Groups and Symmetry (Undergraduate Texts in Mathematics)

This book is a trip, man....

It begins with nonisomorphic groups of order 12, but in a totally relaxed manner as an investigation into symmetries of different types of objects. Then you see subgroups and the center, etc in a very concrete way. This is a fun way to approach group algebra.

This was the textbook for my first course in abstract algebra and the first "yellow book" that I read. I found it an excellent book: rather than starting with axioms and dryly deriving everything, it gets one to contemplate the meaning and motivation behind the axioms. This book will encourage you to play around with mathematics on paper and in your mind, helping you to get a concrete feel for a subject that many people view as painfully abstract.The prose is clear and well-written: there is just the right amount of discussion to elucidate necessary points, while allowing the book to remain fairly compact. Exercises are fun but difficult and many require genuine creativity.I also really like the choice of topics: although this book is introductory (with respect to abstract algebra, it presupposes some knowledge of linear algebra), because it focuses only on groups (as opposed to also trying to handle rings & fields) it is able to get into some more advanced and very interesting topics and applications in later chapters. This book will give you a lot more than can be covered in a single semester undergrad course, and while it doesn't exactly make the best reference text, it will be a book you will want to keep coming back to, if only to study some of the more advanced material.There are differing perspectives on the teaching of abstract algebra: some people like to start with group theory exclusively in a first course, and treat rings, fields, and other structures in later courses. Other people recommend more integrated approaches, or approaches starting from rings. While I can't say that either approach is better, I can say that this book takes the first approach, focusing exclusively on groups and assuming little prior background..and for a first course in abstract algebra, this book is an excellent choice.

Please note that the other reviews here are obviously for some other book. This is not an advanced text on bifurcations and stability. It is an introductory book on group theory. I have been using this book for self study. It is well suited to this purpose. The book uses symmetry to unify and motivate the study of groups. The discussion of the symmetry groups of Platonic solids is both enjoyable in itself and useful for visualizing groups. The chapters are very short. The exercises are well suited to gaining insight into the material.

I used the group theory text as an undergraduate mathematics major. I found the book to be unhelpful from organizational, pedagogical, and motivational perspectives. The book tries to motivate the reader with practical examples, but these examples are fairly run of the mill and most professors have a slew of far more interesting examples. If I had to learn group theory only from this book I would have gone insane. The author does not setup a sense of how various ideas fit into the larger picture and does a poor job motivating theorems with intuitive reasoning. Many proofs are simply stated without true intuitive cognition.This book is not the fantastic learning guid that it's sister book, Understanding Analysis by Stephen Abbot. Abbot's book provides good insight into the subjects theoretical core helping build intuition for the subject. Group theory is a subject that can be presented in such a manner, but this book simply does not provide.As a reference text this is also poor. Many crucial proofs are given as exercises and the book's layout and structure are not conducive to finding what you're looking for.Bad text to learn from and a bad reference. As with war, what is this good for?

I used this book for my introductory group theory class (Math 109 at Stanford). The book is alright, but the entire thing is written in the style of a proof. Theorems are introduced, then promptly proven. As a result, the exercises are often dramatically more difficult than material covered in the corresponding chapters. Another result of this style is extreme concision. Be prepared to read every sentence twice. This is a good book, but be comfortable with proofs and discrete math before attempting to read it.

I'm using this book for a first course in Group theory and it makes a good introductory text. Topics are neatly arranged and follow an order that makes reading easy. But it is definitely not a text for any sort of rigorous proofs. Rather, it focuses on learning from examples.

The book consists solely of exercises and hints for every exercise, which he curiously calls "answers". This book is perfect if you are looking to review geometrically-tinged algebraic structures like matrix groups, symmetry groups, and wallpaper groups. There is also some basic pure algebra in here. I don't think this book would work all that well for a student new to algebra, although someone with some backgroud in algebra can definitely get something out of the geometric chapters.

Très bon livre en introduction, il est utilisé dans certaines universités prestigieuses.Il existe d'autres alternatives mais à un niveau plus avancé.

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