A First Course in Abstract Algebra

by John B. Fraleigh

Considered a classic by many, A First Course in Abstract Algebra is an in-depth introduction to abstract algebra. Focused on groups, rings and fields, this text gives students a firm foundation for more specialized work by emphasizing an understanding of the nature of algebraic structures.

Genres: Mathematics, Textbooks, Algebra, Reference, Science, Nonfiction, Academic

544 pages, Hardcover

First published December 1, 1967

Reviews

[Marius · Rating 5 out of 5]

Extremely well-written. I used it for my first course in algebra and also as a cross reference in other courses, for instance Galois theory. The author explains the concepts in a natural and easy way. A very nice read, indeed.

[Gita · Rating 4 out of 5]

ما ۱۱ فصل از این کتاب را خواندیم. تا اواخر فصل ۶ عاشق این درس بودم. بعد درگیر درس ساختمان‌داده شدم و نمرات میانترم هم اعلام شد. (به اندازه‌ی ۱۶ نمره _مطمئن از خود_ نوشته بودم و ۷.۵ شدم! :]] ) و خب واقعا دلسرد شدم.

در آن مدتِ علاقه‌مندیم چندین کتاب از جبر را ورق زدم. فرالی واقعا زیبا جبر را تدریس می‌کند. فصل‌بندی قابل‌فهم‌تری دارد و با سوالاتی که در آخر هر فصل قرار داده، مطمئن می‌شود که دانشجو مطالب هر فصل را فرا گرفته.

به‌هرحال کلاس جبری که با دکتر کیوانفر داشتم واقعا روی طرز تفکر و استدلال کردن من تاثیرگذار بود. نگاه کردن چیزها در یک هارمونی، در یک ساختمان... جواب تعداد زیادی از سوالات نوجوانیم را گرفتم و یک مدت هم به قدری جوگیر شدم که می‌خواستم بروم ارشدم را زیرشاخه‌ای از جبر بخوانم.

اتفاقات خیلی عجیب و غریبی هم قبل از پایانترم این درس افتاد. یک هفته قبلش زمین خوردم و سر امتحان با پیشانی زخمی و یک بخیه روی سر، سرِ جلسه حاضر شدم. به‌هرحال بر خلاف انتظارم، و بی‌آنکه صحبتی از تصادفم بکنم، استاد کیوانفر با نمره‌ی ۱۰.۵ پاسم کرد. :))
۰۳/۰۵/۱۱

[Geoffrey Lee · Rating 5 out of 5]

This is possibly one of the most elegant books on mathematics I have ever read. It really motivates the many of the definitions rather then just throwing them at you which many other authors do (like Lang, but that's not really an introductory book anyways). The best part of this book is the range of difficulty in exercises. Not only is this book good for learning algebra, it is good for learning the art of doing mathematics. The only one criticism I have on the book is its glossed hand-waving treatment for homological algebra (which the author could very well have just left out completely) which gives a slightly misleading idea on what homological algebra is about. But the author makes up for this by stating that it really isn't an essential part of the book. In my opinion, homological algebra is too sophisticated of a subject to treat in a textbook like this.

[信傑 廖 · Rating 5 out of 5]

I believe this is one of the most succesful textbook designed for the beginners of abstract algebra.I used this book for my first step in abstract algebra. It is clearly written and also well-motivated. Beside the basic part of algbra, it also contains some introductions to Sylow theorem and Galois theory and also some topics related to other areas such as the introduction to algebraic topology. It offers abundant examples after each definition and theorem and the exercises after each section involving some true-or-false questions to help you clarify your concept. Most of the problems are not too difficult, and for some harder problems the author also gives hints. In my opinion, this book is appropriate to use both as a class material and as a book for self-studying. To sum up, I recommand this good book to all beginners of abstract algebra!!

[Jesse · Rating 5 out of 5]

Along with Gallian and Hungerford, this completes the trilogy of the best undergraduate Algebra texts. And older editions of this book include very enlightening discussions of Homological Algebra and homology—quite rare for an undergraduate book.

[Al Capwned · Rating 4 out of 5]

Well-written, in a style that is approachable to the average student and that's really something, considering the difficulty of the subject.

[Lucas Chang · Rating 5 out of 5]

banger

[Matthew Smith · Rating 4 out of 5]

This has been serving as a great companion to my university course in abstract algebra. I appreciate its use of short, but numerous chapters. This makes it easier to read the book in manageable chunks. The proofs are clear and the study of algebra is clearly motivated with minor examples in geometry and analysis. This is also done in the closing of the book with the application to the insolvability of quintic polynomials.

