Assistant Professor of Mathematics
Professor Hews’ teaching primarily focuses on applying mathematical techniques to biological and physical systems. This involves building an intuitive understanding of the concepts and computational tools necessary to tackle complex, real world problems. In addition, all courses emphasize communicating mathematics to a broader audience.
Hews’ research focuses on the dynamical implications and underlying assumptions of mathematical models. She models with a range of techniques including differential equations, difference equations, individual based models, and agent based models.
This course is part of an integrated science learning experience combining water resources, mathematical modeling, and microbiology using the Hampshire College Kern Center, built to the Living Building Challenge Standard, as a case study. Students will meet twice a week to explore the science behind the systems of the living building in their specific discipline. Once a week all three classes (NS132, NS140 and NS156) will meet together to complete interdisciplinary projects, share expertise, and form a collaborative science learning community. Students will read and share primary literature and work collaboratively on projects. We will learn about the campus living building from the architects and design engineers, take field tours, and meet faculty across campus engaged with the project. Students who complete this course may choose to continue their work using the living building in NS280, Collaborative Project Design, during the spring semester. Students enrolled in NS140, Modeling Systems, will focus on using mathematical models to understand the water and energy systems in the living building. We will learn what mathematical models are and when, why, and how to analyze them. We will then build simple models of systems in the Kern Center including the cycling of nutrients in the indoor planters and the energy production by the solar panels.
Calculus provides the language and some powerful tools for the study of change. As such, it is an essential subject for those interested in growth and decay processes, motion, and the determination of functional relationships in general. Using student-selected models from primary literature, we will investigate dynamical systems from economics, ecology, epidemiology and physics. Computers are essential tools in the exploration of such processes and will be integral to the course. No previous programming experience is required. Topics will include: 1) dynamical systems; 2) basic concepts of calculus -- rate of change, differentiation, limits; 3) differential equations; 4) computer programming, simulation, and approximation; 5) exponential and circular functions. While the course is self-contained, students are strongly urged to follow it up by taking NS 261-Calculus II to further develop their facility with the concepts. In addition to regular substantial problem sets, each student will apply the concepts to recently published models of their choosing.
This course extends the concepts, techniques and applications of an introductory calculus course. We'll detect periodicity in noisy data, and study functions of several variables, integration, differential equations, and the approximation of functions by polynomials. We'll continue the analysis of dynamical systems taking models from student selected primary literature on ecology, economics, epidemiology, and physics. We will finish with an introduction to the theory and applications of Fourier series and harmonic analysis. Computers and numerical methods will be used throughout. In addition to regular substantial problem sets, each student will apply the concepts to recently published models of their choosing. Pre-requisite: Calculus in Context (NS 260) or another Calc I course.
This course is a continuation of NS132, NS140, and NS143 and will provide students a path for completing independent and collaborative projects centered around the Kern Center living building on Hampshire's campus. Students will learn skills in independent and collaborative research, project design, grant writing, presentation, and science writing. Students may use this course to develop project proposals for summer work as part of Integrated Sciences III or to prepare them for work in Division II. This course is open to all students from NS132, NS140, NS143 or by instructor permission.
Infectious diseases are a leading cause of morbidity and mortality worldwide. Mathematical models are increasingly being used to understand host-virus dynamics and to determine optimal control strategies for containing and eliminating infections. This co-taught course will cover the basics of virology, epidemiology, and mathematical modeling methods. Students will read primary research articles, explore with well-known models, and contribute to the field with a semester-long project in which they build and analyze their own model. Pre-requisite: Calculus is recommended but not required.