My area of research is chaotic properties of dynamical systems. Systems that I am particularly interested include geodesic flow on surfaces and billiards.
This picture shows an unusal shaped sphere which exists in three dimensional space whose geodesic flow is ergodic.
From the article by Keith Burns and Victor Donnay, Embedded surfaces with ergodic geodesic flow, Inter. J. of Bifurcation and Chaos Vol. 7, No. 7 (1997), 1509-1527.
Together with my students, I have worked to develop ways to bring mathematics to a wider audience in interesting and understandable ways.
In my teaching, I have been working at making connections between mathematics and issues of Civic Engagement as I describe in the article Differential Equations and Civic Engagement. My differential equations (see Ordinary Differential Equations in Real World Situations) was seleced as a 2008 SENCER Model Course.
In spring 2010, I taught a math seminar on Math Modeling and Sustainability in which students did service learning projects in which they used mathematics to analysize problems on sustainability on campus and in the community.
In spring 2012, as part of Bryn Mawr's new 360 program, I was part of a three faculty member team that will examine issues of sustainability from a variety of perspectives. I taught a course on Math and Sustainability, Carola Hein, from the Cities program taught on Urban Design and Sustainability, and Jody Cohen, from the Education program, taught on Sustainability Education.
I have been involved in a number of NSF funded projects to improve math and science education as well as teaching a course called Changing Pedagogies in Math and Science Education.
Principal Investigator of the Bryn Mawr - Haverford Noyce Program, which aims to encourage math and majors to go into teaching, particularly in high-needs school districts. To support STEM majors at liberal arts institutions to go into teaching, we have developed a summer program in math pedaogy at Brown.
Principal Investigator of the Philadephia Regional Noyce Partnership in which the seven institutions in the region with Noyce programs (Bryn Mawr - Haverford, Drexel, La Salle, Penn, Saint Joseph's, and Temple) will exploit synergies to develop joint programming to support the Noyce scholarsin the Philadelphia region.
Co-Principal Investigator for a NSF funded START planing grant which aimed to support teachers and school districts in teaching (environmental) sustainability to their students.
Co-Principal Investigator for the Math Science Partnership of Greater Philadelphia (MSPG), which received a $12.5 million dollar grant from the National Science Foundation to improve pre-college math and science education. Bryn Mawr and Haverford Colleges are core partners in the MSPGP. I am a Board Member of the organization 21st Century Partnership for STEM Eduation (21PSTEM), which is a non-profit successor to the MSPGP that was founded in 2007.
I am chair of the college's Sustainability Leadership Group. Information about Sustainability at Bryn Mawr can be found here. We sponsored a celebration of the college's achievements in sustainability in January 2013.
In 2013, I was the Chair of the national Advisory Committee for Mathematics Awareness Month - the Mathematics of Sustainability. We created a beautiful poster about sustainability, collected short essays describing how mathematics get used in sustainability and teaching units incorporating sustainability topics into math courses.
Starting in fall 2013, I became the Director of Bryn Mawr's Environmental Studies program.
360 Perspectives on Sustainability:
Math 151 Introduction to Math and Sustainability.
Fall 2009: Math 301: Real Analysis I
Previous Courses taught.
Organizer of the Tri-Co Mellon group on Math Modeling in 2011-12.