 
Summary: Real Variables II: Math 608
Spring 2012, MWF 1:502:40 in Blocker 148
Professor: Michael Anshelevich, Milner 326, manshel@math.tamu.edu.
Webpage: www.math.tamu.edu/manshel/m608/m608.html.
Office hours: MW 12:301:30 p.m., T 12 p.m., or by appointment.
Textbook: Folland, REAL ANALYSIS, MODERN TECHNIQUES AND THEIR APPLICATIONS, 2nd
ed., Wiley, ISBN 0471317160.
Prerequisites: Math 607 or equivalent.
Learning Objectives: This course, together with Math 607, covers the fundamental theorems and
examples of graduate Real Analysis: basic results from Functional Analysis, the study of Lp
spaces,
and (in Math 607) measure theory and analysis on topological spaces. These are the topics whose
knowledge is tested on the Real Analysis qualifying exam. The course also provides the background
for further study and research in various fields of Mathematical Analysis, including Functional
and Harmonic Analysis, Banach spaces, Operator Algebras and Operator Theory, and Probability
theory.
Brief course outline:
· Elements of functional analysis (weeks 16).
Banach spaces. Bounded linear operators and functionals. Baire category theorem.
HahnBanach theorem. Open mapping theorem. Closed graph theorem. Uniform
