Writing
On this page I put some mathematical notes not directly relevant to my research or current teaching, but that might be useful enough still to be worth making publicly available.
- Notes on Galois Theory
A fairly rapid account of Galois theory, complete with exercises, starting
from elementary principles. Not much more than the basics of group theory and
linear algebra, and the definition of rings and fields are needed.
- Non-Commutative Probability Theory
Mostly self-contained notes on free probability theory, starting from first
principles. Topics covered include the free central limit theorem, random
matrices, and the R- and S-transformations.
- Measure Theory and Integration
These notes are a rapid account of measure theory and the Lebesgue
integral, starting from first principles.
- A Primer on some Methods in Homotopy Theory
This article is an exposition of the theory of simplicial sets and spaces,
classifying spaces, homotopy colimits, the plus construction and the group
completion theorem. The techniques are applied at the end of the article to
compare constructions in algebraic $K$-theory.
- A brief review of the theory of Symmetric Spectra
This article is a very short summary of some aspects of the theory of
symmetric spectra that I find useful in my work.
- Notes on Partial Differential Equations
These are notes for a course I gave on partial differential equations in Spring 2001 at Odense
University. The file is in PostScript format.
You are welcome to e-mail me at mitch@uni-math.gwdg.de if you have any
questions.
Back to main menu