Yvonne Lai

Research

Areas of interest:
Mathematical Knowledge for Teaching, Proof and Proving

Mathematical interests:
Hyperbolic Geometry, Geometric Group Theory

Current project work:

• Developing the Theory of Mathematical Knowledge for Teaching by Investigating its Nature, Measurement, and Growth. Principal Investigators: Mark Thames, Hyman Bass, Deborah Ball, Laurie Sleep.
• Teaching Mathematical Knowledge for Teaching (K-8): Adapting Local Materials for Use in Diverse Institutions and Settings. Principal Investigators: Hyman Bass, Mark Thames, Laurie Sleep.

Related projects: mod4, LMT, MTLT.

Dissertation:
An Effective Compactness Theorem for Coxeter Groups. Geometriae Dedicata, Vol. 145, Issue 1 (2010), pp. 195-217. DOI 10.1007/s10711-009-9416-8. (arXiv) (journal)
(supervised by Misha Kapovich)

Teaching

Canada/USA Mathcamp
Since 2000, I have worked at the Canada/USA Mathcamp. It's a wonderful place where graduate students and faculty teach high school students about mathematics that has been personally inspiring.

I have taught the Banach Tarski paradox, Dehn invariants, the Scissors Congruence Problem, Disrete Fourier Transforms, and various pieces of hyperbolic geometry and geometric group theory (such as a class on SL(2,Z).)

At Mathcamp 2010, Ilya Grigoriev and I organized a viewing of Not Knot interspersed with a Q & A about the math. The film is visually beautiful, but can be frustrating to watch without a friend with whom to delve into the mathematics. It was great fun to examine the film with enthusiastic students and a fellow geometer.

Algebra Project
Throughout the academic year 2009-2010, I visited the Ypsilanti cohort of the Algebra Project and participated in the weekend planning sessions for the class. Here are some mathematical and non-mathematical highlights of the year.

University of Michigan

[transformation applets] -- play with linear transformations of f(x) (for f(x)=sin(x) and f(x)=x³-x). (created with GeoGebra)

I have drawn pedagogical inspiration from:

• Loren Larson, who showed me the importance of motivation, and who compassionately coached me through my very first mathematical presentation, at the 1996 Canada/USA Mathcamp.
• Misha Kapovich, who impressed upon me the power of well-chosen examples.
• The 2005-2006 and 2006-2007 TAC groups at UC Davis, for giving the space for graduate students passionate about their disciplines and teaching to debate and compare the teaching philosophies prevalent in mathematics, computer science, physics, biology, linguistics, and literature.
• The Elementary Mathematics Laboratory, which gave insight into how children think about fractions, offers a public teaching experience, and introduces a broad spectrum of people who care about teaching and mathematics to each other.