Main Question or Discussion Point
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".
alright, I'll go ahead and check out Spivak's calculus first.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.
Apostol mostly shows important results, which I like very much. Spivak makes you derive a lot of important thing, but his reading is very fun until you hit extremely difficult problems. In the end, both books contain the same information but if you don't like finding answers yourself you might prefer Apostol (you can still do this in Apostol, just cover the proof and try and work it out yourself). Also, Apostol has a volume 2 covering multivariable calulus. Spivak sort of does this with his manifolds book, but I find his treatment way too terse. Lastly, I think Spivak is overkill - good or bad depending on whether you have the time.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...