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Finite vs. Infinite Problems

Nikolay Brodskiy
Organization: The University of Tennessee

Wolfram Technology Conference 2013
Conference location

Champaign, Illinois, USA

My recent explorations of Calculus and its teaching revealed the following observations.

1) Calculus is the first course where students consider a new kind of problems: infinite problems. I call a problem infinite if it does not allow a finite solution. Infinite problems (as opposed to finite problems) require a different thinking process.

2) A typical way of teaching Calculus avoids the thinking needed for infinite problems in two simple steps. First, students are given a list of standard infinite problems with the answers to memorize. Second, any other problem of the course is reduced to one of the standard problems in a finite sequence of steps.

3) The concept of directed set plays the central role in explorations of problems involving limits (and therefore in any Calculus problem).

4) Mathematica online would be extremely useful for teaching and learning Calculus. It would allow to focus on the new thinking while any finite computational process could be delegated to Mathematica.

*Wolfram Technology

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