''It has been well said that the highest aim in education is analogous to the highest aim in mathematics, namely, not to obtain results but powers, not particular solutions, but the means by which endless solutions may be wrought.''

                                                                              George Eliot, in an essay about Thomas Carlyle

I am a preceptor in the Mathematics Department at Harvard University. In Fall 2011, I taught Math 1a: Introduction to Calculus I, Fall 2011 and Math 152: The Math of Symmetry, Topics in Discrete Math and Abstract Algebra . I am also a co-coordinater of the Calculus Course Assistant Program and Math Table, the dinner-time seminar for undergraduate math concentrators.

My primary scholarly interests are in math education at the secondary and undergraduate levels. I'm particularly interested in how to create opportunities for current and future math educators to develop and exercise mathematical habits of mind in themselves and in their students.

Along those lines, I co-facilitate a study group for middle and high school math teachers in the Cambridge Public Schools with Jeremy Orloff at MIT, sponsored by the Focus on Math NSF-funded math-science partnership of schools and universities in the Boston area. We've explored various topics related to and going beyond school mathematics, for example Transformations in Geometry, Fermi problems, Symmetries of Polygons and Group Structures, Farey Sequences, Polygonal Numbers, and Conic Sections in Taxi-cab geometry. For examples of materials, please feel free to contact me.

Since Spring 2011, I have also facilitated a seminar for Master Teachers (from Math for America, Boston and Boston University's Math Teaching Scholars) on current issues in mathematics teaching and education and in particular, the impact of the Common Core State Standards. For more on this work, see slides from my talk at JMM 2012. I also have worked multiple summers as counselor and assistant director with the PROMYS for Teachers program at Boston University where secondary math teachers spend six weeks immersed in elementary number theory.

My mathematical research interests are in algebraic number theory and arithmetic geometry, with an eye towards cryptography. I completed my PhD in Mathematics in May 2008 at the University of Maryland , working with Professor Larry Washington, on number theoretic algorithms for elliptic curves. Here is a copy of my thesis.

Education Talks

Here are slides from a talk ''Designing Professional Development around the Common Core Standards for Mathematical Practice A Mathematician-Teacher Collaboration'' presented at the MAA Session The Mathematical Preparation of Teachers: The Impact of the Common Core State Standards Initiative at the Joint Math Meetings in Boston, January 2012.

Here are slides from a talk '' 'Mathematician' Meets 'Math Educator': The Experience of Co-teaching a Math Inquiry Course Course'' presented at the Mathematics Colloquim at the University of New Hampshire, April 2009.

Here are slides from a talk at the Joint Math Meetings in DC, January 2009, on the same course as above, a mathematical inquiry course for math educati\ on doctoral students.

More Recent Research Papers and Talks

Pairings on Hyperelliptic Curves , with Jennifer Balakrishnan, Sarah Chisholm, Kirsten Eisentrager, Katherine Stange, and Edlyn Teske. Proceedings of the Women in Numbers (WIN) Workshop, Banff International Research Station, Banff Canada, Fields Institute Communication Series, 2009

Talk ''Computing the Hilbert Class Polynomial Using p-adic Lifting'' at M.I.T. STAGE: Seminar on Topics in Arithmetic, Geometry, Etc., May 2009.

For more on my past talks, teaching and publications, check out my old University of Maryland website.