Time: TBA -- Initial meeting Tuesday Jan 18, Math Conference Room
Place: TBA
Text: Adams, M. and Guillemin, V.., Measure Theory and Probability, 1996 Edition, Birkauser, Boston.. supplemented by handouts to be provided during the semester and posted on this page.
Evaluation: Grades will be based on take-home problems sets (75%) and a comprehensive final exam (25%).
This course is a continuation of MTH 535, an introduction to real analysis at the graduate level, particularly integration theory and its applications to Fourier analysis, probability theory and other mathematical areas. The principal topics will be Fourier series and transforms, Hilbert space, L^p spaces and elements of functional analysis, advanced differentiation theory. Additional topics will be selected from ergodic theory, probability theory, information theory, or fractal geometry according to class interest. This course should useful to well-prepared students of electrical engineering, physics or statistics as well as students of mathematics. Students who have had MTH 535 in previous years should have no difficulty with MTH 536 this spring.
Here is a Maple worksheet on elementary Fourier series. It would be best to save it to disk and then run it with the Maple 9 Classic Worksheet interface rather than the new, slower, default interface. Maple worksheet on Fourier series
Here is the animation of the construction of the Cantor ternary function that we discussed in class: Cantor function animation