Preparation for Advanced Calculus?

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Discussion Overview

The discussion centers around preparation for an Advanced Calculus course, which is perceived to be similar to an introductory Real Analysis course. Participants are sharing resources and advice on how to improve proof skills and foundational knowledge in calculus.

Discussion Character

  • Exploratory, Technical explanation, Homework-related

Main Points Raised

  • One participant expresses a desire to prepare for Advanced Calculus and seeks recommendations for books, particularly to improve proof skills.
  • Another participant recommends "Calculus" by Spivak as a rigorous introduction to advanced calculus concepts.
  • A third participant agrees with the recommendation of Spivak and suggests an additional resource focused on proofs and writing mathematics.
  • A later reply shares a personal anecdote about advice received from Lynn Loomis regarding the importance of understanding specific proofs, mentioning a proof from David Widder's advanced calculus book as foundational.

Areas of Agreement / Disagreement

Participants generally agree on the value of Spivak's book as a preparatory resource, but there are multiple suggestions for additional materials and approaches to learning proofs, indicating a variety of perspectives on preparation methods.

Contextual Notes

Some participants reference specific proofs and theorems that may depend on prior knowledge or definitions not fully explored in the discussion.

Who May Find This Useful

Students preparing for Advanced Calculus or Real Analysis, particularly those looking to strengthen their proof-writing skills.

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I'm signed up to take Advanced Calculus 1 for the Fall semester, I think it's the equivalent of an intro Real Analysis course. I want to prepare ahead of time, especially because I heard it's challenging, does anyone know any books I can use to get a feel for the topic? I'm not too good with proofs, so I would like to really improve that skill.
 
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Spivak. Calculus.

A phenomenal book on 'advanced' calculus - calc I but with rigor.
 
Thank you, will look into it!
 
When I asked Lynn Loomis what I needed to brush up on before taking his advanced calculus class he said I should learn the proof that a continuous function on a closed bounded interval has a maximum and minimum value. I learned it from the advanced calculus book by David Widder. Of course that was in 1963, before Spivak wrote his book. That proof is one the the "three big theorems" in Spivak's Calculus book.
 

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