Teaching Calculus minus computation plus understanding

Nikolay Brodskiy

University of Tennessee

Projection as a tool for understanding

Why did you come to my talk?

You want to understand better something about   my abstract.
I      want to understand better something about   teaching math.

What does it mean “to understand better”?
What do we do to understand better?

WHY? Mathematical thinking

Mathematical thinking is different

Why do Engineering students take Math classes?

An extreme example

Conclusion: the ways an actor and a mathematician think are very different (perpendicular).
Probably any student should take a math class as well as a theatre class.

WHAT? Structure of Mathematical structures

I propose to measure similarity and difference of two areas of Math in terms of the structures involved in the areas.

I am working now on the following project:

describe the structures in Mathematics that are well understood;

explain how different or similar those structures are;

explain the benefits of projecting something on a given structure.

My project could be related to the project of Conrad Wolfram computerbasedmath.org

Example: The Fundamental Theorem of Calculus