MATH 7132: Functional Analysis
Spring 2009
Department of Mathematical Sciences
University of Colorado Denver

PREREQUISITE:
MATH 6131: Introduction to Real Analysis, or with instructor's approval

HOURS, PLACE: TR 1-2:15 pm, CU (Dravo) 641.

INSTRUCTOR:
Prof. Andrew Knyazev
Office: CU (Dravo) 644. Phone: 556-8102.
Office hours: by appointment
WWW: http://www-math.ucdenver.edu/~aknyazev/

TEXTBOOKS: Required:
Applied Functional Analysis
by J. Tinsley Oden and Leszek Demkowicz,
Hardcover: 672 pages Publisher: CRC, 1996
ISBN-10: 084932551X ISBN-13: 978-0849325519 Approx. $100

Suggested independent reading
Strongly Elliptic Systems and Boundary Integral Equations
by William McLean
Cambridge University Press, 2000 ISBN: 052166375X
Finite-Dimensional Linear Analysis
by I. M. Glazman, Ju. I. Ljubic, G. Kuerti (Editor), G. P. Barker (Translator)
Dover Publications, 2006, ISBN-10: 0486453324, ISBN-13: 978-0486453323

Optional independent reading
Integral, Measure, and Derivative
by Georgi. Shilov,  B. L. Gurevich , and Richard A. Silverman (Translator),
ISBN:  0486635198,  Publisher  Dover Publications. (Apparently out of print)
Matrix Analysis
by Roger A. Horn, Charles R. Johnson
ISBN-10: 0521386322 ISBN-13: 978-0521386326 Cambridge University Press; 1990.
(Ch. 4 Hermitian Matrices, Ch. 5 Norms)

SUBJECT:
Linear metric and normed spaces, spaces of functions, linear operators, compact operators, elements of spectral theory.

CONTENTS:
The class will follow the outline below, touching on each major topic in a depth that will be determined by the pace of the class.

GRADING will be based on 4 take-home quizzes: one quiz for Ch. 1-3 and one quiz for every chapter 4-6 (25% of the total grade each). Research projects are optional and contribute 20% of extra credit.
REQUIRED INFORMATION FROM CLAS