Notes
Notes
Notes on Various Topics
Under Construction
This is a list of notes on various topics from our research group. This page is, in part, a challenge to all group members, myself included, to produce notes that we can use and share in our teaching and research. If you see a topic that does not have an accompanying set of notes, you can do something about it!
I will frequently update this page, so expect more to come soon. Please contact me if you wish to collaborate on a set of notes, collaborate on improving already posted notes, or post notes of your own with proper attribution and a link to your website. My hope is that this will lead to some interesting scholarly collaborations!
The Weierstrass Approximation Theorem
This note gives a proof of the Weierstrass Approximation Theorem. It is intended for undergraduates in a probability course who have seen the Weak Law of Large numbers. It does not assume a background in real analysis.
The Convergence of Random Walks to Brownian Motion
This is a note outlines the ideas involved in the convergence of random walks to Brownian motion on the real line.
On the Pontryagin Duality of Finite Dimensional Vector Spaces over the p-Adic Numbers
This note gives an introduction to inductive and projective limits from a categorical perspective and demonstrates the self-duality of the p-adic numbers.
On the Determination of Planck Length
Brownian Motion and the Molecular Nature of Matter
The Feynman-Kac Formula
Stochastic Integration
The Spectral Theorem
Structure of a Quantum Logic
Probability in the Quantum World
The Riesz-Markov-Kakutani Theorem
On Bochner's Theorem and its Variants
The Schwartz Kernel Theorem
Classification of Elementary Particles via the Method of L. Schwartz
The Convergence of Finite Dimensional Quantum Systems
Connections on Vector Bundles
On Special Relativity
Determining the Speed of Light