Functional Analysis, Fall 2016

Functional Analysis, Fall 2016 Course Information

PDF syllabus

Course Description: This will be an introduction to various topics in Functional Analysis, focusing on Banach and Hilbert spaces and associated linear operators. We will cover some of the classical theorems (and applications thereof) in the subject, including the Hahn-Banach, Alaoglu, Open Mapping, Closed Graph, and Banach Fixed Point theorems, as well as varoius aspects of the spectral theory of self-adjoint operators.

Reading Assignments: A reading assignment for each class will be posted on the course webpage and in the Canvas course prior to each lecture. This reading should be completed prior to the lecture, as I aim to expound on, rather than merely transcribe, the material in the book.

Homework: Problem sets will be assigned and graded on a roughly biweekly basis. These are perhaps the most important component of the course, and should be started early.

Midterm: There will be one mid-term exam at the end of Module I, with precise date and format (i.e., in-class vs. take-home) to be determined.

Final projects: In lieu of a final exam, you will complete a final project, which will be an expository paper on a topic or theorem which extends or goes beyond the material covered in lecture, of between 10 and 20 pages in length. This will give you an excellent opportunity to develop your skills in mathematical writing.

Assessment: Your course performance (Sat/Unsat) will be evaluated based on homework, exam and final projects, with equal weight given to each. Class participation will be reflected in the narrative evaluation.


Topics: Below is a tentative list topics, which may be subject to revision as the course is underway.