Books like J. Callahan's Advanced Calculus: A geometric view

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Discussion Overview

The discussion revolves around recommendations for books that provide a geometric intuition behind mathematical concepts, particularly in areas such as vector calculus, differential geometry, and topology. Participants seek resources similar to J. Callahan's Advanced Calculus.

Discussion Character

  • Exploratory, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant asks for book recommendations similar to Callahan's Advanced Calculus, emphasizing a geometric perspective.
  • Another participant questions the inclusion of differential geometry in the request and suggests "Linear Algebra through Geometry," although they have not personally reviewed it.
  • A different participant reiterates the focus on differential geometry and appreciates the suggestion of "Linear Algebra through Geometry."
  • Another participant recommends Jänich's book on Topology, highlighting its visual and geometric approach, while noting that exercises may need to be sourced elsewhere.
  • A participant mentions "Visual Complex Analysis" by Tristan Needham as a book with excellent geometric intuitions, although it is not directly related to differential geometry.

Areas of Agreement / Disagreement

Participants express varying opinions on the relevance of suggested books to the original query, indicating some disagreement on the appropriateness of certain recommendations. No consensus is reached on a definitive list of suitable books.

Contextual Notes

Some suggestions may depend on personal experience with the books, and the relevance of each recommendation to the specific areas of interest mentioned may vary.

Who May Find This Useful

Readers interested in mathematical texts that emphasize geometric intuition, particularly in vector calculus, differential geometry, and topology.

Joker93
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Hello,
do you know of any books similar in style to Callahan's Advanced Calculus book(a book that explains the geometrical intuition behind the math)?
This goes for any subject in mathematics(but especially for subjects like vector calculus, differential geometry, topology).
Thanks in advance!
 
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Why did you tag differential geometry with you question? Anyway you might be interested in Linear Algebra through Geometry : https://www.amazon.com/dp/0387975861/?tag=pfamazon01-20 although I haven't worked through it myself, I only heard about it. You can give it a try.
 
Last edited by a moderator:
NathanaelNolk said:
Why did you tag differential geometry with you question? Anyway you might be interested in Linear Algebra through Geometry : https://www.amazon.com/dp/0387975861/?tag=pfamazon01-20 although I haven't worked through it myself, I only heard about it. You can give it a try.
Cause in my question I states "especially for subjects like vector calculus, differential geometry, topology".
Thanks for the suggestion.
 
Last edited by a moderator:
Oh my bad, then allow me to add Jänich's superb book on Topology. It is highly visual and geometric. His approach of metric spaces is just great, but you'll need to get exercises elsewhere.
 
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