Tag Archives: Calculus

A Visit to a High School Calculus Class

It's funny what high school students notice. I paid a visit to a high school calculus class and gave two lectures about applied math. Both lectures were variants of a typical themes; what is mathematics and how is it used in today's society. The talk was very visual and used two mathematical ideas, network theory and optimization, to motivate the study and beauty of mathematics.

I began the talk by asking them to consider the following picture from a children's book. elephant_waterI borrowed this from a talk given by Timothy Gowers on "The Importance of Mathematics." The students very quickly realize the water spouting from the lazy elephant is not obeying Newton's law of gravity. From here I go into a short bit on mathematical modeling. I ask them what they know about bacteria and I receive a typical answer; bacteria grows exponentially. We look at the graph and they realize, through a verbal discussion, that \displaystyle{\lim_{\rightarrow \infty}}e^x = \infty. From here the students understand the exponential growth model needs to be refined. We end with the graph of the logistic equation. read more

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