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.
Connecting with other Disciplines within a Mathematics Course
Project Intermath (also discussed in Part 1, Section 3) ’is a consortium of eight schools and four additional associated schools led by the United States Military Academy at West Point. Interdisciplinary activities included in this initiative are centered around the process and use of Interdisciplinary Lively Applications Projects (ILAPs), small-group projects developed by faculty and experts from more than one discipline [with the aim of promoting] reform through ILAP production, curriculum design, and conferences and workshops [in the belief] that the process of developing and the classroom use of these ILAPs generate the communication, involvement, and connections needed to effect educational change.â? Information on the project website includes complete texts for over 40 ILAPs developed at the United States Military Academy site.
A grant from the Fund for the Improvement of Postsecondary Education (FIPSE) to Allegany College enabled mathematics faculty to sit in on various health courses and for faculty from health career programs to sit in on either college algebra or one of the developmental mathematics courses. These faculty members also obtained information about each others’ disciplines from classes, class notes, books, tutoring, student assistants, software, videotapes, and from health professionals. Faculty members scheduled meetings to share important concepts and applications as they revised the developmental mathematics curriculum. Instead of simply adding applications to the existing developmental mathematics curriculum, this program changed the basic structure of the curriculum.
Deborah Nolan and Terry Speed, University of California at Berkeley, Department of Statistics, developed a course and accompanying text (Stat Labs) to teach undergraduate upper-level mathematical statistics through the use of in-depth case studies or ’labs.â? The labs include datasets and are designed to raise scientific questions that are interesting in their own right and serve as starting points for developing statistical theory. The course is taken by mathematics, statistics, engineering and computer science majors. The prerequisites are single and multivariable calculus and a semester of probability.
Victor Donnay, Bryn Mawr College, whose research specialty is chaotic dynamical systems, collaborated with a colleague in geology to teach differential equations. Donnay used one of the geologist’s programs, based on the logistic model, to simulate the fishing industry, and arranged for the geologist to give a guest lecture. Donnay and his students developed several innovative projects, now posted on the Internet, designed to bring mathematics to a wider audience in interesting and understandable ways. One of their projects, a five-minute video on’The Topology and Geometry of the Costa Surfaceâ?, is on permanent display at the Maryland Science Museum.
Allan Broughton, Rose-Hulman Institute of Technology, teaches a course Methods of Image Processing in which he introduces mathematical background in image processing, in particular: vector and matrix models of signals and images; filtering and convolution, various transforms such as the Fourier; discrete cosine transform, windowed Fourier transforms; and filter banks and the discrete wavelet transform and applies mathematical methods to solve problems in image processing in particular data and image compression. He gives students challenging problems, which they must analyze and explain and, in some cases, prove carefully. Broughton and Edward R. Doering (from the electrical and computer engineering department) gave a presentation about the course in a 1999 MAA meeting.
Mathematical modeling courses often involve cooperation between mathematics faculty and faculty from other departments. The following links offer examples of syllabi for modeling courses:
Mathematical Modeling (Sr. Barbara E. Reynolds, Cardinal Stritch University)
, Mathematical modeling (John Bukowski, Juniata College)
’ Click on ’Example Syllabusâ? next to the course description, Mathematical Modeling (Jeff McGough, South Dakota School of Mines and Technology)
, Introduction to Mathematical Biology (Trachette Jackson, University of Michigan), Quantitative Models of Biological Systems (Russell Jackson, Brown University), Introduction to Discrete Mathematical Models (Erich Kaltofen, North Carolina State University, Mathematical Modeling in the Environment (Sarah Glaz, University of Connecticut).
Additional examples of connecting with other disciplines within a mathematics course are in Part 1, Section 2 and in Part 2, Sections A.1, A.2, and B.1.
Working with colleagues in mathematics, biology, and geology and environmental science, and with support from the National Science Foundation, Janet Anderson of Hope College developed a sophomore-level general education mathematics course, Mathematics in Public Discourse, tied to two science courses: The Atmosphere and the Environment and Populations in a Changing Environment. Some of the materials are available at Group Assignments for GEMS 100.
The course Patterns in Poetry and Mathematics is a cross-disciplinary course taught at Rochester Institute of Technology. Developed and team-taught by Professor Marcia Birken of the Department of Mathematics and Statistics and by Professor Anne Coon of the Department of Language and Literature, the course explores the patterns found both in poetry and in mathematics, as well as the creative and expressive uses of analogy. The instructors examine both disciplines by addressing topics such as patterns and symmetry, proof and contradiction, fractals, and infinity. Students read primary texts from mathematics and poetry, as well as writings in which poetry and mathematics are discussed in terms of or in relation to each other.
