The (quasi)-Duality of the Lie Derivative and Exterior Derivative
A short set of notes that arose out of an enigmatic comment I encountered, to the effect that the Lie and exterior derivatives were almost-dual in some sense. I wanted to ferret out what this meant, which turned out to be more involved than anticipated. Along the way, I decided to explore something else I never had properly understood: the nature of integration from a topological perspective. This led to an exploration of the equivalence of de Rham and singular cohomology.
Read MoreSemidirect Products, Split Exact Sequences, and all that
A detailed discussion of semidirect products, groups extensions, and split exact sequences.
Read MoreDifferential Entropy
A discussion of some of the subtleties of differential entropy. This also contains a review of discrete entropy, various entropy-related information quantities such as mutual information, and a listing of various axiomatic formulations.
Read MoreCardinality
A compilation of useful results involving cardinal numbers (small ones, not huge ones) and arithmetic, along with the cardinalities of certain useful sets. There’s also a small section on bases of infinite-dimensional vector spaces. Proofs and justifications for many of the results are included in an appendix.
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A Place of Sand 