Probability and Statistics in the Core Curriculum

Mathematics is distinguished from most other sciences by a lack of consensus on the content of an introductory overview for potential majors and other serious students. Chemists offer Chemistry 101–102, typically an introduction to the major branches of chemistry. We traditionally offer a year of calculus, followed in the second year by more calculus and perhaps some differential equations and linear algebra. This is hardly a balanced introduction to the nature and variety of mathematics. Attempts at reform have been common, and so has their failure. Table 1 shows one current reform proposal, the contents of a version of “Mathematics 101–102” developed with NSF funding (COMAP, 1997). There is no calculus, which is left for the second year. There is also no statistics, though probability does appear. The absence of statistics in “Mathematics 101–102” should attract comment. After all, CUPM recommended in 1981 that “other mathematical sciences courses, such as computer science and applied probability and statistics, should be an integral part of the first two years of study.” (See Steen 1989, page 5.) This suggestion has generally brought agreement in principle (though little action). I want to offer a partial disagreement in principle. I will argue that, whatever the merits of “Mathematics 101–102,” its authors have done the right thing about probability and statistics. They have included the first and omitted the second. To my taste, they would have done well to exercise the same rigor with respect to computer science, in exchange for some continuous mathematics in the first college year. The point is this: a mathematics core ought to display to students the nature and variety of mathematics, including its applicability, but is not the place to develop the principles of related fields. Probability has an important place within mathematics. Statistics does not, and an attempt to include it will be disruptive.