Anyone know a good, rigorous introductory analysis text?
How introductory do you want?
If you've never seen theoretical calculus, see Spivaks Calculus or Ross' Elementary Analysis. If you already know that the best choice is Pugh "Real Analysis".
I think Rudin's "Principle of Mathematical Analysis" is good if you're up for the challenge, but it might be more helpful to read Spivak's "Calculus" first to get a taste of some analysis.
Then Spivak's Calculus or Apostol's Calculus (yeah, original titles) is definitely the best choice in my opinion.I'm a high school soph and I just finished elementary diffy-q's, so it's safe to say I've never seen theoretical calculus before.
How's Apostol's Calculus compared to Spivak's? Are they essentially the same thing?
Well, in this case they were. Real analysis is more specific, to distinguish it from other branches, like functional analysis, numerical analysis, etc.Oh I thought analysis and real analysis are two different stuff
They're both excellent, as is Apostol's Mathematical Analysis. But after Spivak, you might be able to decide this for yourself better.I know Spivak's gonna make me busy during the summer, and this is probably a question a bit early to ask, but which one would you recommend, Pugh or Rudin? So I know what to look for right after I finish reading...