Associate 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.
Calculus II: 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-requisites: Calculus in Context (NS 260) or another Calc I course
Linear Algebra: Linear Algebra: Linear algebra is valuable for explaining fundamental principles and simplifying calculations in Mathematics, Statistics, Computer Science, Engineering, Physics, Biology, and Economics. In this course, we will focus on different applications based on course design and student preferences. These will include applications to chemistry, cryptography, economics, genetics, geometry, geology, heat distributions, marketing, image compression, Markov chains and networks. They will be based on the study of linear equations, matrices, vector spaces, linear transformations, eigenvalues and eigenspaces, as well as others as time permits.
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.
The risk of potable water scarcity has focused attention towards developing decentralized water system strategies for treating greywater, which can account for 50-80% of total water usage. In Hampshire's Living Building on-site greywater capture, treatment, and reuse is being used and researched as a central part of this course. All students in the Integrated Sciences courses will learn about microbiology, water quality, and modeling and then collaborate on an applied research project to integrate their understanding and knowledge of greywater treatment systems. Students enrolled in NS140 will specifically learn how to use modeling and simulation software. The Integrated Sciences courses are particularly suited for students interested in interdisciplinary sciences and collaborative learning experiences.
This course is a gateway for the Five College Bio-mathematical Sciences Program and Certificate. It also provides an introduction to collaborative research across the Five College Biomath Consortium. The first four weeks of the course are devoted to practice with a software package (Matlab, Rstudio, etc.). Afterward, the two 4-week modules are presented by pairs of faculty including one from mathematical and statistical sciences, and one from the life sciences. Each pair provides the background and data that motivates the research, then introduces a question for students to investigate. Student work in groups to use the tools presented to explore the question. In the final week of each module, students present their finding and hear presentations about 5CBC research projects. Five College students: graded SU only.
In this course, students will be introduced to the modern study of dynamical systems, the interdisciplinary field of applied mathematics that studies systems that change over time. Topics to be covered include: phase space, bifurcations, chaos, the butterfly effect, strange attractors, and pattern formation. The course will focus on aspects from dynamical systems that are particularly relevant to complex systems. Students will complete group explorations and a substantial independent project. Prerequisites are the Calculus in Context sequence (or equivalent).
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.