Self teaching Multivariable calculus

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Discussion Overview

The discussion revolves around self-teaching multivariable calculus, with participants sharing resources, book recommendations, and personal experiences related to learning calculus beyond the AP Calculus BC curriculum. The conversation includes suggestions for textbooks and approaches to studying mathematics rigorously.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant seeks recommendations for resources to learn multivariable calculus, expressing dissatisfaction with their current AP Calculus BC class.
  • Another suggests focusing on the AP exam first before pursuing additional materials, while also recommending consulting a math teacher for resources.
  • Several participants recommend specific textbooks, including Stewart's "Multivariable Calculus," Spivak's "Calculus," and Courant's volumes, noting their varying levels of rigor and suitability for self-study.
  • Some participants emphasize the importance of foundational knowledge in calculus and linear algebra before tackling advanced topics, suggesting that prior learning methods may affect comprehension of higher-level texts.
  • There are differing opinions on the appropriateness of certain textbooks for self-study, with some arguing that mass-market books may not provide the depth needed for serious study.
  • A participant shares their personal approach to studying Courant's book, discussing the balance between thoroughness and enjoyment in learning mathematics.
  • Another participant reflects on their own experiences with rigorous mathematics education, suggesting that exposure to challenging material can be beneficial for ambitious students.

Areas of Agreement / Disagreement

Participants express a variety of opinions on the best resources and approaches for learning multivariable calculus. There is no clear consensus on which textbooks are most suitable, and discussions reveal differing views on the importance of foundational knowledge and the effectiveness of various study methods.

Contextual Notes

Some participants note the limitations of the AP curriculum in preparing students for advanced mathematics, suggesting that students may benefit from seeking out more rigorous materials independently.

  • #31
does courant go in with the same depth?

thanks :smile:
 
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  • #32
I know that Apostol goes much deeper than Stewart, and I really appreciate that; what I was saying is that I don't enjoy proving things that appear to not require any proof.
 
  • #33
courant does not go into things quite as precisely as apostol. courant is deep, but there is a little more taken for granted. i think courant will assume basic facts from trig as needed, whereas apostol will lay out exactly which proeprties of sina nd cos are going to be used.

they are basically the same properties, but apostol has a fanatical commitment to really spelling out every fact and assumption with complete precision and care.

you can get the idea by going to the library and perusing these two boks, and then comparing with a book like stewart or anton, something along those lines.

apostol and courant are answering questions that do not even arise in books like stewart et al.
 
  • #34
I think Courant may be the book I'm looking for! I'm going to try to check it out as soon as I can.
 

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