MATH 501: Graduate Real Analysis
Mathematics Department, Bryn Mawr College, Fall
2008
Professor Victor Donnay
Professor: Victor Donnay 
Class Meeting: Mon, Wed, Friday 12:30pm 
Office: Park Science Building #330 
Office Hours: Mon, Wed, Friday 2:304 pm, 
Phone: 5265352, Email: vdonnay 
and by appointment at other times. 
All
information about the course can be found at the Math 501 website located on
Prof. Donnay’s homepage:
http://www.brynmawr.edu/math/people/donnay
Required
Textbook: Royden, Real Analysis, 3^{rd}
Edition. We will also make occasional use of other texts that will be on
reserve in Collier Library.
Goals of the Course: You will
Content
of Course:

Cardinality
(countable and uncountable), equivalence relations (Ch 1)

Metric
spaces, Open and Closed sets, Continous functions (Ch 7)

Riemann
Integral and associated limit laws. (In other texts)

Lebesque
Measure (Ch 3)

Lebesque
Integral (Ch 4)

other topics as time allows (Differentiation
and Integration Ch 5, Abstract Measure spaces and Integration Ch 11, 12).
Portfolio: We will occasionally
make use of theorems and results that you might have seen in your undergraduate
Real Analysis or Topology course. We won’t necessarily prove these results;
instead we will use them as an opportunity for you to practice independent
learning. You will investigate these theorems and write up the proofs of them
yourself. Your portfolio will consist of five such write ups.
There
will be a midterm and final, the porfolio, regular homework assignments and
also student presentations (of homework or other things).