Better to start learning calculus from precalculus

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Discussion Overview

The discussion centers on whether it is better to start learning calculus from precalculus or to dive directly into calculus texts such as those by Spivak or Courant. Participants explore the prerequisites and challenges associated with these advanced calculus books.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • Some participants suggest that Spivak and Courant are challenging and may require a calculus background, experience with formal mathematics, or guidance from a teacher to be beneficial.
  • Others note that while these texts are rigorous, they can prepare students for advanced real analysis courses, indicating their value despite the difficulty.
  • A participant recommends exploring these texts to assess personal comprehension and suggests alternative, less challenging resources like Lang's First Course in Calculus if needed.
  • One participant expresses uncertainty about whether to study precalculus or start with calculus, highlighting the dilemma faced by learners transitioning into higher mathematics.

Areas of Agreement / Disagreement

Participants generally agree that Spivak and Courant are challenging and may not be suitable for all learners without prior preparation. However, there is no consensus on whether starting with precalculus or calculus is definitively better, as opinions vary based on individual backgrounds and learning preferences.

Contextual Notes

Some participants mention the need for prior knowledge or support to effectively engage with advanced calculus texts, indicating that individual readiness may vary significantly.

philippe311
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Hi Everyone,

I have a question regarding CALCULUS.
Is it better to start learning calculus from precalculus or calculus, say in general? When I mentioned calculus, I meant Calculus written by Spivak or Courant, which I think starts off with basic concepts leading to advanced ones.

Any comments will be highly appreciated.
 
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Just to clarify: are you asking if you could read Spivak or Courant without a prior calculus background?

They are marvelous books but a bit too challenging for most pre-calc students. Most students would need at least one of the following three items to benefit from Spivak or Courant:
- a calculus background
- experience with formal mathematics and proofs
- a good teacher
 


Yes both of these texts are challenging and will prepare you for just about any real analysis text written at the freshman or sophomore undergraduate level (Rudin, Apostol, Kolmogorov & Fomin, etc.). My advice is definitely to try to find these books in a library or on google books and decide for yourself. See if you can follow the author's arguments. If you decide that it's too hard for you, there are other goods texts out there that are less challenging. I recommend Lang's First Course in Calculus.
 


owlpride said:
Just to clarify: are you asking if you could read Spivak or Courant without a prior calculus background?

They are marvelous books but a bit too challenging for most pre-calc students. Most students would need at least one of the following three items to benefit from Spivak or Courant:
- a calculus background
- experience with formal mathematics and proofs
- a good teacher

Although I have studied pre-calculus a year and half ago in a different language, now I am about to start learning calculus and this question came to my mind, what should I do? learn pre-calculus or start calculus first.

And thanks for your reply, I really enjoy being advised.
 


snipez90 said:
Yes both of these texts are challenging and will prepare you for just about any real analysis text written at the freshman or sophomore undergraduate level (Rudin, Apostol, Kolmogorov & Fomin, etc.). My advice is definitely to try to find these books in a library or on google books and decide for yourself. See if you can follow the author's arguments. If you decide that it's too hard for you, there are other goods texts out there that are less challenging. I recommend Lang's First Course in Calculus.

Thanks, I would definitely start looking at these texts, and then see where it goes.
 

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