The trends are also very encouraging when we break enrollments out into four basic categories: Precollege (usually not for college credit), Introductory (including college algebra, precalculus, mathematics for liberal arts, and business mathematics), Calculus Level (including most sophomore courses including linear algebra, discrete mathematics, and differential equations), and Advanced (junior and senior courses). These numbers do not include enrollment in statistics courses.
Precollege courses rose only 4%, Introductory rose 22%, Calculus Level saw an increase of just over 30%, and Advanced course enrollments went up by almost 33%.
Most of the teaching of Precollege mathematics has shifted to two-year colleges, as the following graph illustrates. The category Other is dominated by elementary statistics, but also includes finite math, business math, math for liberal arts, and math for elementary teachers. Here, Calculus refers only to calculus courses, but includes Several Variable Calculus.
While Precollege mathematics continues to dominate 2-year college enrollments, accounting for over half of all the students in mathematics classes, its numbers rose by only 15%. Introductory enrollments rose by 14%, Calculus by 27%, and Other by 35%.
Parsing the data by type of institution, we see strong growth across undergraduate colleges (characterized as highest degree offered in mathematics is the Bachelor’s), comprehensive universities (highest mathematics degree is the Master’s), and research universities (which offer a doctorate in Mathematics).
The one disappointing bit of news is that the number of Bachelor’s degrees awarded by mathematics departments went up by only 6% over the past five years, from 14,611 to 15,499. These numbers include degrees in Operations Research, Actuarial Science, and joint degrees awarded by the mathematics department, but exclude degrees in Mathematics Education, Statistics, or Computer Science as well as degrees that might be considered mathematical science but were awarded by other departments. Here, there was a great deal of variation by type of institution.
At undergraduate colleges, the number of Bachelor’s degrees in Mathematics dropped by almost 9%, while it rose by 27% at comprehensive universities and by 14% at research universities.
This raises three obvious questions: Why have course enrollments risen so fast over the past five years? Why hasn’t this surge been reflected in increased numbers of majors in Mathematics? Why, despite the increase in mathematics enrollments, is the number of Bachelor’s degrees from undergraduate colleges moving in the opposite direction from the number at other types of institutions?
I believe that the answers to all three questions are related and are indicated by the pattern of intended majors of in-coming full-time students. These data are gathered by the Higher Education Research Institute at UCLA from most four-year undergraduate programs at the time of freshman orientation. They are reported annually in The American Freshman.
There is no mystery about what changed after 2007. As I reported in my Launchings column of a year ago, A Benefit of High Unemployment, there is a very high correlation between the economic situation as reflected in the unemployment rate and the attractiveness of scientific and technical majors.
The surge of students who have arrived in Mathematics departments because of the current economic downturn have not been with us long enough to significantly impact the number of majors. The fact that they are swelling enrollment not just in Calculus-level but also Advanced mathematics courses is an encouraging sign. It also presents a challenge for our departments to take advantage of this increased interest in Mathematics.
 Precise numbers are subject to final revision, but the adjustments should be small and the trends are clear.