Math 571 Functional Analysis

Office: Brink 322. Phone: 885-5274. Email: fuchang@uidaho.edu
Office Hour: Monday, Wednesday: 2:30pm -4:00 pm; or by appointment

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Homework will be assigned in class, and will be graded. There will be two midterm exams and a final test. Course grades are determined by homework (30%), midterms (20% X 2), final (25%) and class participation (5%).

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 Tentative Lecture Schedule
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(8/22,24,26)	 Linear Spaces; normed Spaces
                   (Linear Spaces; Holder's Inequality, Minkowski's Inequality) 
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(8/29,31,9/2)	 Linear Spaces; normed Spaces 
		   (Topological and Geometric Notions; Quotient Normed Spaces)	
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(9/7,9) 	 Linear Spaces; normed Spaces    
		   (No class on Monday; Completeness; Completion) 	 
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(9/12,14,16) 	 Hilbert Spaces   
		   (Basic Notions; Cauchy-Schwarz Inequality, Bessel Inequality) 	 						    
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(9/19,21,23) 	 Hilbert Spaces   
		   (Complete System; Gram-Schmidt Orthogonalization Procedure) 	 		
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(9/26,28,30) 	 Hilbert Spaces  
		   (ONB; Parseval Identity; Review) 	 		
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(10/3,5,7)	 Exam 1, Projection  
		   (Exam 1 on Monday Oct.3; Distance from a point to a convex set)	 
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(10/10,12,14)	 Orthogonal Decomposition; Linear Functionals  
		   (Bounded Linear Functionals in Hilbert Spaces)
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(10/17,19,21)	 Dual Spaces 
		   (Hahn-Banach Theorem and its consequences)
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(10/24,26,28)	 Corollaries to Hahn-Banach Theorem 
		   (Examples of Dual Spaces; Applications)
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(10/31,11/2,4)	 Bounded Linear Operators 
		   (Completeness; Compact OPerators; Space of Compact Operators)		
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(11/7,9,11)	 Bounded Linear Operators
		   (Finite Rank; INtegral Operators; Invertible Operators)	
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(11/14,16,18)	 Exam 2; Spectrum,  
		   (Review, Exam 2 on Wednesday; Fredholm Theory)			
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(11/21-25)	 Have a Nice Thanksgiving!

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(11/28,30,12/2)  Fredholm Theory; Self-adjoint Operators
		   (General Properties; Spactrum Theorem)
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(12/5,7,9)	 Functions of Operators
		   (Spectrum Decomposition; Main Inequality; Hilbert Theorem)	
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(12/13)	         Final Exam
		   (10am-12pm on Dec.13)	
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