Lecture Notes

Research notes:

Entropy of compact group automorphisms (Graduate Course 1994, Ohio State)
Valuations and dynamics (Graduate Summer School 2001, Gottingen)

Third year undergraduate:

Topology (3rd year course, UEA)
Functional Analysis (3rd year course, UEA)

Second year undergraduate: Open-entry Science program:

Basic Mathematics I (Open entry course, UEA)

Entropy of Compact Group Automorphisms

Based on MATH932 at the Ohio State University, Winter 1994. They cover a very short introduction to measure-theoretic and topological entropy, and are aimed at understanding part of Yuzvinskii's formula for the entropy of compact group automorphisms. Files are in pdf format.

Table of Contents
Chapter 1: Introduction and examples
Chapter 2: Fourier analysis on groups
Chapter 3: Measure-theoretic entropy
Chapter 4: Properties of metric entropy
Chapter 5: Entropy as an invariant
Chapter 6: Topological entropy I: definitions
Chapter 7: Topological entropy II: homogeneous measures
Chapter 8: Topological entropy III: Yuzvinskii's formula
Chapter 9: Topological entropy IV: Periodic points
Chapter 10: Further reading
Appendix A. Weil's proof of Theorem 8.1
Appendix B. Lawton's proof of Theorem 9.6
References

Valuations and Dynamics

(prepared for PRODYN summer school, Gottingen 2001)

These notes are a summary of several problems in dynamics, and particularly the ergodic theory of Z^d-actions, where the theory of valuations play a role. The lecture notes are available as a single pdf file (560k). Revised 13 July 2001.

Topology

These are a set of lecture notes for a 3rd year undergraduate course in algebraic (simplicial) topology and the fundamental group. The lecture notes are available as a single pdf file (550k).

Functional Analysis

These are a set of lecture notes for a 3rd year undergraduate course in functional analysis. The lecture notes are available as a single pdf file (520k).

Basic mathematics

Lecture notes covering basic algebra and trigonometry.

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