It is, therefore, especially troublesome that Princeton introductory math courses are consistently among the most dreaded classes taken by undergraduates. Many students — usually engineers, pre-med or pure science concentrators — need these math courses for their degree. As a result, introductory math courses are the only exposure to pure mathematics that these Princeton students will receive. Many of these students had splendid relationships with math in high school, defined by competence rather than fear — a relationship that is shattered during their first semester on campus. This reality is bad for both students and the math department, which is then forced to teach droves of disgruntled and often confused undergraduates.
I believe that there are solutions to this problem, one of which is a restructuring of the introductory math courses as follows: MAT 101, 102, 103, 104, 201 and 202, which constitute the majority of math classes taken by undergraduates, would be broken down and cross-listed with other departments. Instead of the one-size fits all model that we currently have, we could have courses such as MAT/CHM 103-104: Mathematics for Chemists or MAT/SOC 105-106: Mathematics for Sociologists. The former would focus more on topics such as the calculus underlying the kinetic theory of gases while the latter would look at various statistics tests that one might use for data gathered from surveys. The syllabi for these courses would be redesigned in such a way that the course would still be principally mathematical but would use the other subject to inform and contextualize the math.
With this system, students could learn about math in context, something that I feel is critical for its appreciation. Instead of being faced with ethereal proofs and astoundingly hypothetical situations, students could see the direct application of the math they are learning to something in which they’re interested. This type of side-by-side learning would help to put math in perspective and demonstrate its significance to students, at the same time helping them realize that math isn’t an intimidating and daunting beast that needs to be feared.
I believe this cross-listing would also leave students with a better grasp of math than would the current system. People learn through association and application, so seeing the applications of the math that you are learning while you are learning it will help you understand it better. At the moment, I feel that a lot of students immediately forget everything that they’ve learned about calculus or linear algebra right after the semester ends. This forgetting isn’t because the math is not important, but because they haven’t connected it in any meaningful way. And when we don’t form these visceral associations, our chances of retention fall precipitously.
We can already see this model being used on campus. The Integrated Math, Engineering and Physics sequence, for example, teaches math and physics side by side with an emphasis on engineering problems that require math to solve. ECO 200: Advanced Principles of Economics is an economics course that teaches undergraduates the higher math that will be relevant to their studies. While some people still struggle with math regardless of the manner of instruction, I find that people tend to like these courses better than the current introductory math courses because they can see the relevance.
To be sure, this restructuring would only apply to the introductory courses that I’ve mentioned. There is no need to change more advanced introductory courses such as 203, 204 and 214. These courses tend to draw those students who are already interested in pure mathematics, so the proposed overhaul wouldn’t affect that core of the math department at all. Its express purpose would be to improve the math experience for non-concentrators.
Princeton offers so many avenues of growth and improvement to us during our stay here. We become better writers, better researchers, better friends and so much more. It would be a shame for Princeton graduates to not have felt that they became better mathematicians as well. Math is too crucial a form of communication to let it slip through our fingers.
Nathan Mathabane is a sophomore from Portland, Ore. He can be reached at nmathaba@princeton.edu.
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