2009 Fall MATH 242-01
Bulletin Course Description Metric spaces, fixed point theorems, Baire category theorem, Banach spaces, fundamental theorems of functional analysis, Fourier transform. Instructor: Staff
(Instructor named in bulletin description above may not be current. For current instructor, see listing below.)
Title FUNCTIONAL ANALYSIS Department MATH Course Number 2009 Fall 242 Section Number 01 Primary Instructor Heymann,Matthias Prerequisites Prerequisite: Mathematics 241 or equivalent.
Synopsis of course content
This course is an introduction to functional analysis. In essence, functional analysis generalizes linear algebra to infinite dimensions: Vector spaces are replaced by Banach spaces (e.g. Hilbert spaces), the Euclidean length of a vector is replaced by the norm, and matrices are replaced by linear operators. Typical examples for Banach spaces are various spaces of functions or infinite sequences. The methods we learn in this course are essential tools in various fields, including PDE, Fourier analysis, quantum mechanics, probability theory, and (a lot) more.
Topics to be covered are: Hilbert and Banach spaces, dual spaces, the Hahn-Banach theorem, the Baire category theorem, bounded/unbounded/compact/self-adjoint operators and their properties, in particular spectral theorems, etc.
Textbooks
I will closely follow the book "Functional Analysis" by Michael Reed and Barry Simon.
Assignments
There will be homework every one or two weeks.
Exams
There will be one midterm exam and the final exam. Both exams are written exams, but it is not yet decided whether these will be take-home exams.
Grade to be based on
exams and homework
