Mathematics: Exploring Biomathematics

Capstone course; students develop, apply and document mathematical approaches to biological and ecological problems. Coursework includes discussions on ethics in science, problem solving, computer (dry lab) assignments, and analysis of research papers and technical writing. Prerequisites: MATH 2522 or MATH 2544; MATH 3230 or MATH 3201; one 3-credit course designated WIL1.

Prereqs enforced by the system: MATH 2522 or MATH 2544; MATH 3230 or MATH 3201; Open to Degree and PACE students

Exploring Biomathematics Textbook: Quantitative Biosciences - Dynamics across Cells, Organisms and Populations by Weitz, Joshua S.: Princeton Univ Press (2024) (Stand-alone lab guides are available in Python, R, and MATLAB) Course Outline and Learning Objectives Latest advances in the mathematical sciences have brought new perspectives to biological research. By answering questions that cannot be addressed using other means, the mathematical sciences can provide indispensable tools for biological research. The result is the interdisciplinary field of mathematical biology, also known as biomathematics. In this capstone course, students will learn how to develop and apply quantitative approaches to biological and ecological problems and use our knowledge from information literacy to document their project work. It will be an introduction to the interplay of mathematics with several disciplines, namely biology, ecology. No previous knowledge of these areas will be assumed. The biological background to each problem will be described in sufficient detail to construct and analyze models. The lectures will show how models are built up and will provide the mathematical tools indispensable for studying their dynamics. With each topic discussed the scenario will consist of (i) a description of the biological problem; (ii) development of the mathematical model and an assessment of its realism; (iii) mathematical analysis of the model and clues to numerical computations; (iv) biological interpretation of the results from a modeling viewpoint; (v) Seminal papers and Project work. The course will draw on real-world case studies in molecular and cellular biosciences, organismal behavior and physiology, and populations and ecological communities. Stand-alone lab guides available in Python, R, and MATLAB help students move from learning in the classroom to doing research in practice. The main emphasis of this course will be introductory lectures, problem solving, analysis of seminal papers, and computer (dry lab) assignments. More specifically, a selection of modeling topics from the following areas (Part I, II & III) will be studied: I. Molecular and Cellular Biosciences: Bi-stability of Gene Circuits II. Organismal Behavior and Physiology: Robust Sensing and Chemotaxis Excitations and Signaling from Cells to Tissues III. Populations and Ecological Communities: Eco-evolutionary Dynamics Outbreak Dynamics: From Prediction to Control We shall cover book chapters from Weitz and allude to other topics, the detailed topics of which will include: Project 1: Assigned lecture topic or journal articles on Part I Project 2: Assigned lecture topic or journal articles on Part II Project 3: Assigned lecture topic or journal articles on Part III. Scope of Individual Projects 1, 2 & 3 Utilizing writing and information literacy skills, student will give an overview of an assigned lecture topic or journal article, highlighting the modeling concepts, and the results. For journal articles, attempt to critique and/or extend the model(s), based upon new assumptions. It may be helpful to analyze the model(s) and perform numerical simulations to compare your results with those presented in the article.

Learning Outcomes: Students completing this course will be equipped with the skills necessary to enter the fast-growing field of mathematical biology or pursue graduate work in biological and other interdisciplinary fields in which modeling skills are expected. Indeed, students will: I. understand a range of biological and ecological questions for which mathematical approaches have been utilized. II. translate biological problems into mathematical models using appropriate mathematical and computational tools, such as Mathematica and Matlab. III. Develop inquiry-based approach to probe interdisciplinary topics for which mathematical techniques may be required. IV. Enhance their writing and information literacy skills, and practice communication skills in interdisciplinary studies.

Assessment: Students will be given assignments and feedback during the entire duration of the course. Emphasis will be placed on writing, which will be a substantial portion of the semester grade, and information literacy skills, coupled with oral presentations, and optional international travel.