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I want to start analysis this summer, because I think it'd give me a heads up on upper year quantum mechanics and differential geometry.

About me? I'm entering 3rd year physics, and have done intermediate level calculus 1,2,3+vector analysis, linear algebra 1&2 (up to Jordan canonical), and abstract math (ie. number theory, cantor sets, impossibility proofs). I especially have a strong intuitive feel for calculus and vectors thanks to electromagnetics.

I don't know if I consider myself a "strong" mathemetician. I found linear algebra really really hard, and the proof questions scared me. While I get the main concepts, quadratic forms and all the way one can diagonilize them was confusing. On the other hand, I always found calculus proofs straight forward. Mind you, this wasn't honors calculus. It was "intermediate". We proved all the theorems, so I've seen my share of epsilon delta. But I didn't deal with set theory or anything like that. The books used were Salas & Etgen Calculus (which is basically rigorous stewart) and Folland Advanced Calculus (which is quite theoretical).

I was wondering... would it be better to reaquaint myself with Calculus via Spivak or Apostol then proceed to Real Analysis? Or go straight into Analysis, because I've heard all of calc is generalized there. I was thinking of using Pugh's Real Mathematical Analysis and see how far I'd get. I was told to stay away from Rudin, and by several people.

Pugh can be seen here:

www.amazon.com/Real-Mathematical-Analysis-Charles-Chapman/dp/0387952977/ref=pd_bbs_sr_1/105-5386852-5102801?ie=UTF8&s=books&qid=1193206090&sr=1-1[/URL]

About me? I'm entering 3rd year physics, and have done intermediate level calculus 1,2,3+vector analysis, linear algebra 1&2 (up to Jordan canonical), and abstract math (ie. number theory, cantor sets, impossibility proofs). I especially have a strong intuitive feel for calculus and vectors thanks to electromagnetics.

I don't know if I consider myself a "strong" mathemetician. I found linear algebra really really hard, and the proof questions scared me. While I get the main concepts, quadratic forms and all the way one can diagonilize them was confusing. On the other hand, I always found calculus proofs straight forward. Mind you, this wasn't honors calculus. It was "intermediate". We proved all the theorems, so I've seen my share of epsilon delta. But I didn't deal with set theory or anything like that. The books used were Salas & Etgen Calculus (which is basically rigorous stewart) and Folland Advanced Calculus (which is quite theoretical).

I was wondering... would it be better to reaquaint myself with Calculus via Spivak or Apostol then proceed to Real Analysis? Or go straight into Analysis, because I've heard all of calc is generalized there. I was thinking of using Pugh's Real Mathematical Analysis and see how far I'd get. I was told to stay away from Rudin, and by several people.

Pugh can be seen here:

www.amazon.com/Real-Mathematical-Analysis-Charles-Chapman/dp/0387952977/ref=pd_bbs_sr_1/105-5386852-5102801?ie=UTF8&s=books&qid=1193206090&sr=1-1[/URL]

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