Rudin Real and Complex Analysis Ch1
I covered the first chapter in Rudin’s Real and Complex Analysis. I’m planning to go over this book before I take Math 6110 this fall (since I don’t technically have experience in analysis). Here are some of my first impressions
The book introduces many new topics. Some of these are different from the way that John Hubbard, my Math 2230 - 2240 teacher introduced them. Notably the concept of “open sets” differs as Hubbard introduces them in space and Rudin introduces them with topology.
The book is pretty well written. It is pretty readable, the proofs are relatively accessible and the theorems are well explained. However, there are a lot of concepts to memorize, and switching between pages get’s annoying at times. I’ll often find myself needing to recall a specific theorem number, and having to backtrack to 5 pages to find the specific section.
The concepts are really interesting. I always hated calculus in high school because it always felt really bashy to me. However, by taking a more abstract view and relying less on numerical methods, continuous functions become much more inspiring.
For the specific items I worked on, I elaborated on one theorem and did all the odd questions. My writeup can be found below