How Can I Succeed in a Directed Study of Real Analysis?

[trancefishy]

Well, this semester I'm in my first directed study in real analysis. I'm on my own. sort of worried about doing it, just got the book, and it looks kinda tough. I'm going to have to rethink how i go about classwork. i won't be rushing to get anything done before it's due or anything like that, so I'm hoping i will in fact get things done, period.

anybody have any advice on stuff, either in doing the course in general, or just doing math in a directed study setting (just me, and i get to go talk to a former prof of mine now and again for guidance).

i'm using Bartle and Sherbert's Introduction to Real Analysis 3e. thanks

 

[fourier jr]

when going through it, always try to figure out how proofs go without looking at the proofs in the text. do as much as you can without looking at the book, & peek only when you're desperate for a hint. i myself am trying to get to the point where i guess what the theorems are & to prove them, all without looking at a book, except to get the definitions.

 

[quasar987]

My advice, as a normal-sized-brained student (*cock an eyebrow to fourier*), is that you read the proofs only in diagonal, just to get a rought idea of the proof methods. Almost all of the proofs you won't understand the first time you read them. And understanding them will sometimes take a huge precious amount of time. Save your precious time to do the exercices, which are actually designed for your skill level (unlike the proofs). Be sure you understand every exercices in your book; don't make the mistake (again!) of saying (bah, he's not going to ask about that in the exam.. because you know he WILL). These are my advices; they worked quite well for me. Good luck.