Introduction to Harmonic Analysis and Wavelets

Tamiyo Britton

Mentor: Professor Leslie Cheng, Department of Mathematics, Bryn Mawr College

This summer I am working with Professor Leslie Cheng, assisting in the development of "Introduction to Harmonic Analysis and Wavelets", a textbook that Professor Cheng and Professor Rhonda Hughes are writing for a 200-level harmonic analysis course. I also intend to prepare myself for future research in harmonic analysis.

One aspect of studying harmonic analysis involves using the Fourier series; examining a function by breaking it down into its constituent sine and cosine curves, for example. Learning this subject (which requires graduate level real analysis) will also assist me in understanding Professor Cheng's research on "Lp Estimates for Oscillatory Integral Operators." A well known example of the oscillatory integral operator is the Fourier transform. Possible applications of the Fourier transform include solving heat and wave equations, signal processing, probability, and physics in the area of the Heisenberg inequality and uncertainty principle, etc.

This research project will enable me to see how a course is developed and to explore various aspects of the pedagogy of mathematics. This summer research experience will also give me an opportunity to find out more in-depth what it is like to study pure mathematics, and it will show me how mathematicians communicate new discoveries to students. Studying Professor Cheng's research in particular will provide me with an idea of how mathematicians lay the groundwork for theories that are to be applied in
many different fields.

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