Suggestion: Work ahead. If you have looked at the section and the corresponding problems before the lecture, then you will usually have two opportunities to ask questions (and at least a couple days) before we move on.

Homework: Homework for the week will be listed on each Tuesday and due the next Tuesday (excluding the assigned problems that were done in class).

   Date    Chapter.Section/Topics   or   Page/Problems

T   Aug 23  Lecture 1: Course Overview
            Assignment 1  Due Tuesday September 6
Th   25     Lecture 2: History
T    30     Lecture 3: Topological Spaces (notes section 1.2.3) 
            Riesz Representation (notes section 1.3)
Th Sept 1   Lecture 4: Riesz representation theorem (continued)
            Continuity and Linearity:  Bounded Operators (notes section 1.2.5)
            Assignment 2  Due Tuesday September 13
T     6     Lecture 5: Systematic introduction to inner product spaces 
                       (Kreyszig Chapter 3)  
                       Completion of an inner product space
            "to do" list items:  (a) cases of equality in the Cauchy-Schwarz 
                                     and triangle inequalities
                                 (b) Every linear operator with a finite dimensional 
                                     domain is continuous.
            Assignment 3  Due Tuesday September 20
Th    8     Lecture 6:  Completion of an inner product space (continued)
T    13     Lecture 7:  Definition of inner product on the completion
                        Completeness of the completion
Th   15     Lecture 8:  Completeness of the completion (continued)
                        Uniqueness of the completion.
T    20     Lecture 9:  Summary of the completion theorem(s)
                        Complete and closed sets and spaces  (didn't do this; forgot to do it in LLecture 10)
            Assignment 4  Due Tuesday October 4
Th   22     Lecture 10: Examples
                        Mentioned construction of norms from sets:
                        Here is a nice lecture on constructing norms in finite dimensional spaces
                        Here is a paper on constructing norms in infinite dimensional spaces
T    27     Lecture 11: Complete and closed
                        More examples
            Assignment 5  Due Tuesday October 11 
Th   29     Lecture 12: the little ell p sequence spaces
T  Oct 4    Lecture 13: seminormed spaces 
                        characterizing sets for  which the Minkowski functional is a norm
            Assignment 6  Due Tuesday October 25
Th    6     Lecture 14:  Lebesgue Integration and L^p
T    11     Lecture 15:  Kreyszig Section 4.3 (Riesz representation)
Th   13     Lecture 16:  Kreyszig Section 4.3 (continued)  
Oct  17     Fall Break
T    18     Fall Break
Th   20     Lecture 16: L^infty(a,b) is complete
T    25     Lecture 17: Riesz-Fischer theorem:  L^p(a,b) is complete
Th   27     Lecture 18: Bernstein polynomial approximation
                        Mollification
            Assignment 7  Due Tuesday November 1 
            (this is a relatively easy assignment but posted late; 
            take your time on handing it in.)
            Assignment 8  Due Tuesday November 8
T  Nov 1    Lecture 19:  Mollification:  Definitions and examples
Th   3      Lecture 20:  Mollification:  L^p estimate  
T    8      Lecture 21:  Mollification:  Pointwise Convergence
            Assignment 9  Due Tuesday November 22
Th   10     Lecture 22:  Distributions 
            Assignment 10  Due Tuesday December 6 (part)
T    15     Lecture 23:  Topologies (of topological vector spaces) 
Th   17     Lecture 24:  Review concerning distributions
                         Preliminaries on topological bases/subbases 
                         Weak convergence
T    22     Lecture 25:  Shur's Theorem
W    23     Student Recess
Th   24     Thanksgiving Holiday
F    25     Thanksgiving Holiday
...
Th Dec 1

M     5     
T     6     Last Lecture (Final Instructional Class Day)
Th    8     Final Exam 6:00-8:50