# Good Algebra Textbook: Basic to Graduate Level

• Cexy
In summary, Can anyone recommend me a good algebra textbook that starts out quite basic and goes up to graduate level? I'm familiar with the following topics: -Elementary group theory-Elementary ring theory-Basic representation theory-Differential geometry- elementary properties of Lie algebras.
Cexy
Can anyone recommend me a good algebra textbook that starts out quite basic and goes up to graduate level? I'm familiar with the following topics:

Elementary group theory e.g. normal subgroups and quotient groups, isomorphism theorems, group actions. Elementary ring theory, e.g. ideals, polynomial rings. Basic representation theory, e.g. characters. Differential geometry, e.g. basic properties of manifolds, Lie groups, curvature and connections, elementary properties of Lie algebras.

More advanced group theory, e.g. Sylow theorems, simple groups. More advanced commutative algebra and theory of ideals, perhaps Noetherian rings? More about modules as a generalization of vector spaces. Group rings and connection to representation theory. Galois theory, number fields, more representation theory.

If any of it can be tied into equivariant dynamical systems (i.e. symmetric dynamics) then that would be great as that's what I'm doing my PhD in! Thanks a lot. :)

Maybe Dummit and Foote?

I would suggest reading like the first half of a textbook by Gallian or the basic one by Herstein and then start from the beginning from Rotman's Group Theory (Graduate Series from Springer).

If you know the basics well, you heard of normal subgroups and such. Then go right into Rotman's. Surely, that is only group theory.

Then for Ring Theory, I would do something similiar. Read half of an elementary textbook and jump into a full blown graduate textbook (they all start from the beginning anyways).

Also, you don't need to read all of Rotman's textbook. The first half will give you more then you generally need. It's an easy read such that you don't need to solve any problems to keep going. Although, if you don't solve problems, you miss out a lot on comprehending the stuff. The bright side is that if you can't solve the majority of the problems of one chapter, you can still keep going as long as you understood what you read. We all have a our "weak" chapters so it's completely reasonable to assume we will get stuck on a chapter at some point.

For my undergrad algebra course we used A First Course in Abstract Algebra by Fraleigh, and I liked it a lot. For my grad course we are using Algebra by Steinberger (who is also the prof). I find it very readable, and it's free online.

http://math.albany.edu/~mark/classes/520A/

One grad level book that I would avoid is Hungerford. He almost completely avoids semidirect products, which are extremely useful in classifying groups of a given order.

Tom Mattson said:
http://math.albany.edu/~mark/classes/520A/
Thanks, that's exactly what I'm looking for.

well if that's what you want, i don't suppose you want my notes on algebra, since they cover most of that material in only 100 pages. but i offer them anyway. see my webpage for math 8000 notes.http://www.math.uga.edu/~roy/

## 1. What topics should a good algebra textbook cover?

A good algebra textbook should cover basic algebra such as solving equations, graphing, and working with polynomials, as well as more advanced topics like matrices, complex numbers, and abstract algebra. It should also include applications of algebra in real-world situations.

## 2. What level of difficulty should a good algebra textbook be suitable for?

A good algebra textbook should be suitable for a wide range of levels, from basic algebra for high school students to more advanced topics for graduate-level students. It should include clear explanations and examples to cater to different levels of understanding.

## 3. How should a good algebra textbook present the material?

A good algebra textbook should present the material in a logical and organized manner, starting with the basics and building upon them to more complex topics. It should also include plenty of practice problems and exercises to reinforce the concepts learned.

## 4. What makes a good algebra textbook stand out?

A good algebra textbook should have a clear and concise writing style, use real-world examples, and provide a variety of practice problems with detailed solutions. It should also include visual aids such as diagrams and graphs to aid in understanding.

## 5. How can I determine if a textbook is suitable for my needs?

Before purchasing a textbook, it is important to read reviews and browse through the table of contents to see if it covers the topics you need. You can also ask for recommendations from teachers or colleagues who have used the textbook before. Some publishers also offer sample chapters or online previews to help you make a decision.

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