@article{049ee53af95e4d819810a80874a2e694,
title = "Mathematics + Cancer: An Undergraduate {"}bridge{"} Course in Applied Mathematics",
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 Mathemat-ical 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 corequisite but no previous pro-gramming 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 = "Cancer, Differential equations, Mathematical modeling, Undergraduate education",
author = "Stepien, {Tracy L.} and Kostelich, {Eric J.} and Yang Kuang",
note = "Funding Information: Acknowledgments. Much of the course content is derived from the authors{\textquoteright} experiences in mentoring undergraduate students as part of the National Science Foundation Mentoring through Critical Transition Points program under grant DMS-1148771. Funding Information: Our course is also an attempt to respond to recent programmatic initiatives of professional mathematical societies, including those by the Mathematical Association of America{\textquoteright}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{\textquoteright} 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. Funding Information: 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{\textquoteright} experiences in advising undergraduates in a program funded by the National Science Foundation{\textquoteright}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 prob- Publisher Copyright: {\textcopyright} 2020 Society for Industrial and Applied Mathematics Publications. All rights reserved.",
year = "2020",
doi = "10.1137/18M1191865",
language = "English (US)",
volume = "62",
pages = "244--263",
journal = "SIAM Review",
issn = "0036-1445",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "1",
}