Hours:
Class: TTh 1:30PM-2:50PM, location TBA.
Instructor:
Elon Lindenstrauss
Office: 606 Fine Hall
Phone: 609 258 4186
E-mail: elonl at math
Office hours: Mon 1:30-2:30
Teaching Assistant & Grader:
Jonathan Holland
Office: 507 Fine Hall
E-mail: jholland at math
Office hour: TBA
Text: E. Stein and R. Shakarchi: Real analysis: measure theory, integration & Hilbert spaces and other sources as needed.
Homepage: http://math.princeton.edu/~elonl/333
Prerequisites: MAT 332 or MAT 314 (the basic prerequisite is good knowledge of real analysis up to Lebesgue measure and integration on R)
Syllabus: This is an advanced undergraduate course in analysis. Topics to be discussed include:
general measure theory
mean and pointwise ergodic theorems
ergodicity and unique ergodicity; equidistribution
Hausdorff dimension and measure
fractals
Besicovitch (Kakeya) sets
projection of fractal sets
Erdos Bernoulli convolution problem
One of the aims of this course is to present some interesting open problems in analysis which are topics of active research.
Grading: (preliminary) Grading will be 45% Final Exam, 20% Midterm, 35% Homework. Midterm will be with closed books, final: take home exam.
Please note that attendance in class is expected
Homework policy: Homework
assignments will be given weekly, and are due each Th in class. If
you are unable to attend class, bring your assignment to the TA's
office (Fine 507) by 1:00 PM on Th.
Sorry, late homework assignments will not be accepted. Homework counts for 35% of the final grade. The
lowest homework score will be dropped.
You may discuss the problem sets with other students, but PLEASE - write down the solutions by yourselves. I encourage you to think on the problems first, but you may use what you find in the mathematical literature. Please do not copy verbatim but rewrite the proofs/solutions in your own words, and don't forget to give the appropriate references.