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

Rudin Chapter 1