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.
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 is part of an integrated science learning experience combining microbiology, biogeochemistry, hydrology, and mathematical modeling using the new 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 will meet together to complete interdisciplinary projects, share expertise, and form a collaborative science learning community. Students will read and share primary literature, complete problem sets, 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 Design Projects, during the spring semester. Students enrolled in NS-140T: Modeling Systems, will use mathematical models to build our understanding of the processes occurring in the living building. We will learn how to build mathematical models, simulate solutions, and investigate dynamics. We will then build models to explore the cycling of water, carbon and nutrients, and the microbial processes involved in water and waste treatment in the living building.
What happened to the passenger pigeon, the dodo bird, and the wooly mammoth? Why did the Tacoma Narrows Bridge collapse? How can we explain the destruction of the World Trade Center? How did smallpox get eradicated? Why did the stock market crash in 2008? All of these are examples of full or partial collapses that could be explained by the following mathematical mechanisms: randomness, emergence, evolution, instability, nonlinearity, and networks. This course will explore the basics of these mathematical mechanisms in the context of collapses. Each student or group will spend the semester on a collapse event of their choosing and apply the previously listed mathematical mechanisms to explain the collapse phenomena. Students will also use the mathematics to predict future collapses. A mathematical background is not assumed and students from a range of disciplines are encouraged to enroll.
This course develops the basic geometric, algebraic, and computational foundations of vector spaces and matrices and applies them to a wide range of problems and models. In addition to containing real finite dimensional vector spaces, linear independence, linear transformations and inner product spaces, the course will cover eigenvalues and eigenvectors, diagonalization, and linear programming theory with applications to graph theory, game theory, differential equations, Markov chains, and least squares approximation. Basic programming will be taught and used throughout the course. Problem sets will be assigned weekly.
Rhythmic activity is observed in many biological systems, such as with pacemaker neurons, hormone secreting systems, sleep-wake circuits, and cardiac muscle contractions. In this course, we will explore the biological mechanisms and mathematical representations of biological rhythms. Mathematical topics may include periodic functions, factor analysis, differential equations, and Fourier transforms. We will consider examples of periodicity from different time scales, including those that affect behavioral activity. Students will work as a class on questions drawn from primary research literature and analyze equations and patterns, with room for individual projects at the end of the course. Students should have had Calculus in Context (or equivalent)and at least one college-level biology course, such as physiology, prior to this course. Prerequisites: Calc I (or equivalent) and one college-level biology course.