I'm studying math by myself, and now I'm wondering what is the most appropriate for me to study. I think my interest goes to rather pure mathematics than applied math or math for engineers.
So far I finished studying Thomas' Calculus (12th Edition), and I'm basically done with reading the first half of Baby Rudin. In the fall semester, I'm thinking of studying the second half of that and also starting something else together with that. The followings are some options that I'm considering.
- Linear Algebra.
- Algebra (These two seem to be very important in mathematics)
- Topology (I kinda liked the chapter of the basic topology in Baby Rudin)
Abstract Algebra (I found it very powerful in problem-solving while preparing for Putnam. However, I don't know if I can study it or not.)
I also need some recommendations for textbooks. I kinda liked Rudin's style, the repetition of Definition, Theorem and proof. Though it is really tough, I like to fill in the gaps and read between the lines. Last but not least, I prefer old books like Rudin to new books.
Any advice and recommendation are welcome :)