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I read an interesting article earlier this year about the future of mathematics. It claimed that math research is possible in the United States because of service courses (especially calculus).

Calculus is by far the most common course taught at research universities, so their argument holds some water. It's hard to make this into one specific question, but here goes (feel free to suggest alternative formulations):

To what extent is the budget of a research department in the United States correlated to the number of students taking calculus each semester?

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I'm not sure what a complete answer would look like to this question, but since I know how to find the data for the University of Illinois at Urbana-Champaign, I'll answer for that school. Hopefully others will be able to answer in other ways or from other schools. The data I used is publicly available at http://dmi.illinois.edu/cp/, bless their hearts. Disclaimer: I worked there teaching calculus and advising undergraduates for three excellent years before moving on to a full-time teaching role at another school.


Summary of What Follows

I use publicly-available employment data to estimate the amount of math research that was done at University of Illinois from 2004-2013. Then I use publicly-available course data to estimate the amount of calculus taught on the same time period. If you don't care about the details of how my estimates happened, you can skip to the results.

The results section suggests that there has been a massive increase in calculus taught with no corresponding increase in math research done. The conclusion, which is essentially from my personal experience, is that an increased calculus population is much more likely to drive up class sizes and academic professional employment rather than lead to the hiring of many new math researchers.


An Estimate of the Amount of Math Research Done at UIUC, 2004-2014

I'll start with this chart of Full-Time Equivalent Employees of UIUC's Math Department, 2004-2014:

                        '13-14  '12-13  '11-12  '10-11  '09-10  '08-09  '07-08  '06-07  '05-06  '04-05
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Tenure Track            65.25   62.25   62.17   64.67   62.78   65.73   70.74   67.87   66.67   65.67
Visiting Faculty        9.00    9.75    8.50    4.00    3.00    2.00    7.00    6.50    5.00    9.25
Other Instructors       21.12   20.20   12.06   16.42   18.18   19.98   14.53   20.00   17.97   22.52
Academic Professionals  17.10   15.60   14.35   10.85   10.35   10.35   9.85    9.55    7.80    6.05
Teaching Assistants     69.56   66.88   64.60   64.80   69.69   66.55   63.79   65.30   61.52   60.07
Research Assistants     5.75    8.25    8.37    6.96    8.36    7.00    9.50    4.50    2.83    6.35
Civil Service Staff     10.75   9.75    10.19   9.75    9.75    9.75    9.75    9.75    9.75    9.25
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**Total**               199.53  193.68  180.23  177.94  182.11  181.86  185.16  183.47  171.91  179.16

The units here are "full-time equivalents." So a part-time employee working 28 hours per week would count as 0.7 FTE's toward their row. What you should notice is that there is a nearly-constant amount of math research being done, as best we can tell from this data: besides one outlier year involving a retirement policy, there have always been between 74 and 82 full-time-equivalents of math researchers employed by the department. I added the tenure-track faculty, visiting faculty, and research assistants to find an estimate of "math research done":

                        '13-14  '12-13  '11-12  '10-11  '09-10  '08-09  '07-08  '06-07  '05-06  '04-05
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Tenure+Visit+Research   80      80.25   79.04   75.63   74.14   74.73   87.24   78.87   74.5    81.27

An estimate of the amount of calculus taken at UIUC, 2004-2013

We can start with the number of Instructional Units taught by the math department. An instructional Unit is awarded when a student completes one credit hour of a math course.

                '13-14  '12-13  '11-12  '10-11  '09-10  '08-09  '07-08  '06-07  '05-06  '04-05
100 level               8119    9104    8751    9556    9940    10004   10901   12477   11695
200 level               46530   44647   41731   39170   38897   32870   29437   28964   25211
300 level               1486    1213    1192    1204    1234    3438    6363    6360    7024
400 level               13195   12165   10730   10648   9848    9360    9481    9043    9860
500+ level              5086    5138    5089    5055    4906    4806    5193    5591    5740
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Total                   74416   72267   67493   65633   64825   60478   61375   62435   59530

We are lucky in that the vast majority of the 200-level classes are calculus classes (exceptions are other "service courses" like Discrete Math, beginning Linear Algebra, and Differential Equations, which presumably fit under the same question anyway), and all of the calculus classes are 200-level, so the publicly available data is pretty good for our purposes: the row of 200-level data is almost exactly the "amount of calculus taught," in units of credit hours.


Results

Using the above methods, I arrive at the following estimates (no '13-14 data for courses yet, so drop it):

                                    '12-13  '11-12  '10-11  '09-10  '08-09  '07-08  '06-07  '05-06  '04-05
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Math Research (in FTEs)             80.25   79.04   75.63   74.14   74.73   87.24   78.87   74.5    81.27
Calculus Taught (in credit hours)   46530   44647   41731   39170   38897   32870   29437   28964   25211

Sorry about all the data being in reverse order; that's how it is on their website. At least my chart is in the correct order:

UIUC Estimates of Math Research vs Calculus Taught, 2004-2013


Conclusion

This is not a complete answer to the question of course, but at least for one research institution for the last ten years, you can see that there has been a massive increase (nearly doubling) in the amount of calculus taught over the past ten years, with no corresponding increase in the amount of employment for math researchers. This suggests that at least at this school, a possible future crash in the amount of calculus taught would also not have a corresponding disastrous impact on the amount of math research completed at the school.

Instead, calculus increases (at this school) were mostly handled by increased class sizes and by increases in the "Academic Professional" categories -- employees who are wonderful usually-full-time employees who are teaching calculus part-time and doing other things (advising, recruiting, careers, directing initiative) but not doing math research.


I welcome and wish for criticism on my methods and conclusions!

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  • $\begingroup$ A comment: If outside funding declines for research mathematics (e.g., the NSF experiences cuts in the United States) then one might expect Calculus enrollment to increase so as to make up for this. In particular, probably what is really needed is some account of where the mathematics department gets its money from: the number of employees is likely to stay pretty constant with respect to tenure. $ $ Still: Very nice, +1. $\endgroup$ – Benjamin Dickman Mar 26 '14 at 20:32
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    $\begingroup$ +1 for actual numbers, and not mere opinions! $\endgroup$ – Gerald Edgar Mar 26 '14 at 21:12
  • $\begingroup$ I would love to learn the reason that the 100 and 300 level classes have consistently shrunk in size while the 200 and 400 level have grown while the 500 level has stayed constant. I'm hoping there's an intuitive reason of which I am unaware. $\endgroup$ – David G Mar 27 '14 at 14:27
  • $\begingroup$ 100-level shrinking in size has to do with more of the incoming student population having a very good math background. This means fewer precalculus sections. For 300-level, I'm not sure. The main 300-level math classes are the probability for engineers and numerical methods classes. I guess the Electrical Engineers started teaching their own probability course... but I'm not sure if that is the cause. I don't have access to the more detailed data on which specific courses are increasing or decreasing, anymore. $\endgroup$ – Chris Cunningham Mar 27 '14 at 16:57

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