MATH 501: Graduate Real Analysis

Mathematics Department, Bryn Mawr College, Fall 2008

Professor Victor Donnay

Professor: Victor Donnay	Class Meeting: Mon, Wed, Friday 1-2:30pm
Office: Park Science Building #330	Office Hours: Mon, Wed, Friday 2:30-4 pm,
Phone: 526-5352, E-mail: 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

• Continue to develop your abilities as an independent learner of mathematics and be able to communicate, both verbally and in writing, clear mathematical argument.
• Be able to self-assess your work, to know if your proofs and arguments are correct or not.

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 mid-term and final, the porfolio, regular homework assignments and also student presentations (of homework or other things).