Reddit reviews Elements of Abstract Algebra (Dover Books on Mathematics)

Most of the books on this list that I'm familiar with are really good. And I may use the list's recommendations for a few areas that I'm unfamiliar with.

But what do people think of the abstract algebra recommendations? I've tried to work with both Gallian, and Dummit & Foote and I found both of them to be boring (each in their own unique way). I'd be happy to elaborate on this if people strongly disagree.

For abstract algebra, my favorite introductory book is Elements of Abstract Algebra by Allan Clark. You can't beat the price, and it's just fun to read. It's organized into manageable sections, with just the right amount of relevant problems for each section. The problems are pitched just right for a person who's had some--but not a lot--of experience with proofs (I think this is the case for most students of intro abstract algebra).

I found Elements of Abstract Algebra to be very accessible. Some people seem to hate it though. For $7, it's not much of a risk. With that said, I have some doubt about the potential for a non-mathematician to learn abstract algebra without developing some "mathematical maturity" with easier material first.

Have you studied algebra? How about linear algebra? The easiest way to understand it is to think of C is as a vector space of degree 2 over R, with the basis {1, i} (although there are of course infinitely many bases for C over R, as).

If you really want to understand why the complex field works the way it does, I’d suggest checking out a book on algebra, with a focus on field theory and maybe some Galois theory if you find it interesting. I’m finishing up the process of working my way through Allan Clark’s book on the subject and I definitely have a better understanding of what C really is and why it’s defined the way it is now. I’m sure other books will work just as well, but this one was a freaking steal at $10.

I don't know what level of group, ring and field theory you are looking for, but Allen Clark's Elements of Abstract Algebra seems up your alley. Mostly they state definitions and ask you to prove almost everything.

I don't have as much experience with this book, but I think A General Topology Workbook is basically the same idea for introductory topology.

I'd recommend Linear Algebra Done Right. I think there are links to the pdf floating around, but I don't know if it's free or not. If not pay the money. I heard you like proofs.

Also good not because of but despite being way cheap, Elements of Abstract Algebra which is like a puzzle book, Socratic method. There are a lot of good books to recommend, I chose this one.