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An introduction to abstract algebra. Provides valuable experience for any further axiomatic study of mathematics. DLC: Algebra, Abstract.
Terrible book
| Customer Rating:   | | Terrible book, that was extremely overpriced. It had bad examples and few that pertained the the practice problems. it gave no insight into proofs. |
Fraleigh? awesome, sure
| Customer Rating: | 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. |
No Student Solution Manual
| Customer Rating: | | As a student, how can I study without a solution manual? Is all Abstract Algebra classes this way? I have an awful time to study. I'm sorry. |
Fraleigh put into perspective
| Customer Rating: | [...]
Although, I did not use Fraleigh's textbook directly in the class I attended, I did use it as a frequent source of
explanation and/or practice with it's problem sets. Lets be realistic here, I've seen too many reviews of differnt Algebra
texts from D&F, Artin, Lang, Galian etc., saying something along the lines of "Textbook is not rigorious enough," or
"textbook is weak on theory," "textbook is not approrpiate for undergraduate course," and so on and so forth.
Although I do not deny that certain texts may be written poorely, the vast majority of complaints seem to be generated by certain percieved "defencies" in texts that do not attempt to be laconic (i.e D&F). Obviouslly, there exist suffecient
differences amongst the students who will take Abst. Algebra such that differnt types of textbooks are created to meet the
varying needs of these students.
It is in this context that Fraleigh's textbook should be reviewed. After looking at all the major texts out there for basic undergraduate Algebra (Artin, D&F, Rotman, Herstein, Gallian), I'd say Fraleigh belong somewhere between Galian and Herstein. It is true that it does not cover as much material as D&F, but clearly it was not written with the same purpose in mind as D&F.
If we compare Fraliegh with Herstein we admit that they both cover most of the same subjects in more or less similiar depth.
Herstein beats out Fraliegh 10-1 in all things Linear Algebra. However, I'd say the first 250 pages of "Topics in Algebra" is
roughly equivelent to the 493 pages of Fraleigh. So the question that is asked is why is Fraliegh almost double the size of Herstein?
A quick browse of both books reveals that although the font size (for my copy) is the same, Fraliegh is much more liebral
with the placement of paragraphs and spacing. Whereas "Topics in Algebra" looks cramped and squeezed, Fraleigh's book is much more cosmetic, the pages are littered with
pictures/diagrams, "Historical Notes," numerous drawn out examples. I personally like the spacing in Fraleigh as opposed to Herstein since I feel the former text is much easier to read because of this layout.
If we delve into the actual text-material we do again admit that Herstein is slightly more "mature" then Fraleigh. I believe the exposition in Herstein is probably a little clearer, however, Fraliegh does more "work" for you and gives you more detail. Further Fraleigh gives more application such as to coding, chemistry, and quantum physics etc.. Those who do not believe that the exposition is roughly at the same level, I invite you to turn to p. 83 in Herstein and p. 253 in Fraliegh. Both start with the defintion of rings. Again Herstein spells out the actaul defintion in all 8 axioms. Fraleigh has 3 shortening them by merely giving the condition that a ring must be an abelian group under addition (note it is not always the case that Herstein introduces everything out the long way and Fraleigh the short, more on that later). After defintions, both text introduce examples, again I think most of the examples given by Herstein are rather trivial, whereas Fraleigh's examples are more intresting with some useful links back to Group Theory.
But Fraliegh clearly does more to motivate the reader to learn every new bit of material displayed in the book, althoguh the outline is not always the clearest. This is very evident when comparing the section introducing Fields. Fraleigh commutes the introduction of the topics of fields and homorphisms. Introducing homorphisms of rings first, although it makes little differnece in understanding the material, I muchl liked Herstein's direct introduction. I felt it was more natural to introduce fields then homorphisms, then ID, PID, ED
etc. It just made mroe sense to me, but this is my POV.
Fraliegh again says almost the exact same thing that Herstein does except he has far more exposition (although i found sometimes that the exposition could be a bit confusing). Another observation I'd like to make was I felt Fraleigh was far stronger in its Group Theory sections then it was with Fields and Polynomials. For some reason, the sections on polynomial rings were rather weak for the work we were doing in class and I cannot recommend Fraliegh for this if thats what you need. However, in general I found Fraleigh was easily digestable and could be read very leisurely.
The major drawback of the book of course is its problem sets. Although they are good for extra practice, they are by no means challenging. In this respect, Herstein and the rest are lightyears away from Fraleigh. This setup again is proabbly mroe to do with the differnt philosophies of how a student should learn rather then some weakness in design. Fraleigh nurtures a student so he can take his first steps in the subject and walk. As opposed to D&F whose terse exposition is akin to throwing a child onto the floor and yelling at him to return to you on his own. Which is better? I don't know, but I must certainly say I felt much "happier" when I was reading "A First Course in Algebra."
Again, I feel that Fraleigh's text is a wonderful introduction and supplement to a student (like myself) who did not come from a long and prestigious mathematics background. For this audience, the book is perfect for the first half of Algebra (Group Theory) and somewhat lacking for the second half (Rings, Fields, and Galois) but no book is perfect and given its size and the wealth of knowledge (historywise and application wise) that is stored in this volume I am content with what it offers to the reader. Also, as mentioned, since it covers roughly the same as Herstein, a more difficult class could utilize this book by just offering differnt problem sets to the students with additional supplementary exposition from the instructor. Overall the book is, gentle, flexible, and broad. |
Decent Book But Has Flaws
| Customer Rating: | I am laughing at the good professor's review below. I do believe he must be a professor: he writes a lot and conveys little in terms of detail or example.
Speaking of examples, an introductory book should have ample amount of them. The reviewer below says Dummit and Foote as well as Artin is too "sophisticated" for students. I disagree. They are wonderful books. Fraliegh, I have to agree with another reviewer on here, is really best kept as a supplement. Fraliegh lacked good examples that were of any real sophistication or had often masked some important developments in the exercises. Also, soem of the standard notion such as for automorphism (i.e. Aut) and others were blatantly missing. It is best to get students new to the subject emerged in the notation from the start and give clear examples that represent an easy one for clarity and introdcution, and then at least one other, preferably two, which take the reader to a more detailed and more challenging, sophistitcation of development. Fraliegh does not do that. Moreover, I think the transition to another higher level book will be more painful after Fraliegh alone. It should be read along side Dummit and Foote or Artin--two fantastic books.
Also I hated Galian's text myself, I have to agree with that reviewer on this: it is indeed to damn wordy. I like succint, straight to the point books that have well chosen exercises and especially numerous examples. Dummit and Foote (D&F)do that especially well, then Artin next. Fraliegh, while and excellent book, doesn't compare but after D&F and Artin, it is the best thing.
So, I give is three stars. Not bad at all. |
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