12 Days of Christmas (Day 8): Top 5 Courses I Teach

Welcome to my latest theme week:  12 Days of Christmas!  Each day, I'll be counting down by one - and with it, a new list that encompasses the day's number.  

For today, I'm veering sharply away from baseball cards and into my "real life" which as you may know, is being a math professor.  I thought it'd be interesting to countdown my favorite courses that I teach (note:  this is based on the content of the course, not any individual students that I may have had during a given semester)!

Top 5 Courses I Teach:

5.  Calculus I

Calculus I is a foundational mathematics course for math majors but it's also necessary for Physics, Astronomy, Chemistry, Pre-Med, Economics, and a variety of other disciplines.  As such, I get a wonderful mix of students (and their corresponding interests) in that class.  Unfortunately, I also get a fair bit of "math phobia" and/or students who simply have to take the course but want no part of actually being there.  I have decent success at converting most of them into at least tolerating Calculus but there often is a holdout or two each semester.  As for the content of the course, I think it's quite interesting but I've been teaching Calculus I for so long it has become a bit more routine than perhaps even I'd like it to be!

4.  Calculus III

The next four classes in the countdown are all classes that I truly enjoy teaching.  Calculus III ended up 4th on the list mostly because I think of Calculus III as Calculus I but in three-dimensions.  It's amazing how many of the lectures line up with exactly what I taught that day in Calculus I, except now I have a z-axis to consider.  It's probably worth noting that you won't find Calculus II anywhere near my list of favorite courses (to teach, to take, or otherwise).  I love Calculus I and III but Calculus II is for the birds.

3.  Mathematics of Games & Gambling

One of my "pet" courses in that I conceived of, pitched, developed, and now teach this course.  This course started out as a general distribution course but when my college switched over to offering first-year seminars, I revamped the course to fit into that mold instead.  The course combines my love of all things games with mathematics - we look at all sorts of interesting things in the class including most classic casino games, lottery games, and even modern board and card games.  

One of my favorite stories about this class comes from when it was a general distribution course.  That particular year, I was teaching it during the fall semester.  I had one student in the course (let's call her Jane) who was a senior who hated mathematics.  She never seemed to love class and, quite frankly, by the time of Thanksgiving break was hanging on to a passing grade by the skin on her teeth.  However, she relayed a story to me that happened over Thanksgiving.  She went back home to Maryland (I think) and was at a bar with all her friends when she saw the automated Keno machines.  A week or two prior to Thanksgiving, we had discussed Keno at length in class but as I said, I didn't exactly think she was overly engaged in the material/lesson.  Anyhow, upon returning to campus after break, Jane told me how she was yelling at all her friends in the bar to avoid Keno and what a terrible game it was for the player.  She was so proud of the fact that she had learned something and was able to apply it in the real world.  As for me, I figure if I've got a seemingly disinterested student drunk in a bar in a different state remembering my lessons, well..then this course is a good one indeed!

2.  Introduction to Graph Theory

I don't know about you, but if I could relive my life over again there are a few things I'd do different.  One of those would have been to follow my heart and gone into more Graph Theory courses while in graduate school.  I had the belief that if I wanted to be a math professor at a small college then I'd have to either specialize in Algebra or Analysis and neither of those two disciplines excited me (which is probably why graduate school didn't excite me).  Instead, I was much more interested in "applied math" which includes Graph Theory - at least the parts of it that I enjoy!  

I should note here that Graph Theory has nothing to do with graphs of functions such as y=x^2 or cos x.  Instead, think of a collection of dots with lines connecting some (or all) of the dots.  That's the kind of stuff graph theory cares about - and you can use it for all sorts of things including modeling populations, examining strategies in games, and finding shortest routes along a series of roads. 

1.  History of Mathematics

History of Mathematics takes the cake for me as my favorite course to teach for two reasons.  First, I genuinely enjoy the content and how I get to present it.  The course begins with the earliest known mathematics of cultures like the Babylonians and then the course ends near the time of the introduction of Calculus.  Projects in the course are super cool - one of the first things students do is learn cuneiform and then actually complete a mathematics "worksheet" on a tablet of clay in the art building.  That clay tablet eventually gets fired in the kiln and then the students walk away with a truly unique memento from the course!

The other reason why I love this course is that it has an attached travel component that goes with the course.  The course takes students to both Italy and Greece (a perfect blend of ancient mathematics and "modern" mathematics).  I even got to give a short lecture in the same cave in Greece (on the island of Samos) that Pythagoras himself was thought to have given lectures while hiding from the tyrant Polycrates.

Honorable mention:  Introduction to Robotics using LEGO

Finally, an honorable mention goes out to my Introduction to Robotics using LEGO.  This is technically not a course I've taught yet - it was approved in the semester prior Covid ruining everything and then had to be cancelled due to social distancing procedures.  I'm hopeful that I'll be able to finally run the course for the first time next fall and if I do so, I'm even more hopeful that this course will quickly make it's way onto my Top 5 Courses I Teach List!