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Minicourse: Fourier Analysis and Wavelets, Prof. Cristina Pereyra. Fourier analysis has rich computational and theoretical aspects and provides something of interest to all students. In this course we give the students a glimpse of time/frequency analysis. We start from Fourier and Haar decompositions in finite dimensional space which can be understood using linear algebra. We then move to infinite dimensional spaces, and discuss different notions of approximation and convergence: Fourier series, approximation of functions by polynomials, Haar expansions and more general wavelets. We will hold problem sessions and explore Fourier decompositions and wavelets using Matlab. Professor Pereyra has taught several courses on this topic in Mexico, Argentina, and at the Institute for Advanced Study in Princeton. She has written a book, {\em Wavelets, their friends and what they can do for you} and another {\em Harmonic Analysis: from Fourier to Wavelets} that was just published in July 2012. The latter book is an upper level undergraduate or lower level graduate text, with prerequisites of linear algebra and advanced calculus. She has also developed a course at UNM on the same topic which now meets regularly once every three semesters on average. She was our Graduate chair 2006-209. From 1999 to 2005, she was the composer and grader of the Math Contest. She has also mentored several students doing undergraduate research projects. She has repeatedly been chosen as ``Best Teacher of the Year" by our undergraduate and graduate students. |
