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Mathematics & Statistics

When the semester started, the pandemic was merely a whisper on the other side of the world. But something ominous was in the air. A large branch fell from one of the laurel oaks that had long towered in front of the building, and it turned out that the trees were compromised. Down they came, and the building looked bare without them...

The grounds people planted some magnolias in front, and some day they will tower over passersby. But for now, the building towers over them.

By the time the magnolias were planted, the campus was closed, and most faculty, staff, and students had left — although groundskeepers stayed, keeping the grass at bay and planting the occasional magnolia.

The Morsani Center continued to have patients, but with precautions in place.

Meanwhile, with students gone, the squirrels had to make do without nachos or butter brickle. Back to acorns (sigh).

But on campus or off, classes must continue. Here are a few of our stories...

*Joel Rosenfeld is an assistant professor. This is his story.*

When the quarantine hit during spring break, I was teaching Introductory Differential Equations. Like everyone else, I had Spring Break to put a plan together and run with it. I had no previous experience with Teams or Zoom, and I had only a passing familiarity with Discord.

I was reluctant to require any attendance, or to do anything synchronously, since everyone’s schedule was upended (including mine). If a college student has a job, it’s likely in the service industry, and it was obviously about to crash. That means my students would have to turn to more flexible employment options, such as Uber, Doordash, etc. to make ends meet. They likely would have little time for my class, and it’s very unlikely that they’ll be able to meet at the previously scheduled time.

In the meantime, my home situation was a bit of a mess. My wife, my children (twin toddlers), and I were all really sick. I had a nasty cough, a fever, and I couldn’t cough enough to clear my lungs. My wife’s ribs hurt from all the coughing she was doing. My children dealt with it better, but were still sick. Does this all sound familiar? We don’t know if it was the novel coronavirus or not, since no one was doing testing at the time.

Under these constraints and conditions, I had to put together a class. My wife was expected to maintain the schedule she had before the quarantine, and I did my best to squeeze what I could around that. This meant that we had to give up our weekends to make sure everyone was getting their work done, and to make sure that we actually fed our children.

While Teams, Zoom, and the other options seemed interesting, I didn’t want to subject my students to a new system, when they didn’t actually sign up for an online class to begin with. I had a YouTube channel that I posted to occasionally, Th@MathThing, and every student would be familiar with and have access to YouTube, if they had access to the internet. If they didn’t have access, well there was no helping them. (Here’s my latest video, be sure to check out the MATLAB at Midnight segment in the middle.

Before becoming a mathematician, I spent six years as a graphic designer for an educational technology company, The Athena Group. I worked together with a team composed of professors of education (Drs. Richard Ledbetter and Sebastian Foti) and programmers to develop digital content for middle school and high school teachers. I also helped develop a graduate course at the University of North Florida [?] on Education Technology together with the late Dr. Sebastian Foti. Most of our products were fun little science experiments, educational videos, websites, etc, that could all be accessed either online or from a CD (remember those?). During that time, I developed skills using PhotoShop, Premiere, and 3DS Max.

Turns out that the entire Adobe suite can be leased for $20/mo with an academic account. So I brushed the dust off my decade old graphic design skills and set to work putting together my first lecture. It took me all day, but as I kept working, I got much faster. I can now put together an entire edited lecture in about 3 hours (if I don’t want to do anything fancy). I used a combination of a camera on a tripod to give face time to a problem, then transitioned to me working in GoodNotes on my iPad, and then back to a closing blip with the camera on the tripod. Basically, I took the model of “Tell them what you are going to tell them, tell them, and tell them what you told them”.

My students responded very well to my efforts. One student told me that it helped keep her son’s attention, who would otherwise be a big distraction. As I went on, I found new ways to introduce content in my videos. I added some music from a colleague that did covers for my favorite video game, Marathon. This colleague is Dr. Craig Hardgrove, who is an Assistant Professor of Geology at ASU, who was also transitioning to online teaching. He graciously gave me permission to use the music on my YouTube channel, and I feel that his contribution really improved my videos. The outro to every video is now his cover of “Guardians”.

My students ended up doing fairly well in my course. I don’t know if this was because of rather liberal examination policies on my part, or if they actually learned from my videos. Looking at the free response questions I had them photograph and upload to the Canvas quiz program, I see that many of them got the basic mechanics of the problems down, and given the circumstances, that’s all that I could ask for. If they want to refresh that content, well my YouTube videos will always be up there.

I signed up to teach differential equations again this summer. That way, I can provide a complete class on my YouTube channel for all of my students (and anyone else) that might want to refer to them in the future.

I’m just glad that my students were able to weather the class and move on with their academic careers. No need for this Pandemic to become a barrier to their educational and career goals.

*Greg McColm is an associate professor. This is his story.*

In Spring, I was teaching Symbolic Computations, which consists of using programs to solve computational problems — including differential equations. Then we all went online.

Most students stayed at home in the Tampa Bay area, but some were in other states or even in other countries. The pandemic was on everyone's mind, and it seemed appropriate to look at where models of pandemics come from. And most models of the pandemic are constructed of differential equations.

About a century ago, epidemiologists started modeling epidemics using systems of differential equations. The basic one was the SIR model (for Susceptible / Infectious / Recovered), which consisted of three differential equations, all three with time as the independent variable. \(S(t)\) is the number of susceptible people at time \(t\), \(I(t)\) is the number of infectious people at time \(t\), and \(R(t)\) is the number of recovered people.

Susceptible people become infectious when exposed to infectious people, so the first differential equation is $$ S'(t) = -bS(t)I(t), $$ for some parameter \(b\), which depends on social distancing and other measures to slow the epidemic. Meanwhile, at any given time, a certain proportion of infectious people recover, so the third differential equation is $$ R'(t) = gI(t), $$ for some parameter \(g\), which depends on available treatment. That means that the second differential equation is $$ I'(t) = bS(t)I(t) - gI(t). $$

Here was a new homework assignment. Assuming that a city of 2 million susceptible people has a few infectious people; graph the solution. Here, the horizontal axis is time, and the susceptible people are green, the infectious people are red, and the recovered are blue.

Now, assume social distancing (which reduces \(b\)). What happens then?

The red curve flattens, and fewer people get the disease, but it takes longer to get through the epidemic.

Finally, I asked an extra credit question: suppose that people practiced social distancing until the number of infectious people went down. What would happen then?

An argument for waiting for a vaccine.

This is a very simple model, focused on a single city with a homogeneous and well-mixed population exhibiting simple behavior, with no improvements in medical treatment. The “compartmental models” used by experts are much more sophisticated and project much more complex outcomes.