COURSE OUTLINE - Mathematics 9054L - Functional Analysis

Location and Times: MWF 12:30-1:45; offered online. In addition to required reading, recorded lectures will be made available. Course times will be used for some combination of one-on-one meetings, lectures and testing; all via any of several audio- and video-conferencing software options. The exact composition will be determined taking into account student preferences, and may change as the course progresses.

Instructor Information: Gord Sinnamon (sinnamon@uwo.ca) Professor, Department of Mathematics.

Course Description: Hilbert spaces: L2 spaces, orthogonal complements, dual spaces, Riesz representation theorem, the Fredholm alternative, spectral resolution of compact normal operators. Banach spaces: Hahn-Banach theorem, bounded linear operators, adjoints, closed graph and Banach Steinhaus theorems.

Textbook: Linear Functional Analysis, Second Edition, by Rynne and Youngson, Springer-Verlag, London, 2008. This is a free download from Western Library: For the Rynne and Youngson Textbook follow the "SpringerLINK eBooks - English/International Collection (2008)" link. You will have to log in to use the proxy server if you are off campus.

Supplementary Textbook: (Optional): Elementary Functional Analysis, by MacCluer, Springer Science+Business Media, LLC, 2009. This is a free download from Western Library: For the MacCluer Textbook follow the "SpringerLINK eBooks - English/International Collection (2009)" link. You will have to log in to use the proxy server if you are off campus.

Coursework: Students are expected to keep up with the pacing of the presentation of online material and complete all tests, assignments, and examinations. Regular homework, over and above assignments, is an essential part of the course; it is the student's responsibility to keep up with the assigned homework and to seek additional help if and when it is needed.

Evaluation: Assignments - 40%; Testing - 60%. There will be seven assignments tentatively due on May 15, May 22, May 29, June 5, June 15, June 22, and June 29. Testing will be accomplished by a combination of video-supervised written tests/exams, oral examination and presentation.

STATEMENT ON SCHOLASTIC OFFENCES: Scholastic offences are taken seriously and students are directed to read the appropriate policy, specifically, the definition of what constitutes a Scholastic Offence, at the following Web site: http://www.uwo.ca/univsec/pdf/academic_policies/appeals/scholastic_discipline_grad.pdf.

ABSENCE OR MISSED WORK: If you are unable to meet a course requirement due to illness or other circumstances, contact your instructor immediately.

STUDENT ACCESSIBILITY SERVICES: Western is committed to achieving barrier-free accessibility for all its members, including graduate students. As part of this commitment, Western provides a variety of services devoted to promoting, advocating, and accommodating persons with disabilities in their respective graduate program. See http://www.sdc.uwo.ca Graduate students with disabilities (for example, chronic illnesses, mental health conditions, mobility impairments) are encouraged to register with Student Accessibility Services, a confidential service designed to support graduate and undergraduate students through their academic program. With the appropriate documentation, the student will work with both SAS and their graduate programs (normally their Graduate Chair and/or Course instructor) to ensure that appropriate academic accommodations to program requirements are arranged. These accommodations include individual counselling, alternative formatted literature, accessible campus transportation, learning strategy instruction, writing exams and assistive technology instruction.