A First Course in Abstract Algebra

by John B. Fraleigh

Book Overview

Considered a classic by many, A First Course in Abstract Algebra is an in-depth, introductory text which gives students a firm foundation for more specialized work by emphasizing an understanding of the nature of algebraic structures. The Sixth Edition continues its tradition of teaching in a classical manner, while integrating field theory and new exercises.

• Format: Hardcover
• Language: English
• ISBN: 0201104059
• ISBN13: 9780201104059
• Release Date: January 1982
• Publisher: Addison Wesley Publishing Company
• Length: 496 Pages
• Weight: 1.75 lbs.

Customer Reviews

Fraleigh? awesome, sure

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.

Instructor's perspective: Excellent text for a university course

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. F

Still Using it after 36 years

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.

Well-written Book for beginner

I used this book for my 1st Abstract Algebra course. At first, the discussion seemed to be somewhat lengthy but if you can get yourself into the author's style, you will enjoy it. True, it's not a book for those who want a well-structured proof but that won't matter much considering this book is intended to a beginner who take his/her 1st algebra course. Lots of examples to test your understanding and lots of problems with increasing difficulty. Most of the problems are very stimulating. Even after I took my second class in Algebra (i used diff book), i often go back to this book to see some additional information. What I like best about this book though is that the author likes to explain things in terms of mappings and, of course, lots of diagram to help you better understand the concept!If you're a beginning student and considering to buy this book, then go for it - it worths the money! I think i'll bring this book with me to grad school. :) good luck.

Superb explanations, great excercises,not sacrificing rigor.

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!