Math department figures out new (course) numbering system

As of this year, “Math 6A” and “Stat 2,” among other course numbers, have no meaning. In fact, all first- and second-year math courses have been renumbered for the 2005-2006 school year and thereafter, if not revamped content-wise. The former Calculus II series (Math 6A, B, C, D) of half-semester courses has been completely abolished. In its place are full-semester courses that offer comparable material to that of popular combinations of the Math 6 courses.

Professor Stephen Maurer, Math/Stat department chair, explains the changes by pointing out the history of first-semester calculus (Math 15, the course formerly known as Math 5) at Swarthmore. At one time, calculus was taught in colleges only, and was the standard beginning of science majors. The course itself as taught on campus has not changed much since then; however, secondary education has.

Today, because of AP and other forms of advanced credit, most students interested in a natural science major placed out of first-semester calculus (and often half a semester more, justifying the division of Calculus II into halves); therefore the students who ended up in Math 5 were those with either a weak or no calculus background, who often were leaning more towards social science-related majors. The manner in which the course was taught, that is, stressing technical proficiency, became rather inappropriate for its attendees.

Hence, out with Math 5 and in with Math 15. The textbook used is an example of the math department’s new focus for the course. “We’re using ‘Applied Calculus’ [Hughes-Hallett, et. al.], which is less heavy on the algebra and offers more in the way of biology and social science examples,” said Professor Maurer.

As for the old Calculus II series: “It was hard to explain to other departments and students what we were doing,” the professor offers, “and while you could mix and match courses to suit you, there was an administrative concern of professors having to give twice as many exams and keep twice as many grades. More importantly, Math 6B was a whole half-semester devoted to just sequences and series, whereas if the calculus courses were semester-long, the professor could use another week or so for 6A material…the instructors were pedagogically constrained.”

The solution? Students placing into Math 6 could take it as Math 6AB, the complete Calculus II semester, or 6AC, skipping sequences and series and going on to non-major-track multivariable calculus, or 6BD, which exposed them to an unfamiliar topic in mathematics chosen by the professor.

The difference now is that the department offers one combined course roughly corresponding to each of those options: Math 25 (Math 6AB) takes students through second-semester calculus up to an introduction to differential equations. Math 6AC is like Math 23, a survey course through single- and multivariable calculus, and Math 6BD “is more like 6BE,” comments Maurer, “because instead of some variable topic it will mostly cover differential equations.”

The new numbering system (a project that will continue next year with the upper-division courses) stemmed from the changes to Math 5 and 6 as well as the misleading state that the old system was in. For example, Topics in Algebra, number 48, can be taken around the same time as Introduction to Modern Algebra, Math 49. However, while Introduction to Real Analysis is Math 47, one will not find the analogous Topics in Analysis for the next two pages in the course catalog, as Math 85.

“It made Math 85 seem super-advanced compared to Math 47, which is not necessarily the case,” Maurer says. There is hope that these changes will be better for students and faculty alike in the future. For the time being Professor Maurer shares this amusing story: “About three years ago Haverford switched to half-semester courses— they saw what we were doing and said, ‘Hey, that’s a great idea.’ They were pretty shocked when they heard that we were changing our system.”


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