Office: Jeffery Hall, Room 506
Office hour: Wed 12:30-1:30 and by appointment
The lectures are in Jeffery Hall, Room 116
time slot: 21
Monday, 2:30-3:30 pm
Tuesday, 4:30-5:30 pm
Thursday, 3:30-4:30 pm
I have marked the final exam. If you want to know your result, send me
an email. You can take a look on your exam if you come to my office,
either by appointment or on Wednesday, May 5, 10am-12noon.
You should have had some introduction to real analysis
(dealing with topology and convergence properties of
R^n and continuous functions with respect to sup-norm),
like Math 281.
In particular, you are expected to have some fluency in
the language and methods of mathematics, as, for example,
summarized in Chapter 1 of the book of Davidson/Donsig.
are also a few handwritten notes by myself on this.
Assignment 1 (due January 21)
Assignment 2 (due February 8)
Assignment 3 (due March 1)
Assignment 4 (due March 23)
Assignment 5 (due April 6)
Topics of Course
Sets and Cardinality
Properties of R: Completeness and Bolzano-Weierstrass
Properties of C[0,1]: sup-norm and Completeness
Compactness in complete normed vector spaces: Heine-Borel versus
Finite dimensional normed vector spaces
Inner product and Hilbert spaces
Fixed point theorems: contraction principle versus compactness
Connected and path connected metric spaces
Compact metric spaces
Completeness of Hausdorff metric: construction of fractals
Completion of metric spaces and abstract integration
Sets of measure zero and interpreation of L^p-spaces as function
The Stone-Weierstrass Theorem
More on Hilbert spaces and Fourier Series
if time permits: differentiable functions in several variables, higher
derivatives and Taylor's Theorem, inverse function theorem
No book is required, but the following one is recommended as the the
course will be somewhat based on it
Another useful book might be:
K.R.Davidson and A.P. Donsig: Real Analysis with Real Applications.
This book is available
J.E. Marsden and M.J. Hoffman: Elementary Classical Analysis.
final exam: 40%