When did you realize Spivak was a meme, and Apostol was superior?

>>8959515
Calculus on Manifolds (Spivak)?
How so if I may ask?
I've never used Apostol.

When did you realize Apostol is too much and you only need based Stewart

>>8959558

When I realized I didn't want to learn math.

>>8959515
>He doesn't learn analysis before calculus

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How long would it take(in hours) for the average student who has already taken the first three calculus (using Stewart) to go through Spivak or Apostol.

>>8959515
Courant > Apostol.

>>8959572
Why would you want to? Move on to an analysis book and cut out what you already know.

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>>8959617
>Why would you want to? Move on to an analysis book and cut out what you already know.
What book would you recommend? Is baby Rudin hard?

>>8959617

What is with the spergs who think that you aren't learning anything new by tackling Apostol/Courant/Spivak after getting through Stewart's rudimentary calculus? Sure, you'll cover the same calculations as before, but there's so much more in these books than the calculations of calculus. At the very least, you'll learn how to proof (which you've rarely been asked to do before), and at the best, you'll understand calculus at a level far deeper than you thought possible as a high school student or a freshman.

>>8959724

Or you could skip the junk you already know and just read a book on proofs then a book on analysis. Apostol/Courant is for people who want to learn calculus and analysis at the same time.

>>8959713

If you haven't don't any other proof based courses, read Zorich's "Mathematical Analysis I && II".

>>8959724
>you'll understand calculus at a level far deeper than you thought possible as a high school student or a freshman.
That's literally what analysis is. Not only that but it teaches more than just calc by introducing general spaces and topology. Spivak and Apostol are a waste of time.
>>8959713
Rosenlicht is easy to learn from. Look at Rudin afterwards.

>>8959729
I only flipped through it but Zorich seems like a very good book. have you actually read it all ?

>>8959729
>>8959849

They're not a waste of time for students wanting to transition from calculations into proofing. Finish Stewart, finish How To Prove It, then finish Apostol, and then you should be ready to tackle any entry-level subject in upper level mathematics. They're fantastic training wheels for people who want to develop mathematical maturity but aren't autistic prodigies.

>hurr you already know it

I guess brainlets are satisfied with unrigorous plug-and-chug explanations of a concept, aren't they?

>>8959974
In that case just use Tao's analysis. He assumes no experience with writing proofs at all. In any case I still don't see the point. Read a proofs book then read an analysis book. It's doable and it builds maturity figuring out how arguments in math work.

>>8959983

If Apostol is tough for a person new to proofs, even with prior experience in calculus, then Tao's Analysis is going to be downright discouraging and frustrating, even if it's otherwise a great book for a more advanced student. Do you nerds get off to this gatekeeping garbage or something? Terrible recommendations to "skip" Apostol or whatever because you learned plug-and-chug calculus that didn't try to hint at the concepts necessary to prove the most fundamental theorems.

>>8959996
I don't think I'm gatekeeping. I'm speaking from my experience. This is actually what I did. I read Strang and Stewart's calc books in 11th grade because I was curious, it made 12th grade calc a breeze. Then Axler and Hoffman/Kunze's LA books around the end of highschool. This is where I learned how to prove things by reading and rereading them. Then I read Rosenlicht and then Rudin much later, since I was a physics major as well I didn't need to bother with analysis for a while. I really didn't need a proofs book(except for induction) or a rigorous calc book. It may have been easier to read those but I'm certain the difficulty made me better at math than I would have otherwise.

>>8960016

If you've read Hoffman/Kunze then you're perfectly justified in skipping Apostol. Reading Hoffman/Kunze after reading Strang is like reading Apostol after reading Stewart. It's the same "transition" mathematical experience--covering what you did before but now with rigorous foundations through proofing. Add a book like How to Prove It or The Book of Proof, and your transition will be perfect, though I guess it isn't always necessary.

I don't mean to be rude earlier, but you have to consider how you organically learned mathematics before prescribing books for other people. What you were advocating was skipping the training wheels necessary for analysis that you benefited from and laughing it off like it's no big deal. Maybe if you're extremely motivated, intelligent, and experienced, but most people aren't that blessed.

Is it worth reading either if don't plan to major in pure maths?

>>8960356
I'm reading Spivak and don't major in pure math, I don't know if reading them will benefit you in any other way than being interesting.

>>8959996

You're going to get the proofs of calculus theorems in an analysis course but you won't repeat the plug and chug stuff you already know. If you're not ready for analysis, there are other areas of math to study.

Rudin and Fichtengolz are all you need, all these spivaks and apostols are for fags