Sarah Hews, assistant professor of mathematics, received a B.S. in Mathematics at the University of Michigan and a Ph.D. in applied mathematics from Arizona State University. Her postdoc at Swarthmore College, funded by HHMI, focused on developing new courses at the interface of mathematics and biology and introducing quantitative tools in a range of biological courses.
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.
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.
Assistant Professor of Mathematics
Mail Code NS
Cole Science Center
893 West Street
Amherst, MA 01002