A book of abstract algebra by Charles C Pinter

by Charles C. Pinter

This text is aimed at the abstract or modern algebra course taken by junior and senior math majors and many secondary math education majors. A mid-level approach, this text features clear prose, an intuitive approach, and exercises organized around specific concepts. New to this edition are additional applications exercises to improve student learning.

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

Hardcover

First published March 1, 1982

Reviews

[David Mario Mendiola · Rating 5 out of 5]

Holy morphism, this book is great. I can't wait until they inevitably publish the gilded-leaf KJV of it.

The first chapter is enough to get you psyched about Abstract Algebra. He makes it perfectly clear what our motivation is, so when groups and rings start coming, they feel so natural rather than like arcane math objects. I've been evangelizing to friends and coworkers the spirit of algebra with (very) limited success.

If I may be so bold as to skirt on the edges of blasphemy, some other people might have a fleeting thought that it would possibly, be it Pinter's will, benefit the neophyte to have an ever so slightly extended answer key.

I'm sure there are other great books on abstract algebra, but this is just perfect as an introduction. The conversational style feeds me the material just the way I like it: discussion of general concepts that we feel are true, exploration of some examples, and then a theorem that shows it is actually true. A lot of the learning is in the exercises, which I feel are organized masterfully to let the reader continue teaching himself.

It wouldn't be weird to start some Pinter's Abstract Algebra fanfiction, would it? I'm thinking of shipping Abel and Galois in some romantically commutative operations...

[Cameron · Rating 4 out of 5]

good for if u stopped taking algebra in second year but then decide to do a PhD in it

[Drew Henry · Rating 5 out of 5]

A Book of Abstract Algebra gives an excellent introduction to abstract algebra. The contents cover groups, rings, and fields as well as some history and additional related topics (such as a brief introduction to number theory). It is one of the most accessible books published by Dover and reads like a novel. Solutions to selected exercises are available in the back of the book.

[Darian · Rating 4 out of 5]

A really useful book for those interested in learning algebra through self-study as a first exposure! The book is good in that it contains a big variety of topics (groups, rings, even a material on number theory and Galois theory), but is still very straightforward in its exposition, and builds on more conceptually straightforward concepts to bridge the gap between a person used to more computational math to someone who could learn abstract algebra.

Main gripes with the book is that the exercises are a little too straightforward at times, as someone with some exposure to proof-based mathematics (and also doing self-study in analysis). Overall, the book is also less comprehensive than the well-known Dummit and Foote. I also think it would be useful to have a review on proofs or logic/proof techniques, since this may be many individual's first foray into modern algebra.

[Aurora Lucie · Rating 5 out of 5]

The love I have for this book at times seems beyond what one should have for a theoretical book like this. However, it genuinely feels like what made me understand and love algebra - to the extent of pursuing it as a degree.

From time to time, I still pick it up just for fun, or to sharpen my understanding of a concept I haven’t used in a while. The book works well in so many ways: learning algebra for the first time, doing lookups, even reading from cover to cover (not joking - there’s honestly a fair amount of humour between the covers).

Reading David’s review on here made me jump up and down in excitement. There are other people enjoying this book at a similar level and it makes me incredibly happy! Best review I have ever read.

And David; give me a shout when the fanfic is out - beyond eager to read!

[Lance Johnson · Rating 3 out of 5]

Generally a good book, it does have some downsides. The explanations are good and start out with a minimum of assumed knowledge. The exercises are generally good and interesting, but only a few of them have solutions provided, making it very difficult to know when you have made a mistake. Additionally, there are a number of small errors in the book, some of which are difficult to catch. There is no published errata so the reader is on their own in trying to avoid these errors. In short, this books makes for a good primer or supplement, but to truly gain a deeper understanding of the topic you will need to cover a more rigorous text (my recommendation would be to check out the classic Dummit and Foote).

[Yash Patel · Rating 5 out of 5]

Great book on abstract algebra! There were a number of things that I either did not understand or find strong motivation for when I originally learned the subject, but this book walked through these for all the material it presented extremely well! Coverage of groups, rings, field extensions, FHT, and applications to polynomials followed roughly what I did in class, so this book served as a really nice cover-up. There are also a TON of exercises in the book, though they generally weren't especially challenging. Still, the great number made it quite nice to test understanding of material

[Ryan Lavin · Rating 5 out of 5]

While the book shies away from some important group-theoretic theorems (particularly several isomorphism theorems, Sylow's, correspondence theorem, this book has easily the best exposition of quotient groups I've found. If you're looking for an accessible but rigorous introduction to abstract algebra (in particular if you don't have experience in calculus or linear algebra) this is the canonical introduction

[Kevin K. Gillette · Rating 5 out of 5]

Despite the title, I found this monograph by Pinter surprisingly accessible! It would make an excellent accompanying text for any upper-level undergraduate or graduate-level course in modern algebra, to go along with (for example) Herstein's legendary text.

[Richard · Rating 4 out of 5]

Positives: This is a lovely book, making algebra (groups, rings, isomorphisms...) less scary.

