A First Course in Abstract Algebra, 7th Edition | 
 enlarge | Author: John B. Fraleigh
Publisher: Addison Wesley
Category: Book
List Price: $124.00
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Rating:  24 reviews
Sales Rank: 320257
Media: Hardcover
Edition: 7
Pages: 536
Number Of Items: 1
Shipping Weight (lbs): 2.1
Dimensions (in): 9.3 x 7.5 x 1
ISBN: 0201763907
Dewey Decimal Number: 512.02
EAN: 9780201763904
Publication Date: November 16, 2002
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Product Description
This is an in-depth introduction to abstract algebra. Focused on groups, rings and fields, it should give students a firm foundation for more specialized work by emphasizing an understanding of the nature of algebraic structures. Features include: a classical approach to abstract algebra focussing on applications; an accessible pedagogy including historical notes written by Victor Katz; and a study of group theory.
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| Customer Reviews: Read 19 more reviews...
 Instructor's perspective: Excellent text for a university course June 27, 2005
No Fixed Abode
51 out of 56 found this review helpful
I am a mathematics professor at a small liberal arts university in Canada, and I use Fraleigh's book to teach a 300-level full-year introductory course in abstract algebra. I find it excellent. It is clear to me that Fraleigh has been teaching a course very similar to mine, to students very similar to mine, for probably three decades. He has figured out almost exactly the right way to introduce a difficult subject. He makes my job easy.
The book is broken into many small chapters, each of which can be easily translated into one or two hours of high-quality lecture. Thus, I can structure my lectures to closely follow the book, which has two advantages: (1) less preparation time for me (important when you have a heavy teaching load but still want to do a good job) and (2) The students have effectively a preprinted copy of the classroom lecture notes (so they can spend less time writing notes and more time paying attention and learning).
Fraleigh avoids the countless pitfalls which bedevil the naive algebra instructor (and many other textbook writers). He keeps things simple without making them stupid. Math students at my university have a wide range of background and skills. Some are highly talented and motivated, and I want to adequately prepare these students for graduate school. Others students are `future highschool teachers' (may God help our children) who apparently chose to study math because they thought it would resemble the polynomial arithmetic which they enjoyed in highschool, and who are often quite upset to discover otherwise. For these people, math is `supposed' to be computation, and any kind of logic or abstraction is anathema.
There are some abstract algebra texts (such as Bloch) which are designed to appeal to the `computational' crowd. Abstract algebra is one of the most beautiful and important parts of mathematics, and I describe these books as `algebra murdered and come back rotting from the grave'. There are also algebra books (such as Dummit & Foote, or Michael Artin) which are designed for `future graduate students'. Although I love these books, they are too sophisticated for most of my students. Also, their long chapters and sometimes poor organization means that preparing a decent lecture is often a lot of work.
Fraleigh finds an excellent compromise between these extremes. He develops some quite sophisticated material (including Galois theory and homology), but always finds a way to explain things simply and clearly. He provides exactly the right amount of information (e.g. the right number of examples and corollaries) to allow the instructor to move through the material efficiently (so you can actually finish the syllabus), while still explaining everything clearly. The exposition is lucid, and the books tightly organized. There are plenty of exercises which are challenging, but not too challenging, which is a boon when you are designing homework assignments.
I have a few small issues. For example, I don't think it's a good idea to develop group theory in terms of `abstract binary operations; one should develop it in terms of concrete symmetry groups. Also, I found that the section on the structure theory of finitely generated abelian groups and the chapter on homology theory were both a bit weak and needed to be supplemented. However, these are both very minor complaints compared to the overall quality of the book.
Teaching an advanced pure math course with a poorly designed textbook is a nightmare (and I should know). Teaching algebra using Fraleigh was a snap.
excellent book October 31, 2001
avraham stoler (San Francisco)
37 out of 42 found this review helpful
this is the best first book on abstract algebra that i know. while there are books that are deeper and more advanced, this book does a great job of motivating the concepts. try to look in other books and see if they explain why is a group defined as it is. rigor is not sacrificed (although the problems arent that difficult), and explanations are very clear. overall, a great FIRST read after which u might want to turn to hernstein or one of the other advanced books, and understand everything that goes on there. but dont make the mistake of getting a totally abstract and advanced book for a first course - u will probably not get much out of it. especially suitable for self study.
odd numbered problems not requiring proofs are solved, and there is a reasonable amount of examples
Fraleigh? awesome, sure July 3, 2007
Lucius Schoenbaum (Athens GA)
6 out of 6 found this review helpful
This book was my introduction to algebra, and I can say that with me it hit its target - I not only learned and understood abstract algebra, but I grew to love it and be thrilled by it. If you are outside of mathematics and looking for the way in, I don't think you can do much better than Fraleigh. You'll outgrow it - almost as soon as you put it down. But that's just testament to how far it can take you in just a dozen or so chapters.
I would recommend, if you can afford it, also buying a copy of a zippier book like Hungerford or Dummit & Foote (ask around) and using it together with Fraleigh. Fraleigh won't let you down in terms of giving you the space you sometimes need to grasp things (for example, he gives Tons of examples, and there are plenty of easy exercises that allow you to soak in patterns in the structures for yourself) and an advanced book will give you increased perspective and power.
Superb explanations, great excercises,not sacrificing rigor. August 14, 1998
f93-eaa@sm.luth.se Erik Alapaeae (Luleaa, Sweden)
7 out of 8 found this review helpful
One of the best mathematics books I have ever read! If you like pure mathematics, and want a book that helps you learn abstract algebra fast without sacrificing depth, this is it! Easy to read, and the excercises after each section are split into "Computations", "Concepts", and "Theory", and doing them helps to ensure that you have grasped it all and not misunderstood anything. I love this book! And no, this is not an advertisement!
Still Using it after 36 years November 24, 2004
John C. Kotelly (Boston USA)
12 out of 16 found this review helpful
Having taken Algebra (e.g, using van der Warden, Herstein, Lang, MacLane etc) courses in1950's, I found Fraleigh's delightful and informative book the one I continually refer to (still have my 1968 copy) for 'tune ups'. His style is that of a chalk covered tutor/mentor/ friend standing next to you to grasp inductively algebraic mental metaphors which allow you to further grasp their elaborations from Topolgy to Topos. His humor pervades the book (e.g. p11"..e) Mathematicians are eager to have some ambiguity in their work so that it has a better chance of being right [grin]).
Never having had the honor to meet him in person may I use this review to thank him for his pedagogical gem.
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