therefore forces you to make your own), he's not your friend, and in fact helps you learn better than Artin. There are plentiful examples, but Artin's obsession with the rotation groups gets quite annoying; even if you're not interested in the rotation groups, you have to study them in-depth in the earlier chapters so that you can understand all the later examples, many of which refer back to these (e.g., the examples in the Group Representation chapter are almost entirely dependent on the tetrahedral group!). The examples in a high-level introductory book should be like those in Rudin's, throwing light on historically and theoretically important problems.The exercises can range from hard and interesting to routine, with a pleasantly surprising number of the former. But Artin also seems to be obsessed with linear algebra and rotation groups; this can be frustrating. Also, some problems are just computationally hard--a consequence of the linear algebra fetish; there shouldn't be so many computational, almost-routine problems in a rigorous book.(To those who don't know Rudin--I don't think he ever wrote an algebra text; I was only comparing presentation styles. Rudin does analysis.)

Review of Intermediate Algebra for College Students (3rd Edition)

Editorial review
This textbook for a one-semester course in intermediate algebra covers functions, systems of linear equations, polynomial factoring, rational expressions, radical exponents, quadratic equations, logarithms, conic sections, sequences, and series. The second edition has been rewritten to make it more accessible, and adds a separate chapter on inequalities.Book News, Inc.®, Portland, OR

Reviewed by a reader, from Hollywood CA
Blitzers' step by step is very helpful but does not always use the best path to the solution. He could use more examples of different types of the same problem, ie. What occurs when using negetives on this problem? Great book, but with anything, could be better.

Review of Intermediate Algebra (4th Edition)

Editorial review
Progresses from linear equations and polynomials through to quadratic equations and exponential functions. Bright colors and countless graphics will keep even nodding-off students up to speed. The new edition focuses on real world math problems and includes practice problems with solutions, application problems, and chapter summaries presented in chart form. Book News, Inc.®, Portland, OR --This text refers to the Paperback edition.

Reviewed by Theresa Froehlich, from Lynnwood, WA
I am a mother who didn't do well in Algebra in high school. I am now having to help my 8th grade daughter with her Algebra. Having used Tobey & Slater's Basic College Math and Beginning Algebra (whenever her textbook doesn't make sense to me or to her), I am exceedingly impressed with their exceptional ability to explain clearly yet simply the mathmatical concepts. My experience with these books gave me the confidence to buy their Intermediate Algebra (4th Edition 2002). This updated edition provides clear explanations that make sense to someone who is not a math whiz. It includes not only exercises, but also practice problems, real-life applications, cumulative reviews, and writing exercises to teach students to translate numbers into words. It is a very comprehensive approach to empower the student to not just grasp the concept but also to retain it.

Reviewed by a reader, from Somerville, New Jersey USA
This textbook is extremely frustrating for the novice, who, after all,will be using it! It omits critical steps in its examples, and leaves the user confused. It is very difficult to succeed in class with this book as a resource. I am online to purchase a book which has a comprehensive format, to get me through the course I'm taking!

Review of Introductory and Intermediate Algebra

Editorial review
Provides readers with a strong foundation in Algebra. Designed to develop readers' critical thinking and problem-solving capabilities and prepare readers for subsequent Algebra courses as well as service math courses. Softcover.

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