The University of Puget Sound offers a year-long course, Integrated Physics and Calculus that is team taught and meets eight hours per week. The goal of the course is to increase student understanding by synchronizing related topics in calculus and physics and to clarify differences in terminology, notation, and style between the two subjects. The prerequisite is an understanding of the fundamental ideas of first semester calculus.
Quantitative Reasoning at DePaul University was developed by faculty in mathematics, the natural sciences, computer science, psychology, and communications and is regularly taught by faculty from all these departments. The goal of the course is to address the growing need for quantitative and computer literacy in the face of an enormous expansion in the use of quantitative methods and information in the social and physical sciences as well as daily life.
In 1970, the Worcester Polytechnic Institute (WPI) faculty developed a program called the WPI Plan. It eliminated required classes and substituted a project-based curriculum in which students, guided by their advisors, design their own programs to suit their interests and aspirations. Students engage in three significant independent projects, usually completed in teams, which challenge them to identify, investigate, and report on open-ended issues. One is a project intended to synthesize knowledge in the student’s major; the second examines how science and technology interact with societal structures and values; and the third is a project in the humanities and arts on how knowledge is obtained and expressed in a non-technical discipline. Many of these projects are sponsored by corporations, government agencies, professional societies, and nonprofit organizations, both in the United States and around the globe.
The Interdisciplinary Science Program (ISP) at Rensselaer Polytechnic Institute is intended to provide an education in the sciences for students whose interests range outside the traditional disciplines and career paths. The introductory courses recommended in these programs are the same as those recommended for departmental science majors. However, the deep undergraduate concentration in a single science area that is characteristic of departmental majors is replaced by a broader coverage of science areas and also by a greater choice of courses, including nonscience courses. Students vary their programs to emphasize preparation for their own particular professional objectives.
The Interdisciplinary Science Program (ISP) at Trinity College is a non-major curricular program designed to broaden and enrich the study of science and mathematics by exploring both the links between the various scientific disciplines and their connection with the external world. Designed and supported by faculty in Biology, Chemistry, Computer Science, Engineering, Mathematics, Neuroscience and Physics, the core of the ISP consists of a team-taught seminar and a research apprenticeship, both in the first year, and a course investigating the impact of science and technology on public policy.
The mission of the Carleton Interdisciplinary Science & Math Initiative (CISMI) is to promote and expand the inquiry-based study of complex and integrated systems, drawing on the power of disciplinary perspectives. The program includes curriculum development of multi- and interdisciplinary learning experiences, faculty learning and collaboration, and disciplinary and interdisciplinary student-faculty research.
The Foundation Coalition (FC), funded by the National Science Foundation, ’was established as an agent of systemic renewal for the engineering educational community.â? They describe their mission as ’curriculum integration and inclusive learning communities: helping students make connections between various disciplines and between academic topics and lifelong careers and helping them to build learning relationships with other students ... FC partner campuses have restructured their curricula, renovated or built new classrooms, and created faculty development projects. Most projects have focused on the first two years, the foundational years, of the engineering curricula. Now, the FC is creating resources to assist campuses that are engaged in their own efforts to improve their learning environments and curricula.â?
Project Links, based at Rensselaer Polytechnic Institute, is one of several projects funded by the National Science Foundation dedicated to linking the concepts of higher mathematics to real-world applications in other disciplines. Instructors use interactive web-based modules in the classroom to engage students in guided learning about applications in science and engineering to provide them with concrete experiences unavailable in traditional lecture or textbook lessons. The modules are designed so that their use can be extended to other institutions.
The goals of the Mathematics Across the Curriculum project at Dartmouth College are to (1) Make mathematics welcome and even indispensable across the entire curriculum, (2) Motivate students to take mathematics seriously, (3) Broaden the diversity of those undergraduates enrolling in math or science courses, (4) Increase the ability of students to approach data in a mathematical manner, and (5) Increase the ability and willingness of students to use mathematics they already know to facilitate their understanding of other subjects and to draw upon other subjects to improve their mathematics, (6) Stem the flow away from science and math of students with talent and ability, and (7) Make the methods and materials designed to further these goals available, accessible and outright friendly to the broad national audience of faculty in undergraduate institutions. In its first four years the project created sixteen new courses and influenced another thirteen.
At Carroll College, one of the Project Intermath sites, mathematics majors are required to complete a concentration in a cognate field. Students may select from biology, business and economics, chemistry, computer science, engineering, environmental science, or secondary education, or they may work with an advisor to develop an individual plan based on their interests.
Additional information and resources on promoting interdisciplinary cooperation are in Part 2, Sections B.1 and C.5.