**Algebra:** This is for use in my class
Math 5353/5363 (Fall 2015/Spring 2016).

Chapter
1
2
3
4
5
6

**Functional Analysis 1:** This is the revised version (last revision: Fall 2020) of older notes on the same subject, for use in
Math 6473.

Chapter
1
2
3
4
5
6
7
8
9
10

**Functional Analysis 2:** This is the version used in my Spring 2021 edition of the course. It differs
quite substantially from earlier versions.

Chapter
11
12
13
14

**Statistics:** This is for use in my class
Math 4743/5743 (Spring 2015). The main focus is on estimators and their properties.
The approach is abstract and theoretical, with an attempt to give coherent, reasonably complete arguments,
but all heavy machinery (measure theory, for example) is avoided.

Chapter
1
2
3
4
5
6

**Hardy spaces:** The topic was originally planned as a 5 week segment in a normal class, but ended up being
delivered in the socially distanced form of these
notes.

**Distributions:**
pdf

**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.

**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.

**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.