Functional Analysis 1: This is the revised version of my old notes (see below), for use in
Math 6473 (Fall 2008). In particular, this new version is in English.
Chapter 1 2 3 4 5 6 7 8 9 10
Or Chapters 1-10 in one file: Part 1
Functional Analysis 2: This just continues my notes from above, as used in my class
Math 6483 (Spring 2009). The division into two parts is quite arbitrary and probably pointless, but
somehow I felt that I deserved the joy of opening a new section here.
Chapter 11 12 13 14 15
Harmonic Analysis on SO(3): A very cursory treatment of a number of related topics (spherical harmonics, representations of SO(3)), adapted from Dym-McKean, Fourier Series and Integrals. Occasionally, things are proved, but don't expect much in this direction. If still interested, click here.
Random Walks: An elementary treatment of various rather amazing properties of 1D random walks, taken from Feller's book. It may be better to work with this source directly, but in no case should you miss out on this material. It will change your life (or at least the way you think about coin tosses), so don't forget to click here.
Dynamical Systems: This is by no means a systematic introduction to the subject. Rather, it just gives a rather light presentation of two crowd-pleasers (this is the idea, at least): chaotic dynamics for the logistic map and the period 3 case of Sarkovski's theorem. See here.
Functional Analysis (older version): The prerequisites for this are a good
command of linear algebra, analysis, and German; some knowledge of
(point set) topology and complex analysis would also be helpful.
Chapter 1 2 3 4 5 6 7 8 9 10 11