Re:Ask HN: Resources to learn real analysis?
by x0x0 on Saturday March 24, 2018 @03:03PM
(#16668239)
You have to decide between two things:
1 - you want to learn to prove things. Then yes, Rudin is a shitty text to learn by yourself because he really likes a certain type of, for lack of a better phrase, "beautiful" proof that requires a bunch of insightful jumps to get to. He'll then show the proof and really not discuss about how he got there. What a student needs is the ability to string facts/theorems that he or she knows together and how to turn that into a proof. Without a good professor, Rudin is (imo) terrible for that.
2 - you want to learn analysis, and care less about proving things. Reasons for this may be you need a bit the underpinnings for various reasons, and you care less about proving things and more about understanding. I think Rudin is a pretty good text then.
Spivak's calculus is a great book but be prepared to spend a lot of hours on it.
1 - you want to learn to prove things. Then yes, Rudin is a shitty text to learn by yourself because he really likes a certain type of, for lack of a better phrase, "beautiful" proof that requires a bunch of insightful jumps to get to. He'll then show the proof and really not discuss about how he got there. What a student needs is the ability to string facts/theorems that he or she knows together and how to turn that into a proof. Without a good professor, Rudin is (imo) terrible for that.
2 - you want to learn analysis, and care less about proving things. Reasons for this may be you need a bit the underpinnings for various reasons, and you care less about proving things and more about understanding. I think Rudin is a pretty good text then.
Spivak's calculus is a great book but be prepared to spend a lot of hours on it.