Mathematics turned inside out: the intensive faculty versus the extensive faculty

Abstract

Research universities in the United States have larger mathematics faculties outside their mathematics departments than inside. Members of this "extensive" faculty conduct most mathematics research, their interests are the most heavily published areas of mathematics, and they teach this mathematics in upper division courses independent of mathematics departments. The existence of this de facto faculty challenges the pertinence of institutional and national policies for higher education in mathematics, and of philosophical and sociological studies of mathematics that are limited to mathematics departments alone.

Errors and Corrections in Mathematics Literature

“…The highest, or "mathematical", rigor is regarded as an obstacle to investigation [14]. 4 The issue of appropriate rigor cannot be excised from a discussion of mathematics by restricting the literature, because interdisciplinary mathematics largely develops in the allied fields [18], as, for example, the analysis of algorithms.…”

“…Olga Taussky [38, pp. [18][19] relates that David Hilbert's collected works were "edited" by very talented and very junior temporary workers. "Hilbert's work was not free from error of all magnitudes…We worked very hard on all this, but later even more errors emerged.…”

Mathematical prerequisites for non-STEM programs

“…Indeed, mathematics is employed by a variety of academic disciplines inside and outside of mathematics departments (Steen, 2001;Mulhern and Wylie, 2006;Alcock et al, 2008;Grcar, 2011;Laging and Voßkamp, 2017), so its paramount role in college access does not come as a surprise. However, some scholars question whether the same mathematics education is fitting for all majors (Steen, 2006;Bryk and Treisman, 2010; National Center on Education and the Economy, 2013; Logue, 2016) and suggest curricula which highlight the use of mathematics by a multiplicity of disciplines (The Mathematical Association of America [MAA], 2004; Saxe and Braddy, 2015;Parker et al, 2018;Transforming Postsecondary Education -Math, 2018).…”

“…Put bluntly: "The math pathway for students pursuing majors in the math-oriented disciplines is well established [i.e., from algebra to calculus], " but "many students in the social sciences, arts, and humanities, and those seeking careers in business, applied technologies, health sciences, and other fields, could be served just as well by another pathway" (Bryk and Treisman, 2010, no page). As a consequence, Grcar (2011) calls also for the involvement of university instructors who teach outside of mathematics departments in informing mathematics education: "their view of the mathematics skills needed by university students would appear to be relevant to K-12 education" (p. 712).…”

Education for Computational Science and Engineering

“…Second is, academic departments for mathematics or computer science do not serve as nuclei for CSE education. Elite mathematics departments in the USA shun interdisciplinary subjects [32,33,34]. Computer science departments do have interdisciplinary research interests, but mostly apart from CSE [35,36].…”