In the interest of full disclosure, I must confess that though I was once a mathematician, I have since gone over to the Dark Side—computer science. And like any self-respecting Dark Sider, part of my job is to entice others to follow my path. For an undergraduate math major, this translates simply—if you truly want to experience the power of mathematics, then, while there’s still time, take as many applied mathematics, computer science, and statistics courses as you can.
I know, your major doesn’t require you to take any statistics or computer science courses. Sadly, such programs still exist. And I understand that it’s comforting to live in the cocoon of pure math. Theory is clean. It is elegant. Yes, pure mathematics can be beautiful in the same way that great literature, art, and music are beautiful. Real-world math, on the other hand, is messy. Hypotheses are not always clear. Boundary conditions and transition phases complicate analysis. Models have to be carefully balanced between being simple enough to be tractable, yet sufficiently detailed that they accurately model phenomena. Dealing with this can be nasty business. But it’s what is required if you want to really use mathematics.
And there are at least two good reasons why you should explore real-world applications of math. First, you like math, and applied areas are where you’ll get to see some really amazing mathematics. In the corridors of my department (a combined math and computer science department), there are 45 AMS “Mathematical Moments” posters. These fliers, which in some math departments should be considered false advertising, depict problems or research areas where math plays a fundamental role. Topics covered include robotics, speech recognition, cell biology, protein folding, and even crime solving. Of this (admittedly unscientific) sample, only three posters discuss problems that might be worked on by a pure mathematician—and one of these is solving sudoku. On the other hand, the topics mentioned on the other 42 posters are most likely examined by experts in the techniques of applied mathematics, statistics, or computer science.
The mathematical techniques most often mentioned on these posters include statistics, dynamical systems, graph theory, mathematical models, pattern recognition, image analysis, differential and partial differential equations, linear algebra, combinatorics, and optimization. As a mathematics major, you’re not likely to see most of these techniques, even if you pursue a math Ph.D., although ironically, your non-math friends might very well be introduced to the basics of very useful topics in linear programming, graph theory, probability, combinatorics, and game theory in the non-major courses they take to fulfill their math requirements for graduation.
The second reason you should take more applied courses is that you likely have an interest in technology, and you live in a technological society. You use a computer and cell phone, probably own an iPod (if not several), and are surrounded by devices that are controlled by microprocessors. And let’s be honest: you probably couldn’t exist without them. Do you want to graduate without having even a basic understanding of how these work? Moreover, you live in a world in which you are bombarded by statistics. It thus behooves you, as a more technologically inclined citizen, to understand enough statistics to be able to see what statistical results really tell us—and also how they can be used in misleading ways.
In case you are inclined to dismiss the opinions of a Dark Sider, then perhaps you will listen to the Mathematical Association of America Committee on the Undergraduate Program in Mathematics, which recommends in its 2004 curriculum guide that mathematics programs should promote learning that helps students better understand the uses of mathematics. This is a refreshing change from the historical norm where applied mathematics was often viewed as a debasement of the Platonic ideals of pure math, and undergraduate programs were designed for the less than 10 percent of students who might have the desire and talent to continue their studies at the graduate level.
So, if you are fortunate enough to be a part of a program that has opportunities for engaging the applied side of math, you’d do well to take advantage. I can assure you, it’s more fun on the Dark Side.
The money isn’t bad either.
About the author: Doug Szajda is an associate professor of computer science at the University of Richmond. He is currently general chair of the Internet Society Network and Distributed System Security Symposium.
Aftermath essays are intended to be editorials and do not necessarily reflect the views of the MAA.