# Book on how to write proper proofs in Group Theory

• Algebra
• jstrunk
In summary, the speaker is attempting to learn group theory on their own using the book "Schaum's Outline of Group Theory." They chose this book because it includes exercises with solutions, but they are encountering several problems with it. These include unclear explanations from the author, the use of English instead of math in solutions, and difficulty in determining if their own solutions are correct. They express a desire for recommendations on a book that provides clear and proper proofs for group theory. They also mention a free alternative, but prefer to finish their current book before starting something new.
jstrunk
I am trying to learn group theory on my own from Schaum's Outline of Group Theory.
I chose this book because there are a lot of exercises with solutions, but I have several problems with it.
1) In many cases the author just makes some handwavey statement and I have to spend hours or days trying to figure out the what's behind his
pronouncement.
2) The solutions use too much English, as opposed to Math. English is imprecise and ambiguous. Maybe that's really how you do proofs in Group
Theory. This is the only book I have used, so i don't know. But it seems like clearer proofs could be made.
3) I often solve a problem in a different way that seems simpler to me, and I can't tell if I am missing some subtlety or if the author is being
unnecessarily convoluted. For instance, in many cases I think I can directly prove that G=H, say, but the author proves that G<or=H and H<or=G
so G=H.
The net result is that I never get to see what I consider to be a clear, full, proper proof of anything.
If I was taking a class, the teacher would be able to clear these things up, but on my own they are hard to deal with.
So I would appreciate any recommendations and a book that show how to write proper group theory proofs.

## 1. What is Group Theory?

Group Theory is a branch of abstract algebra that studies the properties of groups, which are mathematical structures that consist of a set of elements and an operation that combines any two elements to form a third element.

## 2. Why is it important to learn how to write proper proofs in Group Theory?

Proving theorems is an essential part of mathematics, and having a solid understanding of how to write proper proofs in Group Theory allows for a deeper understanding of the subject and the ability to solve more complex problems.

## 3. Who is the target audience for a book on how to write proper proofs in Group Theory?

The target audience for a book on how to write proper proofs in Group Theory is typically undergraduate or graduate students studying mathematics, specifically those interested in abstract algebra and its applications.

## 4. What topics are typically covered in a book on how to write proper proofs in Group Theory?

A book on how to write proper proofs in Group Theory will typically cover topics such as basic group properties, subgroups, group homomorphisms, group actions, and the structure of finite groups.

## 5. Are there any recommended resources for learning how to write proper proofs in Group Theory?

Yes, there are many recommended resources for learning how to write proper proofs in Group Theory, including textbooks, online lectures, and practice problems. Some popular textbooks include "A Book of Abstract Algebra" by Charles C. Pinter and "Abstract Algebra: Theory and Applications" by Thomas W. Judson.

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