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Phone: (407) 823-6284;   Fax: (407) 823-6253;   MAP  207 MAA 6508 .0001 Hilbert Spaces Fall 2003 , 3 credit hours INSTRUCTOR Dr. Zuhair Nashed OFFICE MAP 209 (inside 207) OFFICE HOURS T R; 5:00-6:00pm, W; 11:00am-12:00pm or by appt. PHONE 823-0445 EMAIL znahsed@mail.ucf.edu CLASS LOCATION    MAP 406 CLASS TIMES T R 6:00-7:15pm TEXTBOOK Introduction to Hilbert Spaces with Applications, Second Edition by L. Debnath and P. Mikusinski GRADING POLICY Homework: 30%Midterm Exam: 30%Final Exam: 40% GRADING SCALE Average Grade 90 - 100% A 85 - 89% A- 80% - 84% B+ 75% - 79% B 70% - 74% B- 60 - 69% C 50 - 59% D 0 - 58% F TENTATIVE LIST OF TOPICS - Fundamental differences between finite and infinite dimensional normed spaces, and linear operators on these spaces.- Basic properties of metric spaces, normed spaces and inner product spaces, with emphasis on Hilbert Spaces.- Bounded linear operators and closed linear operators- Orthogonal projections and orthogonal complements- Continuous linear functionals and the Riesz Representation Theorem- Convex sets and metric projections- Bilinear functionals and adjoint operators- Compact operators and the spectral theory for compact self-adjoint operators. OTHER INFORMATION APPLICATIONS (as time permits):- Contraction Mapping Principle and Applications- Best Approximation Problems in Hilbert Spaces- Least squares problems and generalized inverses- Quadratic Variational problems and variational methods for operator equations- Monotone operators and variational inequalities- Introduction to inverse problems and regularization methods- Introduction to differential calculus in normed adn Hilbert Spaces.