School of Mathematics
Georgia Institute of Technology
Atlanta, GA 30332-0160
(404) 894-9231
h e i l @ m a t h . g a t e c h . e d u
MATH 6328 (Introduction to Functional Analysis),
Spring 2007
- Office Hours: MWF 10:00-11:00 and 11:30-12:00, and by appointment.
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Course Syllabus
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General Reading List
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Real Analysis Review
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Banach and Hilbert Spaces Review
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A Basis Theory Primer
(Chapter 1 is a review of theorems from functional analysis)
- Notes on
Lebesgue measure.
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Lecture notes on metrics, norms, inner products, and topology
(updated 1/18/07).
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Lecture notes on Borel measures on R (updated 3/13/07).
- Additional notes with details on
Radon measures on R (updated 3/13/07).
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Lecture notes on operators and dual spaces (updated 2/5/07).
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Lecture notes on compact sets and finite-dimensional spaces
(revised 2/25/07).
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Lecture notes on quotient and product spaces (revised 2/25/07).
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Lecture notes on the Hahn-Banach Theorem and its consequences
(posted 2/26/07).
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Lecture notes on the proof of the Hahn-Banach Theorem (posted 2/26/07).
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Lecture notes on reflexive Banach spaces (posted 3/5/07).
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Lecture notes on the Baire Category Theorem (posted 3/5/07).
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Lecture notes on the Uniform Boundedness Principle (posted 3/28/07).
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Lecture notes on the Open Mapping and Closed Graph Theorems
(posted 4/2/07).
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Lecture notes on weak and weak* convergence (posted 4/3/07).
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Lecture notes on adjoints in Banach spaces (posted 4/6/07}.
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Lecture notes on topological vector spaces (revised 4/9/07).
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Lecture notes (from Harmonic Analysis) on distributions (posted 4/17/07).
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Lecture notes on the weak and weak* topologies (posted 4/16/07).
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Homework 1 (due January 31, 2007).
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Homework 2 (due February 12, 2007).
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Homework 3 (due March 9, 2007). Revised version posted 3/1/07.
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Homework 4 (due April 11, 2007).
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Homework 5 (due April 25, 2007).
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Exam 1 has been rescheduled for February 19, 2007.
You will be allowed to bring one 8.5x11 sheet of notes to the exam
(you can write on both sides).
Topics will include the material on metrics, norms, inner products,
and topology, and the material on operators through examples of operators.
Measures may be involved in some aspects of the problems, but the questions
will focus on spaces and operators rather than measure theory.
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Exam 2 has been rescheduled for March 16, 2007.
You will be allowed to bring one 8.5x11 sheet of notes to the exam.
Topics will include dual spaces, finite-dimensional spaces,
quotient and product spaces, and the Hahn-Banach Theorem and its consequences.
- Our
Final Exam is scheduled for Thursday, May 3, 2:50-5:40 p.m.
You are allowed to bring one 8.5x11 sheet of notes to the exam
(you can write on both sides).
In addition to the topics covered on Exam 1 and 2, the topics for the
final will include reflexivity, Baire Category, Uniform Boundedness,
Closed Graph, weak and weak* convergence, topological vector spaces,
and the basic definitions concerning distributions.
For some additional practice problems, click here to see the
material that was used in Math 6328 in
Spring 2006.
To contact me, please send email to:
h e i l @ m a t h . g a t e c h . e d u