Abstract

Citation

Researchers should cite this work as follows:

• Stepien, T. L., Kostelich, E. J., Kuang, Y. (2023). 2020-Stepien_Kostelich_Kuang-Mathematics Cancer An Undergraduate Bridge Course in Applied Mathematics. SIMIODE, QUBES Educational Resources. doi:10.25334/666Q-NV56

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Description

This is an amazing article in support of a unique approach to an applied mathematics course based on the relationship between mathematics and cancer. We quote (extensively) from the article after we render the abstract.

Abstract: Most undergraduates have limited experience with mathematical modeling. In an effort to respond to various initiatives, such as the recommendations outlined in [S. Garfunkel and M. Montgomery, eds., GAIMME: Guidelines for Assessment & Instruction in Mathematical Modeling Education, SIAM, 2016], this paper describes a course on the mathematical models of cancer growth and treatment. Among its aims is to provide a template for a “bridge” course between the traditional calculus and differential equations sequence and more advanced courses in mathematics and statistics. Prerequisites include a course in ordinary differential equations. Linear algebra is a useful co-requisite but no previous programming experience is required. The content includes classical models of tumor growth as well as models for the growth of specific cancer types. Relevant research articles are provided for further study. Material for student projects and effective communication is supplied, as well as suggestions for homework assignments and computer labs. This paper aims to assist instructors in developing their own “Mathematics + Cancer” course.

Keywords: mathematical modeling, cancer, differential equations, undergraduate education

We quote from the Introduction of the paper.

"This paper describes an undergraduate course, accessible to students who have completed a standard sequence of calculus and ordinary differential equations, on the mathematical modeling of cancer. The content and format of the course are derived from the authors’ experiences in advising undergraduates in a program funded by the National Science Foundation’s Mentoring through Critical Transition Points (MCTP) initiative. Our objectives in developing this course are threefold. First, we are interested in providing a model of a “bridge” course between the traditional calculus sequence and higher-level courses besides the typical “introduction to proof” class. Second, our effort is an attempt to develop an introductory course in applied mathematics that addresses a compelling scientific and social problem. We motivate the relevant mathematical ideas at a level that is intelligible to a broad student audience and in a way that will help students make informed choices about more advanced courses in statistics, probability, numerical analysis, partial differential equations, and dynamical systems, for example. Our third goal is to adapt some of the pedagogical features of an undergraduate research experience—reading papers from the primary research literature, completing a collaborative project, and giving a talk—to a semester course format.

"Our course is also an attempt to respond to recent programmatic initiatives of professional mathematical societies, including those by the Mathematical Association of America’s (MAA) Committee on the Undergraduate Program in Mathematics (CUPM) and by the Society for Industrial and Applied Mathematics (SIAM) and the Consortium for Mathematics and Its Applications (COMAP). The 2015 CUPM Curriculum Guide to Majors in the Mathematical Sciences [90] makes four “cognitive recommendations” for overall programmatic goals, stressing students’ development of communication skills, ability to apply theory to applications, facility with technological tools, and “mathematical independence and experience [of] open-ended inquiry.” The Guidelines for Assessment and Instruction in Mathematical Modeling Education (GAIMME) report [39] by the SIAM and COMAP working groups discusses “transferable skills” that undergraduates can develop in the context of a modeling course, including identifying tractable questions, using reliable sources, working collaboratively, and communicating effectively. The Modeling Across the Curriculum report [24], which was funded by a National Science Foundation grant to SIAM for “an initiative to increase mathematical modeling and computational mathematics in high school and college curricula,” recommends developing accessible curriculum materials in addition to discussion of the modeling process.

"Furthermore, by providing students with a research experience during a regular class, we are able to reach a diverse group of students who may not otherwise have the opportunity to participate in, for example, a supported project of the National Science Foundation’s Research Experiences for Undergraduates (REU) Program [77]. Many REUs are inaccessible to minority, first-generation, and/or nontraditional students who, for financial, logistical, or child-care reasons, cannot attend an out-of-town program on a full-time basis for eight to twelve weeks. Our course represents an effort to provide a scalable, cost-effective alternative to a traditional REU. The enduring lessons the course aims to impress upon the students are similar to benefits students can obtain from participating in REUs: exposure to problem-solving experiences, awareness of STEM research fields and career options, and adding relevance to standard mathematics courses by applying theoretical knowledge to real-world cancer biology problems [72].

"A final objective of this article is to motivate further efforts to develop courses with analogous goals on topics drawn from other areas of the mathematical sciences. We hope that the outline presented here, and the supplementary materials, will serve as a useful template."