Hello fellow members of Math StackExchange!
Since this is my first post here, I should start with a little introduction of myself. I've recently finished the second year of math at university and I did fairly well in the classes I took this semester (multivariable calculus, intro differential equations, intro linear algebra, intro abstract algebra). Out of the math topics I've been exposed to, I found myself to be drawn more to discrete math (algebra being by far my favourite). For example, I loved the definition-theorem-proof pattern that the abstract algebra course this semester followed.
The algebra course at my school was quite standard, following the groups-rings-fields path. We used Abstract Algebra: Theory and Applications by Tom Judson. We did skip over some chapters in the book, but I will finish learning them in my own time because I'm taking the summer semester off. However, because I get four months off in the summer, I'm hoping to also learn from a more advanced textbook, which leads to the main question of the post:
What do you think is a good second textbook for self-studying abstract algebra for someone who has taken a semester of algebra?
I know algebra is a big topic, so I'm sorry for posing a potentially vague question. Also, I searched this question on the forum before and the posts that I came across seem to be for beginners, so hopefully this isn't a duplicate.
Best regards,
Kevin
Best Answer
Paolo Aluffi's Algebra Chapter 0 is a good text that looks at things from a slightly different perspective as it introduces categories early on.
Another good text (it is not that advanced, but it does cover a lot of topics) is Richard Dummit and Richard Foote's book called Abstract Algebra. I think that this book is excelent.