Functional Analysis I: MATH6461

Fall 2014

General Information:

  • Instructor: Dr. Youness Lamzouri.
                           Office: N515 Ross Building.

  • Time and location : Tuesday and Thursday 10:00-11:30 am in Ross N836.

  • Office hours: Tuesdays 11:30 am-1:00 pm, or by appointment.

  • Text for the course: The course will be based primarily on lecture notes. The following two books are highly recommended references:

    John B. Conway, A Course in Functional Analysis, 2nd ed., Springer, 2007.

    Peter D. Lax, Functional analysis, Wiley-Interscience, New York, 2002

  • Course Description :

    This course will provide an introduction to functional analysis, with some applications to other areas of mathematics such as harmonic analysis and mathematical physics. Covered topics include: Banach and Hilbert spaces, bounded linear operators on Hilbert space, L_p spaces, the Riesz representation theorem, the Hahn-Banach theorem, the open mapping and closed graph theorems, the spectral theorem for compact operators.

    Course Evaluation:

  • 60% Assigments : Assignments will be given every two weeks. In total, there will be six assignments counting for 10% each. For each assignment, a random selection of questions will be chosen for grading. Late assignments will not be accepted except in the event of illness (with supporting medical documentation), or with prior consent of the instructor.

    Assignment 1 (Due Tuesday September 30, at the beginning of class).

    Assignment 2 (Due Tuesday October 14, at the beginning of class).

    Assignment 3 (Due Tuesday October 28, at the beginning of class).

    Assignment 4 (Due Tuesday November 11, at the beginning of class).

    Assignment 5 (Due Tuesday November 25, at the beginning of class).

    Assignment 6 (Due Tuesday December 16).

  • 40% Final Exam: The final exam will be comprehensive. It will be held on Tuesday December 16 from 10:30 am to 1:30 pm in VH 2009.

    Practice Exam (To be reviewed during the lecture of December 4).