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At midcentury it was not at all unusual for a mathematics department to have students of the physical sciences and engineering in its courses. But as the second half of the century proceeded, increasing numbers of students of the biological, management, and social sciences (BMSS) also required more mathematics. For example, the National Academy of Sciences (NAS) referred in 1968 to “the current explosive penetration of mathematical methods into other disciplines, amounting to a virtual ‘mathematization of culture.’” **[44****]**. That report also asserted that “Mathematics is also becoming an essential tool in the world of government, industry and business.”

John Kemeny and his Dartmouth College colleagues Laurie Snell and Gerald Thompson pioneered a "finite mathematics" text and course for a wide range of students, beginning during the 1950s. (Photo source: MacTutor Archive) |

J. Laurie Snell in about 2006. (Photo appears at the Chance website at Dartmouth College. Chance is a quantitative literacy course emphasizing probability and statistics. It was developed by a team led by Snell beginning in 1992.) |

Gerald L. Thompson in about 2006 (Photo provided to the MAA by Thompson in 2006) |

In fact, by the time of this 1968 NAS report, the mathematical community was already acting on this issue. In 1956, John Kemeny (1926-1992), Laurie Snell (1925-2011), and Gerald Thompson (1923-2009) wrote *Introduction to Finite Mathematics ***[23]**, intended for service courses for social science students, a category of courses that didn’t exist at the time. Interestingly, this work had no financial support or prestigious committee behind it. Before long, to the surprise of the authors, the Finite Mathematics course became a favorite of business faculty who were trying to add analytical rigor to their students’ programs. This serendipitous development had a huge effect on enrollments in the course. Data from the Conference Board of the Mathematical Sciences (CBMS) shows a rise from 1000 students enrolled nationwide in the fall term of 1960 to around 100,000 per fall term throughout most of the last decades of the 1950-2000 era.

Finite Mathematics included some internal motivation as well as the desire to serve social science students. For example, the authors were eager to write about linear programming, game theory, and aspects of graph theory, which were relatively new mathematics research developments at the time. See **[41]** for the detailed story of this course and the intellectual and organizational environments that gave rise to it. The second and third editions of *Introduction to Finite Mathematics* are available online from Dartmouth College.

Kemeny, Snell, and Thompson were well respected because of their appointments at Dartmouth, their Princeton backgrounds, and their association at Princeton with A. W. Tucker, who from 1948 onward was known for his work in optimization and game theory. But at the same time they were just three junior professors, not representing anyone’s thoughts but their own. However, by 1964, four years before the NAS report mentioned above **[44],** the prestigious Committee on the Undergraduate Program in Mathematics (CUPM, created by the MAA Board of Governors in 1953 as the successor to CUP **[13]**), speaking as a standing committee of MAA, issued a report which was forthright about the appropriateness of the very concept of service courses: “. . . special courses must be developed for biological, management and social sciences students” **[31, **p. 5**]**.

Sensitivity to the needs of students in the biological, management and social sciences went beyond realizing that the mathematics that had been provided for students in mathematics and the physical sciences and engineering was not exactly what BMSS students needed. There was an additional realization that many of these students would be unable or not motivated to take as much mathematics as traditional audiences in the physical sciences. For example, CUPM, in its 1964 report on mathematics for BMSS students recommended a presentation of single variable calculus of only 39 one-hour classes **[31]**. This undoubtedly gave impetus to the spread of one-term courses in calculus, sometimes called Calculus for Biological, Management, and Social Sciences or Non-mainstream Calculus. Nationwide enrollment in such courses at four-year colleges rose from being too negligible for CBMS to report in the Fall of 1960 to 115,000 in the Fall of 2000.

Similarly, in 1972, a CUPM statistics panel offered suggestions for a one-semester course in statistics with no calculus prerequisite [**27]**. From the Cajori Two Project **[40**] we can see that some schools had such statistics courses well before 1950, so CUPM was putting its blessing on a movement already underway. The blessing, and other merits of the case, worked: enrollments in such courses at 4-year colleges rose from 12,000 in the Fall of 1960 to 155,000 in the Fall of 2000.

The motivations for creating and promoting these service courses surely included a genuine interest by the mathematical community in matters external to mathematics and the physical sciences. An alternative motivation, the desire to increase mathematics enrollments, was probably present but only mildly: as we have shown, the service courses discussed here had roots well before the 60% plunge in numbers of graduating mathematics majors of the 1970s.

Walter Meyer (Adelphi University), "External Influences on U.S. Undergraduate Mathematics Curricula: 1950-2000 - Service Courses," *Loci* (August 2013)