Old notes are available at the the 2010 website. In the present offering, we will replace the second half of the course with the following topics, which are active areas of research:
In the course, we show the following results - Pillai's equivalent characterization of normality using simple normality, the equivalence between finite-state incompressibility and normality, and the proof that a Champernowne-like sequence is finite-state incompressible, hence normal. (This utilizes a combinatorial insight inherent in Lempel and Ziv's 1978 paper on universal compression, and has not appeared explicitly anywhere.) [Notes]