MAA Books Beat: Teaching Isn't the Only Job for Math Majors

Written by Steve Kennedy, MAA Books Beat is a column written for MAA FOCUS. Teaching Isn't the Only Job for Math Majors appears in the August/September issue.

Teaching Isn’t the Only Job for Math Majors

“What would I do with a math degree? I don’t want to teach.” That anyone would ask this question has flummoxed me for years. When I was younger I was tempted (and sometimes succumbed to the temptation) to explain that one does not study mathematics for its possible future income potential. One studies mathematics because it is mankind’s only portal to absolute truth. Science deals in, as its best, approximations to truth; the humanities in speculation; the arts obscure as much as they reveal. Mathematics, using just the power of your mid, reveals eternal, and external to us, absolute truth.

I’m older now, and hopefully wiser, and not only do I see the value in what science, humanities, and the arts illuminate, but also, I see the legitimacy of the question itself. I too can now talk about the many interesting careers my former students have taken up: Nutty Steph, who started a granola company; Kate, who became a dog-musher leading winter tours of northern Minnesota; Liz, who was Stephen Wolfram’s personal assistant. Unfortunately, as the examples illustrate, I tend to remember the unusual and offbeat options.

Details about “Best Job”


CareerCast recently listed “mathematician” as the Best Job of 2014 (university professor, statistician, and actuary round out the top four). This made a nice blurb in our department newsletter, but they didn’t provide an awful lot of detail about what kind of jobs these folks are looking at. Fortunately, we have Andy Sterrett. Andy has been tracking down mathematics graduates with interesting careers and compiling their stories in 101 Careers in Mathematics for more than a decade. The third edition is just out. I’ll give some highlights to share with your students wondering what to do with a math degree.

Alysia Appell has degrees from Grand Valley State University and Rensselaer Polytechnic Institute. She is in charge of the pilot-staffing model for Northwest/Delta Airlines; that means she needs to forecast the airline’s future needs to hire pilots and plan how to cover all flights given predicted vacations and illnesses of current flight staff.

Joel Schneider has degrees from Franklin and Marshall, Washington State, and the University of Oregon. He was the content director for Square One TV, a children’s TV show that aired in the 1990s. Square One has echoes of Sesame Street but was focused on mathematics. My personal favorite bit was “Mathnet,” a Dragnet parody that featured a detective named Monday who was interested in just the facts as she solved mathematical mysteries. Schneider is still in TV, now producing a mathematical game show called Risky Numbers.

Kay Strain King has degrees from Vanderbilt, Makerere (Uganda), and Texas A&M universities. She is a senior environmental mathematician for Theta Engineering. She does mathematical consulting on environmental problems. In her article in 101 Careers, she describes a project to model gas release from a bermed storage tank under various weather conditions.

I bought a copy of 101 Careers to put in our department’s student reading nook. I’m thinking I should buy another copy for my desk. If you teach and advise undergraduates and sometimes find yourself confronting the question with which I opened this column, you should buy one as well.

(By the way, we have already started collecting material for the next edition of 101 Careers. If you are, or know, someone with an interesting mathematical career, please contact Deanna Haunsperger at dhaunspe@carleton.edu.)

MAA Books Beat: Playing to Learn Game Theory

Written by Steve Kennedy, MAA Books Beat is a column written for MAA FOCUS. Playing to Learn Game Theory appears in the June/July 2014 issue.

Playing to Learn Game Theory

by Steve Kennedy

Suppose the graph depicted in figure 1 represents a network of communities. Two doctors are planning to set up practice in one of the nine communities. A practice will attract all the patients in every town closest to it (closest means in terms of number of graph edges joining the vertices). In the case of a distance tie, each doctor will attract half the patients in the town. Where should the doctors locate to ensure their best result? (They are not conspiring; each doctor is acting independently and in ignorance of the other’s choice.)

Of course, neither doctor, presumably desiring to maximize her practice, would choose one of the degree-two vertices. The other six vertices look equally valuable. Suppose Doctor A chooses vertex 2. Were Doctor B to choose any of vertices 3, 5, or 8, each doctor would get 4.5 towns’ worth of business. If Doctor B chooses vertex 6, she “wins” by gaining five towns to A’s four. (If she chooses vertex 7, the payoffs are reversed and A wins five to four.)

If we conceive of the competition as a game between the two doctors, then this game has no Nash equilibrium. Each doctor can guarantee herself only four-ninths of the available customers.

The example comes from the new MAA ebook, Game Theory through Examples by Erich Prisner. The Doctor Locator Game is one of scores of clever, rich, interesting games described and analyzed in this lively text. There are also scores of apps, linked to the etext, so that the reader can play the games, the best way to understand them. In the doctor game, the reader can, with two mouse clicks, choose vertices to represent the doctors’ choices and immediately see a color-coded graph giving the division and the count.

The example games introduce and exposit all the important concepts of game theory. The Doctor Locator Game, on a different graph, introduces the idea of a Nash equilibrium and explains how to find one. The obvious next question of their existence is answered by the above example.