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I'm currently working through Principles of Mathematical Analysis, and I'm thoroughly enjoying it, but I wanted to know from some of you who've read it before, what's the best approach to get the most out of Baby Rudin?

I'm hoping to complete most, if not all of the exercises in it, that I'm sure of. No questions there.

What I'm not so sure about is note taking, currently I'm taking truly copious amounts of notes, to the point where I've copy-pasted almost everything in the first chapter into my own book.

It would be completely illogical to rewrite the whole book out just for the sake of it, and it would take me forever to complete the book that way.

I know as I'm typing this, that this is a very subjective matter, and some people prefer to take copious amounts of notes, while others prefer to take none at all, but since this is my first true Definition-Theorem-Proof style book (if you can call it that), I want to find out what's the best way to tackle the book.

For those of you who've read Baby Rudin, and more generally for all Definition-Theorem-Proof style books, how do you go about taking down notes?

  • Do you copy-paste most of the stuff (i.e as I did)?
  • Do you only take down notes on proofs and use the book as a reference for definitions and theorems?
  • Do you take down all the definitions and theorems?
  • Do you take down any of the exposition stuff (comments etc.)?
  • Do you take as little notes as possible and only worry about doing the exercises?
  • Do you try and reprove everything and not worry about notes as much?

I know that each person studies in their own way, and this may be the softest of soft questions on Math.SE, but I'm highly interested to see how others have gone about working through Baby Rudin.

Perturbative
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1 Answers1

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Here is how to do it. Read the theorem. Put the book down and prove the theorem. If you are really stuck, read the first sentence of the proof. Put the book down and complete the proof. If you are still stuck, read the second sentence. Continue until you have proven the theorem. Read the next theorem.

TQFT
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Rene Schipperus
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    This doesn't seem like the easiest thing for one to do, maybe not possible considering the proof of the existence of nth roots of positive reals using the least upper bound property. I seriously doubt any person with only pencil pushing, and basic logic could get it. – smokeypeat Apr 02 '17 at 20:33