Number Theory & Calculus Theorems: Looking for Interesting Ones to Prove

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Discussion Overview

The discussion revolves around seeking interesting theorems in number theory and calculus for participants to prove. It includes suggestions for resources and specific types of problems that may be engaging for proof exploration.

Discussion Character

  • Exploratory, Homework-related

Main Points Raised

  • One participant expresses a desire to find interesting theorems in number theory and calculus to prove.
  • Another participant suggests working through problems from "Calculus" by Spivak, noting that it contains enjoyable proofs.
  • A participant inquires specifically about number theory problems.
  • One participant mentions that any decent number theory textbook will provide ample proof opportunities but does not offer specific problems.
  • The same participant reiterates the recommendation of Spivak's book for calculus, highlighting its accessibility compared to more advanced analysis texts and mentions the squeeze theorem as an example of a well-known result that can be proved.

Areas of Agreement / Disagreement

Participants generally agree on the value of textbooks for finding interesting proofs, but no specific number theory problems are proposed, leaving that aspect unresolved.

Contextual Notes

The discussion lacks specific examples of number theory problems, and the suggestions are dependent on the participants' familiarity with the recommended textbooks.

UncertaintyAjay
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So, I like proving theorems in number theory and calculus. I'd like some interesting ones to prove. Recommendations?
 
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Pick up Calculus by Spivak and work a bunch of problems from the end of the chapter. Very fun proofs to do.
 
Thanks, will do. Anything to do with number theory?
 
I don't have any particularly good problems or suggestions. Any decent number theory textbook will have plenty of proofs.

I recommend Spivak's for calculus because it's not quite so advanced as an analysis textbook, but it still contains problems in which you prove some very well known results (squeeze theorem being one of them off the top of my head).
 
Right, thanks.
 

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