This is the exercise sheet I use for the class I teach on exponentials. I consider it to be an important skill for students. This is pitched at the level of college students who last did math/physics quite a few years ago, in high-school. Since they're not comfortable with the lecturing style (or much math) it works better to have them see and explore something with their hands and let them discover the math through their own reasoning, while they're gently being nudged in the right direction by me (the instructor). That's the approach with which this lab is built.
The only necessary equipment is sheets of paper varying in size and thickness, for exercise 1. Newspaper is the most convenient, in practice.
Depending on the students comfort with math and how much time they're given to stretch their brains, they might not be able to complete the third exercise in class time. So I sometimes assign it as homework.
This class tries to get them to appreciate a few things:
- How fast an exponential really grows
- The idea of Fermi problems.
- Appreciating how nature has a "fractal" structure, where something interesting goes on at every scale. As humans, we're usually think linearly along the scale we're used to (about 1 foot or 1 metre). It's difficult for us to grasp the very big or the very small, and understanding the exponential helps us with that.
I wonder what other interesting videos/visuals could be incorporated into the class, that lets humans grasp the notion of exponential sizes and growths. Eg: Maybe a video of dividing bacteria, etc.
If you have any nice ideas, I would love to hear from you. Contact me at: sivaramakrishnan at utexas dot edu
I use a wonderful tool called Pandoc to generate PDFs or HTML from markdown. The HTML file in this directory should reflect the most recent version of the worksheet.
(C) Sivaramakrishnan Swaminathan 2014
This files in this directory are made available under the Creative Commons Attribution-ShareAlike 4.0 International license.
