Instructor	Camil Muscalu
Office	Malott Hall 519
Lectures	Tuesday and Thursday 2:55-4:10 in Rockefeller 102
Office Hours	By appointment
Textbook	Functional Analysis, by E. Stein and R. Shakarchi (Princeton University Press, 2011) and Essential Results of Functional Analysis, by R. Zimmer (The University of Chicago Press, 1990). Other sources that we may use include the books on functional analysis by Reed and Simon and by Lax.
Grading	It is based entirely on the homework problems.
Homework	Several homeworks will be assigned during the semester. They should be handed to the instructor in class. Here you can find the homework for the class.
Syllabus	The order may change, but the list of topics planned to be covered include: The Hahn-Banach theorem and applications, topological vector spaces, Alaoglu-Bourbaki theorem, Kakutani-Markov fixed point theorem, Haar measure for compact groups, Krein-Millman theorem, compact operators and Hilbert-Schmidt operators, spectral theorem for compact normal operators, Peter-Weyl theorem for compact groups, general spectral theory, mean ergodic theorem, distributions, Hilbert transform, fundamental solutions to general PDE with constant coefficients, parametrices and regularity for elliptic equations, the Baire Category theorem and applications (uniform boundedness principle, open mapping theorem, closed graph theorem). This whole plan may already sound a bit too ambitious, but if the time permits, we could also talk about L^p spaces in harmonic analysis (interpolation theory, Hardy space, BMO), rudiments of probability theory (central limit theorem, random Fourier series, random walks), introduction to Brownian motion and applications to the Dirichlet problem.