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Calculus Unlimited

Calculus Unlimited. Ben Orlin Math with Bad Drawings Twitter Math Camp NYC August 22 nd , 2018. The Promise of Limits. Primordial questions about number. Rich veins of higher mathematics. A powerful problem-solving mindset. The Tragedy of Limits. Empty formalism. Alienating abstraction.

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Calculus Unlimited

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  1. Calculus Unlimited Ben Orlin Math with Bad Drawings Twitter Math Camp NYC August 22nd, 2018

  2. The Promise of Limits

  3. Primordial questions about number

  4. Rich veins of higher mathematics

  5. A powerful problem-solving mindset

  6. The Tragedy of Limits

  7. Empty formalism

  8. Alienating abstraction

  9. Intuition, rigor, or neither?

  10. Is there another way to tackle limits? • Convergence • Tangent lines • Differentiation rules • Differentiability

  11. Brianna’s Limit With props to Brianna May, and to Kevin Brown of Southern Adventist University

  12. What the heck is going on here? Brianna’s Limit

  13. Another Tricky Limit Again… what the heck?

  14. Not All Survives the Limit • Consider this sequence… • 0.9 • 0.99 • 0.999 • 0.9999 • 0.99999 • Every step of the way is a non-whole number. • Does that mean 1 isn’t a whole number?

  15. The Miracle of Calculus? So much does survive the limit!

  16. The Case of the Bicycle Tracks With props to Ed Bender at UCSD and Siobahn Roberts

  17. The Adventure of the Priory School • “This track, as you perceive, was made by a rider who was going from the direction of the school.” • “Or towards it?” • “No, no, my dear Watson. The more deeply sunk impression is, of course, the hind wheel, upon which the weight rests. You perceive several places where it has passed across and obliterated the more shallow mark of the front one. It was undoubtedly heading away from the school.”

  18. So… which way did the bicycle go? Stop condescending to Watson!

  19. Tangent line

  20. Identifying the front wheel

  21. Trying one direction…

  22. Trying the other direction…

  23. The Miracle of Calculus? A single moment tells so much!

  24. Rectangle Garden With props to Viktor Blåsjö of Utrecht University and Kenny Felder

  25. The derivative of x2… • …is 2x. • This is maybe the best-known, most-memorized fact in all of calculus.

  26. The typical proof

  27. A more geometric path

  28. The derivative, then…

  29. What about x3…

  30. The Miracle of Calculus? We can calculate with infinitesimals!

  31. The Dusty Dance With props to William Dunham of Muhlenberg College

  32. What did the baseball do?

  33. What did the baseball do?

  34. Weierstrass Function

  35. Brownian Motion

  36. The Miracle of Calculus? Unimaginable realities!

  37. What can limits do for our students? • Answer primordial questions about number • Tap into rich veins of higher mathematics • Serve as a powerful problem-solving approach

  38. Thank you so much!

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