David M. Bressoud June, 2005
Recommendation 4: Promote interdisciplinary cooperation
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Mathematical sciences departments should encourage and support faculty collaboration with colleagues from other departments to modify and develop mathematics courses, create joint or cooperative majors, devise undergraduate research projects, and possibly team teach courses or units within courses.
Does mathematics belong among the sciences? Gauss called it the queen of the sciences, but that phrase suggests a separation, that we could see ourselves above other disciplines, a rarified study that is to be undertaken for its own sake. I doubt that this is what Gauss meant, but G.H. Hardy was a great proponent of this view, and it has governed the attitude of many undergraduate programs in mathematics. It grew from earlier priorities of the research community.
In the mid-nineteenth century, mathematics was confronted
with serious foundational problems in analysis and in geometry. These difficulties
had their genesis in practical problems, and the solutions would have practical
applications, but their resolution was accomplished through introspection. Through
much of the twentieth century, this introspection was exceedingly fruitful,
so much so that it spread throughout the entire mathematics curriculum, reaching
its high-water mark in the 1960’s with the New Math, guided by the principle
that all students needed to understand set theory before they could do real
mathematics.
A sea change in the research community began in the 1970s. I like to date it
from Freeman Dyson’s Gibbs lecture of 1972 “Missed Opportunities”
[2]. Dyson illustrated how the mathematical community had
missed opportunities to do exciting, challenging, and important mathematics
because of its reluctance to look outside itself for good problems. Inspirational
as Dyson may have been, the change was driven by the shortage of jobs in pure
mathematics, the explosion of research in the biological and natural sciences,
and the introduction of massive computational power. Classically trained mathematicians
broadened their job prospects by retraining in computer science, statistics,
biology, and many other fields where, to their surprise, they found interesting
mathematical problems that needed to be solved. Throughout the sciences, but
especially in the biological sciences, many of these problems were created by
the need to make sense of massive sets of newly available data.
Almost a third of a century after Dyson’s challenge, Eric Lander gave a comparably stirring Gibbs lecture on “Biology as Information” [4]. Lander received his PhD in mathematics from Oxford University, added expertise in biology, and became a leader of the Human Genome Project. As he explains, many of the most important biological problems are mathematical and call for the creation of new mathematics. John Ewing, Executive Director of the AMS, has echoed this in identifying biology as “the next big thing in mathematics” [3].
This new research focus is struggling to make its way into the undergraduate curriculum. Few existing undergraduate programs prepare mathematicians, biologists, or computer scientists to work in mathematical or computational biology. One of the greatest opportunities and challenges facing the mathematical community is to work with biologists and computer scientists to figure out how to meet this need.
It is a great opportunity in several respects. Meeting it shows to the academy as well as to our students that mathematics is central. It demonstrates the critical importance of mathematics even to the biological sciences, often viewed as a field where scientists who are math averse could take refuge. Meeting it also enables us to tap into the vast reservoir of majors in the biological sciences, encouraging and enabling them to study more mathematics.
The challenges are no less real. Biology majors, especially those in pre-med programs, have little room for additional courses. Biology programs will not require additional mathematics for its own sake. In fact, none of the traditional mathematics courses, as currently constituted, really meet the needs of most biology majors. In a workshop of biologists held for CRAFTY’s Curriculum Foundations Project at Macalester College in 2000 [1], biologists agreed that their students need less calculus, more modeling, more linear algebra, and much more statistics, all of which should be delivered in two semester-long courses. Macalester is one of several colleges that have responded to this challenge with a total restructuring of its calculus and statistics courses.
The other piece of the challenge is to put in place faculty who can foster and support such an interdisciplinary approach. Too often, programs that span mathematics and biology are the exclusive preserve of one biologist and one mathematician who have each made a stretch to establish a connection that will break as soon as either tires. The problem is not just a shortage of scholars with suitable training. We must also overcome institutional obstacles to the accommodation of those individuals who bridge the disciplines.
Fortunately, there is now intense focus on the development of programs that connect biology and mathematics. NSF has established its Interdisciplinary Training for Undergraduates in Biological and Mathematical Sciences (UBM) program [6] under the joint auspices of Education and Human Resources (EHR), Biological Sciences (BIO), and Mathematics and Physical Sciences (MPS). The National Research Council of the National Academy of Science issued its interdisciplinary recommendations in Bio 2010: Transforming Undergraduate Education for Research Biologists [5]. This year the MAA published Math & Bio 2010: Linking Undergraduate Disciplines [7]. This report, edited by Lynn Steen, is an outgrowth of the 2003 conference “Meeting the Challenges: Education across the Biological, Mathematical and Computer Sciences.” It details the challenges and opportunities to which I have alluded and points to a wealth of materials and resources as well as programs that are working.
Today, the mathematical research community finds much of its inspiration in problems that arise in other disciplines. Eventually, this will force changes to the undergraduate curriculum. They are changes we should welcome and embrace. The biological sciences do not provide our only opportunities for interdisciplinary cooperation, but they are some of the most important. The challenges and difficulties are real, but we ignore this opportunity at risk to ourselves and to the futures of our students.
[1] Dilts, Judy and Anita Salem, Biology report, pages 15–17
in The Curriculum Foundations Project, William Barker and Susan Ganter,
editors, Mathematical Association of America, Washington, DC, 2004. www.maa.org/cupm/crafty/cf_project.html
[2] Dyson, Freeman, Missed Opportunities, Bulletin of the
AMS, 78 (1972), 635–652.
[3] Ewing, John, The Next Big Thing in Mathematics? Biology,
The Chronicle of Higher Education, September 20, 2002. chronicle.com/prm/weekly/v49/i04/04b00401.htm
[4] Lander, Eric, Beyond the Human Genome Project: Biology
as Information, pages 42–57 in Genes and Genomes: Impact on Medicine
and Society, Columbia University, 2003, c250.columbia.edu/genomes/
[5] National Research Council, Bio 2010: Transforming Undergraduate
Education for Research Biologists, National Academy Press, Washington,
DC, 2003. www.nap.edu/catalog/10497.html?onpi_newsdoc09102002
[6] National Science Foundation, Interdisciplinary Training
for Undergraduates in Biological and Mathematical Sciences, www.nsf.gov/pubsys/ods/getpub.cfm?nsf04546
[7] Steen, Lynn Arthur, editor, Math & Bio 2010: Linking
Undergraduate Disciplines, Mathematical Association of America, Washington,
DC, 2005. www.maa.org/mtc/projectreport.html
Do you know of programs, projects, or ideas that should be included in the CUPM Illustrative Resources?
Submit resources at www.maa.org/cupm/cupm_ir_submit.cfm.
We would appreciate more examples that document experiences with the use of
technology as well as examples of interdisciplinary cooperation.
David Bressoud is DeWitt Wallace Professor of Mathematics at Macalester College in St. Paul, Minnesota, he was one of the writers for the Curriculum Guide, and he currently serves as Chair of the CUPM. He wrote this column with help from his colleagues in CUPM, but it does not reflect an official position of the committee. You can reach him at bressoud@macalester.edu. |