Courant/John vs. Apostol for In-Depth Studying of Calculus?

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Discussion Overview

The discussion centers around the choice between Courant/John's "Calculus and Analysis" and Apostol's "Calculus Vol.1" for an in-depth study of single-variable calculus. Participants explore the theoretical and practical aspects of these texts, considering their suitability for preparation for the Putnam Competition and their relevance to research in computation theory.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant expresses a desire to study either Courant/John or Apostol for their depth in single-variable calculus, noting prior experience with Serge Lang's text and current studies in algebra and linear algebra.
  • Another participant mentions that while Apostol is formal, it is clear and enjoyable, suggesting it as a good starting point, though uncertain about its effectiveness for Putnam practice.
  • A different participant shares their experience with Apostol and Spivak, indicating that Spivak is easier to read but has more challenging exercises. They recommend Apostol for its clarity compared to Stewart's calculus text.
  • One participant notes a recommendation from their research adviser to focus on real analysis texts instead of advanced calculus, mentioning that Apostol's calculus books are not prerequisites for his analysis book.
  • Another participant agrees that while Apostol's calculus books are not prerequisites, engaging with rigorous mathematics is beneficial for long-term understanding.

Areas of Agreement / Disagreement

Participants express varying preferences for Apostol and Courant/John, with some favoring Apostol for its clarity and structure. However, there is no consensus on which text is definitively better for the intended study, and some participants are uncertain about the implications of skipping advanced calculus for real analysis.

Contextual Notes

Some participants highlight the differences in writing style and exercise difficulty between Apostol and Spivak, while others note the lack of prerequisites for Apostol's analysis texts. The discussion reflects a range of experiences and recommendations without resolving the best approach for studying calculus.

Who May Find This Useful

Readers interested in advanced calculus, real analysis, and preparation for mathematical competitions may find this discussion relevant.

bacte2013
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Dear Physics Forum personnel,

I would like to investigate the depth of single-variable calculus by reading either Courant/John's "Calculus and Analysis" or Apostol's "Calculus Vol.1". Of course, I know the best route of action is to go to mu university library, but I just found out that all of them were checked out! I am seeking one that covers both theories and applications of 1-variable calculus in an insightful manner. Studying either of those texts will also aid my research in the computation theory and also my preparation for the Putnam Compeititon.

As for my background, I had read Serge Lang's "A First Course in Calculus", and I am currently studying Artin's "Algebra" and Hoffman/Kunze's "Linear Algebra". PK
 
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I have Apostol and Spivak. Spivak is easier to read, however, the exercises in Spivak are a bit more difficult.

I have never seen Courant. Apostol is a good book, but it is written in a formal manner. I quite enjoy it. It is very clear. Even clearer than Stewart Calculus for me.

You cannot go wrong with Apostol. Not sure if it meets your demand for putnam practice.

I think Apostol Calculus would be a great starting point, because you can get familiar with his writing style and tackle his other books. I am looking forward to completing both volumes of Apostol, in order to read his analysis book and his number theory book.

If you do go for Apostol. Volume 1 and 2 can each be found around the 30-40 dollar price range for a hardcover 1st edition. Avoid the paperback from the eastern continents.
They are printed on cheap quality paper, pages can be missing, and the font makes the learning experience not enjoyable.
 
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Thank you for the advice! My research adviser strongly recommend to read the analysis books of Rosenlicht, Apostol, Pugh, Rudin, Folland, and Royden, so I switch my plan from reading the advanced calculus books to real analysis books. I have been reading them, and I actually like Apostol's Mathematical Analysis and Pugh's Real Mathematical Analysis. Also according to Professor Apostol, he said that his Calculus books are not prerequisite to his Mathematical Analysis. I really hope that I do not miss anything from those advanced calculus books of Apostol, Spivak, and Courant by jumping directly to the real analysis.
 
bacte2013 said:
^
Thank you for the advice! My research adviser strongly recommend to read the analysis books of Rosenlicht, Apostol, Pugh, Rudin, Folland, and Royden, so I switch my plan from reading the advanced calculus books to real analysis books. I have been reading them, and I actually like Apostol's Mathematical Analysis and Pugh's Real Mathematical Analysis. Also according to Professor Apostol, he said that his Calculus books are not prerequisite to his Mathematical Analysis. I really hope that I do not miss anything from those advanced calculus books of Apostol, Spivak, and Courant by jumping directly to the real analysis.

Not really a pre-rec. However, doing more rigorous mathematics is great! Helps you over the long run.
 

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