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Title: Contemporary Abstract Algebra by Joseph Gallian ISBN: 0-618-12214-1 Publisher: Houghton Mifflin Co Pub. Date: 01 January, 1900 Format: Hardcover Volumes: 1 List Price(USD): $117.16 |
Average Customer Rating: 4.38 (13 reviews)
Rating: 5
Summary: Despite lack of rigor, best undergrad text available.
Comment: I took the regular Abstract Algebra course at Purdue as a sophomore, and this book made me decide to switch majors from Physics into Mathematics. Gallian's treatment of algebra is NOT the most thorough. On the other hand, this book is a relatively gentle introduction to the topic, with plenty of good examples included. This would be a good book to base a 'gifted' Algebra course on. I would strongly suggest that very strong students supplement this with Thomas Hungerford's _Algebra_; similarly I recommend that first year graduate students get this book as a 'softer' perspective for when (not if ;)) they get lost. Profs should pick up this book as an example of how to write a palatible math book in the unfortunate academic climate we have today (although I wouldn't sacrifice rigor); teaching assistants should use this for anecdotal material to throw at students. I especially enjoyed the biographies of famous mathematicians and the background that Gallian provides on topics in Algebra (such as his description of the Twenty Five Years' War), which made this book quite pleasant even in the grueling moments.
Rating: 5
Summary: Excellent undergraduate abstract algebra textbook
Comment: I used this book for my Abstract Algebra course at Whitman College. It is genuinely fun and interesting to read. It has many interesting quotes and biographical sketches. The problems are just the right difficultly to be challenging but not frustratingly hard. One interesting thing is that the problem sets include computer application questions. Our class did not use these sections, but some of the problems looked interesting.
I found the text to be well organized and understandable. Numerous examples are included which help for understanding abstract concepts. Neither my friends nor I have noticed any typographical errors. Theorems and corollaries are shaded in a blue background for ease of reference. Every time new notation is introduced, possible ambiguities are discussed. Also, possible confusions about new concepts and common mixups are addressed.
I have only taken one semester of algebra at the current time, so have only used the first half of this book. I feel that it is one of the best textbooks I have used for a mathematics class.
Rating: 1
Summary: Gallian's poor algebra book.
Comment: I agree with the other reviewers in the sense that it is ture Gallian's book is soft on theory and rigor, but oppositely I find this lack of real substance to be Gallian's deepest flaw. I give Gallian one star, basically for effort.
I divide my critique into the following subcategories:
Organization:
Gallian's book is organized well enough in the sense that he opens each chapter with some commentary about the problems to be studied, or motivation, and then proceeds to go example, theorem, proof, example, example, example, example,..., example. This doesn't work, I think, because he spends too little time actually showing theorems and proofs, and sometimes he'll build an entire chapter on just two or three theorems, and fill the rest with useless commentary (which I'll mention again below).
Readability:
As for readability, for people who read math books at all (i.e., those who study outside of class), this book should be a nightmare. If you were to strip away all of the useless commentary/endless biographical insets/weblinks you would be left with probably about 30 pages of theorems and cumbersome proofs (by cumbersome, I don't mean involved, I mean unrefined). Gallian has failed to make a readable text because he presumes to have the omnipotence and foresight required for putting a full understanding of algebra and algebra history into one book. As a result, the excess commentary he makes and useless statements (for example, "In high school, students study polynomials with integrer, rational, real, and sometimes complex coefficients") distract a reader from the main points, and I rarely found myself rubbing my chin thinking how insightful something he said was. All in all, I feel as though the reading felt "hoakie" at best--like he was elbowing me in the side, winking, trying to get me to lie and say I thought what he was saying was insightful.
Exercises:
The exercises are often clumsily put together and the quotes before each problem set can get extremely patronizing. I remember thinking how cocky this Gallian fellow must be to presume that people can't do "his" problems. A joke, to say the least. In any case, they seem fine for all purposes -- if you're going into chemistry or an applied science that uses group theory. It's very obvious that our author believes that group theory is the pinnacle of the algebra experience and struggles to present topics from rings and fields. IF you are someone who likes group theory, fine. BUT Artin's book does everything Gallian does and more with group theory and builds the same ideas on more solid footing, using linear algebra excessively throuhout the book. For example, if you think I'm joking about Gallian's weakness, just look at the chapters on isometries and compare them to the chapters in Artin, and you'll see what I'm talking about.
Peter Rabbit:
Well, I do have at least one nice thing to say. As anyone can see, Gallian has a lot of examples, but this seems to be the only redeeming quality of the book. But that alone doesn't make an algebra book.
Broad Commentary:
If it's a softer touch you're looking for, I'd say go with Durbin -- he's easy to follow and an excellent writer. If it's group theory, examples, and a lot of wonderful exercises you want, go with Artin. Neither of those books get caught up in useless commentary. I've heard good and bad things about Fraleigh (sp?), but have no direct experience with that book. I would suggest, for those who don't want a hardcore book such as Herstein's Topics in Algebra, or M. Artin's Algebra, you should see Durbin's book. Durbin is also a softer book; it has many nice examples and is very well written. IF you are unavoidably made to use this book for a course, and if you want to learn to be more insightful/challange yourself to think/want to study, then I suggest you use any of Artin, Herstein, or Durbin as a companion (in that order, but I only place Artin above Herstein because Artin has more material in it, Herstein is a much better writer so you might choose him depending on which book you'll spend more time with).
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Title: Schaum's Outline of Modern Abstract Algebra (Schaum's) by Frank Ayres ISBN: 0070026556 Publisher: McGraw-Hill Trade Pub. Date: 01 June, 1965 List Price(USD): $16.95 |
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Title: Schaum's Outline of Group Theory by B. Baumslag, B. Chandler ISBN: 0070041245 Publisher: McGraw-Hill Trade Pub. Date: 01 June, 1968 List Price(USD): $16.95 |
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Title: A First Course in Abstract Algebra, Seventh Edition by John B. Fraleigh ISBN: 0201763907 Publisher: Pearson Addison Wesley Pub. Date: 06 November, 2002 List Price(USD): $108.00 |
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Title: Analysis with an Introduction to Proof (3rd Edition) by Steven R. Lay ISBN: 0130898791 Publisher: Prentice Hall Pub. Date: 15 December, 2000 List Price(USD): $98.00 |
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Title: Topology (2nd Edition) by James Munkres ISBN: 0131816292 Publisher: Prentice Hall Pub. Date: 28 December, 1999 List Price(USD): $101.33 |
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