Course title	Real Analysis
Course number	110.605
Professor:	Steve Zelditch
TA	Sirong Zhang
Course Web Page	http://www.math.jhu.edu/~zelditch/605
Course description	First half of the graduate Real Analysis Course, with emphasis on the syllabus for the Real Analysis qualifying exam.
Meeting time(s)	Lecture: MTW 10:00 noon – 10:50, Gilman
LECTURES and ASSIGNMENTS and Exams
	TBA
Textbooks
Required reading Supplement	Lieb and Loss, Analysis, Graduate Studies in Mathematics 14, AMS Rudin, Real and Complex Analysis, McGraw Hill
Course Description
	Real Analysis is an enormous field with applications to many areas of mathematics. Roughly speaking, it has applications to any setting where one integrates functions, ranging from harmonic analysis on Euclidean space to partial differential equations on manifolds, from representation theory to number theory, from probability theory to integral geometry, from ergodic theory to quantum mechanics. Only a small selection of topics is possible in a one semester course. I have tried to select ones which I believe are most useful, i.e. that you and I will most often use in research. The traditional topics are measure and integration on abstract measure spaces or on locally compact Hausdorff spaces, Banach and Hilbert spaces of functions, L^p spaces, the Fourier transform. In practice, mathematicians often work on Euclidean or locally Euclidean spaces and with the special Banach and Hilbert spaces which are important in solving differential equations. I therefore chose a text, Lieb and Loss, which concentrates on R^n and on Fourier analysis, distributions and Sobolev spaces. It covers the basics in a light, quick, concrete way that avoids the stodginess that I find in many analysis texts. Lieb is one of the leading (analytically oriented) mathematical physicists of our time, particularly well known for `stability of matter’ estimates, and his book reflects the kind of mathematics he does. It uses a minimum of abstract measure theory or general Banach space theory; if the need arises, we can always supplement it with Rudin. We will go through Chapters 1, 2, 5, 6 and parts of 3, 4, 7, 8 (of Lieb and Loss). I may use supplements (e.g. Chapters 1 and 5 of Rudin).
Homework Policies
	Assignments will be collected weekly and returned the following week.
Exams
	There will be one mid-term and a final.
Grading Policies
	The grade will be based on HW (50%), the mid-term (25%) and the final (25%).