For my honors course, we did a neat workshop on growth. The goal of the workshop was to be able to have a mathematically-informed conversation on world population and its environmental impact. Other goals include being able to see a multi-disciplinary project from start to finish and to improve general math and programming skills.

This set took about two weeks to run (an extra week for them to do the work). The class was made up of an array of majors including science majors (chemistry, biology, and one physics major) but also had a mix (about half) of non-science majors (nursing, finance, accounting, and international relations.) The students universally felt it was very intense, but an exciting learning environment. Overall there was a sense of understanding and joy at completing the project and truly understanding it.

Part I: Open Discussion on World Population.

I gave the following graph about world population. I had the students break into groups, and encouraged the students to develop an argument about a particular position (e.g., pro population growth, pro population decline), and then brought everyone together for a full class discussion on it.

Part II: Biology Lab

A special thanks goes out to Professor Galina Fomovska and John Hunter for helping to set up the lab. They basically did the biology prep, growing the initial population of bacteria and getting the broth ready. We more or less followed the procedure discussed in this lab (we did not create this):

There was some piece of equipment that the biologist wanted to use to generate the light to measure the optical depth of the bacteria. We simply grabbed a laser pointer from our first year physics lab at 650nm, a photodiode, and a multimeter and measured by shining the laser through and determining how much light made it through. Easy Breezy Lemon Squeezey!

It took the students about 5 hours to complete the lab. They made up a schedule to come in and make quick measurements every 20 minutes or so. Here are some pictures of the lab

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Looking back I wish I would have told the students to keep track of the relative laser intensity instead of the absolute as there was significant fluctuations in this. (see about 130 min). We just ignored this as it was a general class. If I were in a biology class or a physics class I would have made them retake the data.

Part III: Numerical Modeling Growth Equation

Over the course of a week in class, we did the following workshop in class in small groups:

After completing this, we discussed the non-linear term -bN^2. But I didn’t tell them how to do it or employ it in their model – in fact I even made them come up with the term as a class. Finally, I just gave them time and let them put the pieces together. I was available for office hours.

Here is what they came up with:

They achieved this by solving the differential equation numerically and then hand fitting by adjusting parameters to the data. For Physics Majors, you may want them to solve the differential equation analytically and use a curve fitting routine, but the numerical process was great too.

Part IV: Open Discussion on World Population.

We came back to this graph and discussed it. I was amazed after truly understanding how growth worked the students shifted to a more negative stance on population growth.