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.

MAA Books Beat: Extraordinary Book on Ordinary Differential Equations

Written by Steve Kennedy, MAA Books Beat is a column written for MAA FOCUS. Extraordinary Book on Ordinary Differential Equations appears in the April/May 2014 issue.

Mathematics changes slowly; the mathematics curriculum changes even more slowly. A few years ago, to celebrate the tercentenary of L'Hôpital's Calculus, some colleagues and I read it seminar-style. The most striking thing about the experience was that his table of contents looked shockingly similar to our departmental calculus syllabus. That being said, in the 30 years I've been teaching collegiate mathematics, there is one course in the undergraduate math curriculum that has changed dramatically–the course in ordinary differential equations (ODE).

These changes are rooted in the calculus reform movement of the late 1980s and early 1990s, the easy access to powerful computing and visualization, and the rise of dynamical systems theory and its accompanying qualitative point of view.

The calc reform movement taught us to explain everything from graphical, numerical, and symbolic perspectives. Computing, of course, made it possible to do this in effective ways, especially the numerical and graphical bits. Dynamical systems provided entirely new ways of thinking about the evolution and bifurcation of systems.

The New on View

All these changes are fully on view in Virginia (“Anne”) Noonburg's Ordinary Differential Equations from Calculus to Dynamical Systems, newly released by the MAA. Noonburg has a distinguished record of research in dynamical systems, especially concentrating on equations that model biological systems. You clearly see these intellectual interests in this book.

MAA Books Beat: Collapse and Distillation

Written by Steve Kennedy, MAA Books Beat is a column written for MAA FOCUS. Collapse and Distillation appears in the February/March 2014 issue.

Collapse and Distillation

Things fall apart–but why? And how? Perhaps it is mere anarchy loosed on the world, but Charlie Hadlock has other ideas. In Six Sources of Collapse, published last year by MAA, Hadlock describes a half-dozen mechanisms that lead to collapses that seem abrupt.

He begins with the humble passenger pigeon. Two centuries ago North America was, literally, aswarm with passenger pigeons. In 1813 Aubudon observed a flock that obscured the midday sun and took three days to pass. Alexander Wilson once observed a flock that he estimated contained more than 2 billion individual birds; that is eight times the current estimate for the world’s total rock pigeon population. A single nesting ground near Sparta, Wisconsin, covered 850 square miles and housed an estimated hundred million birds. Flocks were so thick that folks hunted by swinging a stick in the air and picking up what came down.

It seems hard to credit that we hunted such abundance to complete extinction. (The last known passenger pigeon, Martha, died at the Cincinnati Zoo in 1914.) Hadlock explains the mechanism as the blank and pitiless result of evolution–the birds had evolved to live in enormous flocks. Their reproductive success depended on that, and these gigantic flocks were well adapted to a completely forested eastern United States. A flock of half a billion birds could denude and befoul a patch of forest in a few days, then move on to the next patch. Human settlement and forest clearing limited the available resources for this behavior. The combined effect of thinned forest and thinned flock (from a tide of hunting) led to dramatic population collapse.