Negatives: The lack of solutions to most of the exercises means I've no idea if I'm getting any of this right or not. Sometimes I don't even understand what the question is :-(

[Kent Sibilev · Rating 5 out of 5]

I had so much pleasure of reading this textbook. It is a perfect introduction to such a beautiful topic.

[Angel Avitia · Rating 5 out of 5]

A really nice introduction

[Chenguang · Rating 5 out of 5]

The first 30 chapters are very well written and easy to follow. Each chapter builds on top of the previous ones and it's absolutely amazing to see how we start with the simple definition of groups and develop homomorphism/ring/field/field extension on top of it and eventually use these concepts to prove impossibilities in rule and compass constructions.

However, the last 3 chapters (Galois theory) are a bit frustrating to me. Even after reading and re-reading I still couldn't fully understand the proofs. Specifically, it might be better to explain theorem 6 of chapter 31 in more details, and the last chapter just feels cryptic.

But still, this book is a very nice introduction to abstract algebra, especially for self-learners. The book mentions calculus and linear algebra but they are of minor importance and I would say you can still understand the book without prior knowledge in these. The only hard requirement is probably some knowledge of logic, specifically, "if a then b" implies "if not b then not a", and "a iff b" means "if a then b and if b then a".

Recommended for anyone who ever wondered what "ring theory" is.

[José · Rating 5 out of 5]

Cuando vi por primera vez la Teoría de Grupos no tuve un buen profesor. Pero siempre encontré un tremendo reto en una de las áreas de la matemática que me había costado más en su forma más "elemental": la Teoría de Números. Durante ese primer curso (Teoría de Grupos) nos tocó a todos estudiar por nuestra cuenta y hacer nuestros propios apuntes para la clase y fue un verdadero desarrollo que aportó en la maduración de mi pensamiento matemático. Tener que madurar uno mismo las ideas, seguir la lógica de una demostración no fue (ni es, excepto para los genios) una tarea fácil. Pero se logró el cometido, porque el nivel de detalle de este libro junto con otro que usé (dejaré el nombre en los comentarios, por si alguien busca cómo aprender Álgebra) me ayudaron a acabar el curso con un entendimiento aceptable y una buena introducción para cuando vi el curso de Teoría de Anillos. El libro lo utilicé nuevamente cuando estudié los Cuerpos y Espacios. Sirve mucho para el estudio autodidacta, y plantea problemas interesantes a los que recomiendo dedicarles su tiempo para fijar la teoría.

[Maaz Muhammad · Rating 4 out of 5]

Fantastic introduction to abstract algebra at the senior undergrad or beginner grad level. Pinter writes with passion and transforms what may seem like a too-abstract field into a lively study. My motivation for reading this book was to better understand the fundamental ideas behind things like “addition” and “multiplication” on different “objects”: schoolchildren know how to do them for numbers, and later we learn how to do them for more complex objects like matrices and functions. The amazing thing about abstract algebra is that the analogs to these basic operations can yield useful insights into concepts as disparate as stable matchings and genetic inheritance. I will be reading Pinter’s set theory book next.

[S.T. Veje · Rating 4 out of 5]

Probably the best book on the subject I've found so far. Other books of comparable size (it's not a huge book) don't seem to cover as much ground, or as effectively. Concise but still very readable, and it doesn't skimp on exercises. In fact, a lot of its conciseness probably comes from the fact that it explains a lot of its material more in-depth through exercises.

[Thomas Bell · Rating 5 out of 5]

Very good introduction to abstract algebra. Puts it on a very simple level, but that's good for students who are seeing this level of abstraction for the first time in their lives. By the end of the book it does get more difficult, but by then they've had more time to get used to everything.

[Robert · Rating 5 out of 5]

Phenomenally written book. I especially enjoyed the history of Algebra at the beginning.

[Gregory Reshetniak · Rating 5 out of 5]

Great book for self study of the subject.

[Yasmina · Rating 3 out of 5]

Se entiende bien pero no es nada formal, y tampoco profundiza nada en los temas interesantes.

[Effy Feng · Rating 5 out of 5]

awesome

[Choomno · Rating 5 out of 5]

A great intro book, although the last few chapters leave much to be desired.

[Ian Finlay]

My teacher really likes this book. As a student, it's pretty clear and enjoyable to read when I get the concepts.

[Antonio Caballero Sanchez · Rating 4 out of 5]

Great introduction book to algebra. Doesn’t have a chapter on modules, but that is alright.

[Jason · Rating 3 out of 5]

Great subject, okay book.

[Eli · Rating 4 out of 5]

Good book about the modern algebra. I really enjoyed it and am looking forward to learning more on this subject. I recommend this book to nerds like me.

[R.r. Hildebrand · Rating 5 out of 5]

Excellent introduction to the subject matter. The first chapter alone opened my eyes and helped me understand some things I had been puzzling over for years.

[Randy Hildebrand · Rating 5 out of 5]

Excellent introduction to the subject matter. The first chapter alone cleared up questions I had had for years.

[Mike · Rating 5 out of 5]

Better than Wikipedia!

[Daniel · Rating 4 out of 5]

Galois Theory at The n-Category Café.