The only issue I've had with this text, is the relegation of certain results (such as Cauchy's Theorem), to the exercises at the end of the chapters. These theorems aren't even stated in the main text. Although not the most heinous crime a textbook can commit, it hinders the digestion of the theorems. As an alternative, I would suggest a statement of the theorem in the main text, while maybe leaving the proof as an exercise (I understand the point of not disclosing every single proof).

Overall, I would say this makes a great text from which to consolidate upon, or maybe even just learn abstract algebra. Just be sure to look at the exercises.

[dead letter office · Rating 5 out of 5]

i used an oldschool version of this text to learn introductory abstract algebra. it was brilliant.

old-fashioned and clear, with no distracting pictures or annoying applications. i think the new one got spiced up a bit for the modern audience, so try to get your hands on the one with the cloth cover from the sixties. it's all the basics on groups, rings, and fields.

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[Anthony O'Connor · Rating 3 out of 5]

This used to be one of the standard undergraduate texts. Still might be, I don't know.
Groups, Rings, Fields. Field extensions. Galois Groups. Used to prove what can and cant be constructed/solved. Different types of things in different ways. All pretty fascinating. And you always remember fondly your first exposure to something new.
However, looking back at it decades later - and (slowly) re-reading it - you find that its not really all that clear. Once it gets past the absolute basics its a bit tangled and messy and hard to follow. And the author has the VERY annoying habit of periodically asserting how simple and beautiful it all is - with the clear implication that if it isn't to you well then .. maybe you should trot off and do something else instead. I wonder if he ever did that as a classroom teacher/lecturer. Would have been infuriating. Everything is easy once you know it. The task is to explain it simply and clearly to someone who doesn't. I don't think this text accomplishes that very well.

[Nicholas Cotton · Rating 3 out of 5]

Honestly cannot recommend. Good exercises but bad text. I felt like ideas weren’t really presented rigorously but rather as part of examples. This made the book longer than it needed to be imo.

I personally used Judson’s book as a primary text for abstract algebra.

3 stars because the exercises in here are great

[V · Rating 4 out of 5]

Está bien, tengo que leerlo mejor porque es contenido evaluable y no he leido todas las páginas de pe a pa... Lo que vi, me gustó, aunque tengo algo de trauma con álgebra. Si os queréis introducir en los conceptos de álgebra abstracta lo recomiendo porque es bastante visual <3

[Jaci · Rating 5 out of 5]

This book teaches step by step. It is a good Algebra book.

[Yılmaz Bilgi · Rating 5 out of 5]

gg

[Shahid · Rating 5 out of 5]

i think i take my all study related material from this book

[Daniel García]

super

[Vilas Pawar · Rating 5 out of 5]

Nice book

[Alper Çuğun · Rating 2 out of 5]

Much prefer the book by Gallian.

[tiffanie · Rating 4 out of 5]

kind of epic tbh...maybe need to read the parts not covered in class when I get the chance

[Erickson · Rating 4 out of 5]

In general, for physics students there is no need to read the whole book and only the above chapters are needed for all practical purposes at undergraduate level. In particular, one at least need to learn Group Action. Chapter 1-3 are the most essential introduction, while chapter 4,5,7,8 are for completeness.

The style is rather informal and hence should be accessible to many first readers. However, for some reason I did not find it very 'accessible'; indeed there are abundant examples to look through and tons of exercises to work with, some of them extremely useful to cement understanding. However, for unknown reasons (which I suspect to be just a matter of compatibility of style of the user and the author), I do not find his explanations enlightening, nor the informal discussion particularly explanatory of some difficult concepts. For example, factor groups are well written here but I do not find it comfortable enough to understand it fully. I do agree on the fact that his examples help very well.

Therefore this review was read up to chapter 3 only up to group action. I will come back again for the exercises/review or if there is a need to visit other chapters such as groups in topology.

[Steve Alx · Rating 5 out of 5]

A really well written introduction to abstract algebra. This should be studied first before moving to the more mature text by Artin. Picking up Artin's text before having some background in abstract algebra can be a nightmare.

[Joe Cole · Rating 5 out of 5]

Abstract Algebra is one of the most interesting and engaging math classes. I think it's a very good book with a sufficient number of examples and detailed explanations.

[Pedro Zavala · Rating 4 out of 5]

really good book, besides clear it has a different point of view.

[Ed Boyno · Rating 5 out of 5]

The absolute best text book I ever used.

[Xingyu]

I like that the exercises have a variety of easy and hard problems, both about definitions and proof of theorems.