Shitty major, need to learn calculus, both rigurous and applied books welcome... Halp
It's a TERRIBLE, HORRIBLE idea to self study analysis from Rudin.
First study calculus from something like stewart + mit ocw lectures. Then read a book on proofs like "How to prove it, a structured approach". Then you can start with analysis. Terence Tao's Analysis I and II are amazing books that guide you through the process of understanding formal math as well as giving you a construction of the number sets and a nice description of naive set theory which is amazing to have early on.
do NOT fall for the rudin meme. it's an amazing and concise reference book but it is notoriously terrible for self study
honestly, This, I started out doing some analysis with rudin, but quickly found myself drawn to other books. Naturally, everything in the Rudin is really required learning if you are thinking about a graduate degree, but it can be frustrating for, even strong, students new to analysis.
stewart is recommended because it's easy, a light introduction and I think it has a lot of exercises or something? seems like a pretty good book for starting off for what I've seen, but really the MIT OCW lectures by themselves are enough if you want
Rudin is an excellent book. Some people would say it's bad because it doesn't focus on calculating integrals and stuff. Well, you shouldn't calculate integrals by hand. It's 2016, we have computers.
However, be careful and don't try to do all exercises in Rudin. Some of them are really hard and not very useful for understanding material.
>rudin is good!
>don't do the exercises
you clearly don't know what you're talking about. if you're not able to do the exercises, you're not understanding shit. rudin is an excellent reference book and a lousy book for self study.
absolutely nobody thinks that rudin's bad because it "doesn't focus on calculation", what the fuck?