Back to Minicourse List The foundational results of Fourier analysis involve the convergence and approximation techniques of analysis combined with fundamental notions of linear algebra. Fourier analysis introduces very subtle notions of convergence and it has countless applications from the very abstract, in algebraic number theory, to the very concrete, such as the Fast Fourier Transform.
Moreover, Fourier analysis has rich computational and theoretical sides and thus should provide something of interest to all students while also giving them a chance to stretch their minds in novel directions. In this course we will give the students a glimpse of time/frequency analysis.
We will start from Fourier and Haar decompositions in finite dimensional space which can be understood with linear algebra. We will 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.
There will be problem sessions to help students digest the information, and laboratory session to explore Fourier decompositions and wavelets in Matlab.
This course will be taught by Professor Cristina Pereyra.