This article was downloaded by: [Dr Brian Winkel] On: 19 November 2014, At: 04:59 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/upri20 Introduction to the Special Issue: Application Activities to Enhance Learning in the Mathematics-Biology Interface Gerald Kobylski & Brian Winkel Published online: 16 Feb 2010. To cite this article: Gerald Kobylski & Brian Winkel (2010) Introduction to the Special Issue: Application Activities to Enhance Learning in the Mathematics-Biology Interface, PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 20:2, 91-94, DOI: 10.1080/10511970903484280 To link to this article: http://dx.doi.org/10.1080/10511970903484280 PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the Content ) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content.
This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions
PRIMUS, 20(2): 91 94, 2010 Copyright # Taylor & Francis Group, LLC ISSN: 1051-1970 print / 1935-4053 online DOI: 10.1080/10511970903484280 Introduction to the Special Issue: Application Activities to Enhance Learning in the Mathematics-Biology Interface* INTRODUCTION Gerald Kobylski and Brian Winkel In his address to the 2006 Mathematics Biology Conference held at West Point, Dr. Ben Cole, the then Technical Director for the National Security Agency and a former Distinguished Visiting Professor in the Department of Mathematical Sciences at the United States Military Academy (USMA) at West Point, stated that In 2075, when historians look back upon the opening decades of the twenty-first century, they will remember it as the dawning of the Age of Biology. Mathematics will play as important a role in this new age as it has in all the previous ages of technology that preceded it. The contributions of mathematics to biology are now being realized, but general awareness of where mathematics will have its most important impact is still limited. During the same conference, BG(R) Chris Arney, currently Professor of Mathematical Sciences, West Point, and a former Chair of the Department of Mathematical Sciences at West Point, stressed the following: * We present a collection of some of the papers offered by authors from this project and in future issues we will present other papers from the project. The views expressed herein are those of the author(s) and do not reflect the position of the United States Military Academy, the Department of the Army, or the Department of Defense. Address correspondence to Gerald Kobylski, Department of Mathematical Sciences, United States Military Academy, 646 Swift Road, West Point, NY 10996, USA. E-mail: Gerald.Kobylski@usma.edu
92 Kobylski and Winkel The science of biology has been important throughout life s existence; yet as we enter the 21st century it has stepped to the forefront of significance in our world. In particular, several subjects in the life, behavioral, information, and social sciences with significant mathematical content (e.g., evolutionary biology, genomics, bioinformatics, intracellular imaging, complex disease modeling, neuroscience, neuroinformatics, psychology, economics, cultural geography) appear to be involved in many of the capacious social issues and technological needs of our society such as public health, disease control, biowarfare, biotechnology, bio-inspired science, robotics, information overflow, network saturation, nanotechnology, and stem cells. This makes biology pervasive in the major challenges and opportunities to advance and sustain our world. The growing infusion of mathematics (modeling and inquiry) into biology and related subjects will transform the life, behavioral, and social sciences during the future years. This transformation will have profound effects on the links between mathematics and biology and these links must be encountered in the education of our students. When awareness of the emerging age of biology is coupled with the fact that learning mathematics in an interesting new and different context improves student motivation and results in better comprehension, we have a rationale for offering materials to help create the interface between biology and mathematics. Our goal in this collection of activities is to present mathematical applications in an arena unfamiliar to most students, biology. Certainly, learning mathematics in the context of any number of applications would be equally effective. However, we believe that biology is an important area of focus for our students for reasons in addition to those mentioned above. The National Research Council Bio 2010 [1] and Mathematical Association of America Math & Bio 2010: Linking Undergraduate Disciplines [2] reports also highlight the need for both undergraduate biology and mathematics educators to include significantly more of each others disciplines in their curricula. The biology activities that are offered in this publication further support advances in the core mathematics program at West Point as well as comparable programs at other colleges and universities through the introduction of biology applications into mathematics coursework. Each of the activities develops a modeling and inquiry approach to problem-solving through biology applications. They also enhance an interdisciplinary problem-based curriculum by focusing on how mathematics is applied to biological concepts and investigations. This effort began with a team of six faculty members from the Department of Mathematical Sciences at the United States Military Academy meeting with colleagues from several other departments of the Academy. The team
Introduction 93 identified 15 potential activity areas that would be relevant and of interest to our students. These 15 areas cover a wide range of topics in mathematics including: mathematical modeling, differential calculus, integral calculus, probability and statistics, and differential equations both ordinary and partial. This publication effort (Application Activities to Enhance Learning in the Mathematics-Biology Interface) has been supported by Grant #0309909, from the National Science Foundation, which was awarded to the Department of Mathematical Sciences at USMA. This work has been part of a main grant thrust entitled Core Mathematics. The overall goal for the project was to create a four-semester modeling and inquiry-based program that enhances the mathematical maturity and problem-solving skills of students while preparing them for the content requirements of future courses. Some additional areas addressed in the wider project include: expanding COMAP s model from a two to a four-semester program, developing a modeling and inquiry approach to problem-solving, enhancing an interdisciplinary problem-based curriculum by focusing on how applied mathematics is practiced, incorporating a strong technology component into the program, and enhancing faculty development in a problem solving environment. With help from faculty from the Departments of Mathematical Sciences and of Chemistry and Life Sciences at USMA, Department of Mathematics at California State University at San Bernardino, Department of Mathematics at Trinity University (San Antonio, TX), and Georgia Gwinnett College (Lawrenceville, GA), we have developed 15 mathematics application activities which relate biology and mathematics to one another. Each application includes a detailed background of the topic, a specific listing of student requirements along with fully explained solutions and a notes section for the instructor on ways to further develop the ideas in the project. Over half of these projects have been tested in class, all receiving praise from the students. ACKNOWLEDGMENTS We acknowledge the efforts of the many reviewers, the authors and their students, and our Technical Editor, MAJ Carlos Fernandez, Department of Mathematical Sciences at the United States Military Academy, for his efforts in producing the final elegant versions of the manuscript.
94 Kobylski and Winkel REFERENCES 1. National Research Council. 2003. BIO 2010: Transforming Undergraduate Education for Future Research Biologists. Washington, DC: National Research Council. 2. Steen, Lynn Arthur, Ed. 2005. Math & Bio 2010: Linking Undergraduate Disciplines. Washington, DC: Mathematical Association of America. BIOGRAPHICAL SKETCHES Gerald Kobylski is an Academy and Associate Professor in the Department of Mathematical Sciences at West Point. He serves as a member of the teaching faculty and a Program Director at West Point. He has received a research grant from the Defense Advanced Research Projects Agency and a faculty development grant from the National Science Foundation. Brian Winkel is a Professor of Mathematical Sciences at West Point where he teaches cadets applicable mathematics, mentors both cadets and faculty, and has been involved in many mathematics and fill in the blank efforts for years the latter before, and some much before, his West Point days and during those days and nights! He is also the editor of PRIMUS.