Carl Cowen - Actuarial Science Program at Indiana University–Purdue University
If you think about the history of science, mathematics sits in a unique position: everything that has ever been true in mathematics is still true! We no longer believe that the elements are Earth, Air, Fire, and Water, for example, but Euclid’s description of geometry in the plane is still correct. Modern physics rests on developments from the late 19th century onward, with recognition that Newton’s discoveries provide a working foundation. Modern chemistry is largely a 20th-century science, and molecular biology starts with the discovery of the role of DNA in the mid-20th century. A fundamental difference between undergraduate education in mathematics and that of the other sciences is that we (mostly) take students to the early 20th century or so while the other sciences take students to the research forefront.
As an example, a few years ago I taught a course on computational neuroscience for juniors and seniors with a mathematical background or a biological background (prerequisites: two semesters of calculus for biology students; differential equations for math students; and at least junior standing in a mathematics, statistics, engineering, or biological sciences major. Note that no biology prerequisites were asked of the math students). During the semester, we read a research paper from 1988. The math students were astonished: they mostly had never seen a research paper, or if they had, they had never seen one that new! The biology students were also astonished: they had seen many research papers, but they had never seen one that old!
Thus, our science colleagues have a quite different perspective on undergraduate and graduate education than we do. A Ph.D. in chemistry at Purdue University requires two (two!) classroom courses, and the rest is research. A Ph.D. in mathematics usually includes 10 to 15 classroom courses! My own opinion is that the study for the Master of Science degree is the most intensive learning experience in the mathematical sciences. Much more mathematics is learned than at the undergraduate level because the study is so much deeper, and more is learned than at the Ph.D. level because there the learning is specialized and research focused. Thus, first and foremost, I regard the M.S. as the time when students acquire a broad and deep understanding of mathematics.
Further, most of the master’s program is devoted to studying late 19th-, 20th-, and 21st-century mathematics. Indeed, an M.S. program should put a student close (say 1950s–1970s era) to the research forefront in at least one area. Most M.S. programs include Ph.D. qualifier courses. This is fundamental, broad, and deep material in comparison to undergraduate work.
As a profession, we put too little emphasis on the M.S. and give it too little respect. We should be encouraging many more of our undergraduate students to go to graduate school and get an M.S. degree. Mathematics faculty are good at encouraging the “best” students to go to graduate school, but we should be encouraging the top third of our students to go on—they are surely qualified for the experience and would benefit greatly from the added education.
Moreover, the job surveys I’m familiar with suggest that the M.S. is the most marketable degree in the mathematical sciences. This is a consequence, I believe, of the fact that M.S. students know much more mathematics than undergraduates and are less likely than Ph.D.s to be “distracted” by research interests (in the minds of those who are looking for mathematical expertise in filling job openings).
There are several important career paths for M.S. degrees. The M.S. in statistics is the professional degree for a statistician. As I understand it, except for specialized areas such as the pharmaceutical industry where the Ph.D. is preferred, most “working” statisticians have an M.S. in applied statistics or biostatistics. The two-year college faculty member in mathematics is usually expected to have a “plain vanilla” M.S. in mathematics with enough statistics background to be able to teach beginning statistics courses. Both of these career paths are full of opportunities!
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About the author: Carl Cowen is professor of mathematical sciences and director of the Actuarial Science Program at Indiana University–Purdue University at Indianapolis. He is a former president of the MAA. Email: firstname.lastname@example.org