Calculus Sequence

Calculus Sequence

Math 135, Applied Calculus, is Macalester’s revolutionary new introductory course designed specifically for students interested in the natural and social sciences.  “Revolutionary” might seem an overly strong word for a calculus course.  After all, introductory calculus has been taught in something like its present form for more than 200 years.  But times have changed.  A wider range of students --- biologists, geologists, economists --- need strong calculus skills. 

Traditionally, introductory calculus was intended to lead students into more advanced courses --- Calc III, Differential Equations, Linear Algebra --- a sequence designed to serve physics, math, engineering, and chemistry students.  The topics in those courses are still extremely valuable, indeed the foundation of much of science.

The problem has been that most students who start in Calc I never go on to take the more advanced courses.  These students never have a chance to see the powerful ways that calculus and linear algebra topics inform the study of the natural and social world.  At many schools these students are taught symbolic manipulation techniques that they will never use again.

And increasingly Macalester students who will go on to take the advanced courses have already had a introductory calculus course in high school. 

Applied Calculus has been designed specifically to give introductory students the “advanced” skills needed for productive work in the sciences and statistics, topics such as functions of multiple variables, modeling techniques, the geometry of high-dimensional spaces. This is not just a matter of moving faster through the traditional material, but fundamentally rethinking what topics are essential.  Figuring out how to teach the new topics at an introductory level has been a 4-year project involving Macalester professors Kaplan, Halverson, Saxe, and Flath.  The project, which has attracted national attention, was supported by a grant from the Howard Hughes Medical Institute.

The change has important consequences.  In the past, entering students with high-school work in calculus (AP, IB) were advised to take Calc II. Although Calc II is an excellent class for teaching mathematical reasoning, many of the topics most useful to scientists--both natural and social scientists--are multivariate and not included in a traditional Calc II course.  With the new system, entering students are now encouraged to take MA 135, Applied Calculus, even if they have had substantial work in high-school calculus.  The one exception---particularly relevant to math, CS, physics, and chemistry majors---are students who expect to continue on to Calc III or beyond.  These students are encouraged to take either MA 137, Single Variable Calculus, or go directly into MA 237, Calculus III, or one of our other advanced courses.  The key idea is that all students who take calculus at Macalester will have had a solid exposure to multi-variable topics.

So, if you are at Cafe Mac or Dunn Brothers and run into a first-year biology or economics student talking about subspaces, don't be surprised.  This is just an ordinary student taking an introductory Macalester mathematics course.