density of primes / factors
[03-06-23]
how dense can a numbers factors be? and how dense are primes?
Measure Theory
[measure_theory]
Read this if you are interested in any of the following questions: "what is a meausre space?", "what's a set in R that has no well defined inner-measure?" / why do measure spaces need sigma-Algebra's defined on them?", "what's a Lesbegue integral?", "what's Lesbegue's dominated convergence theorem?" (note: work in progress)
Functional Analysis
[functional_analysis]
Build up to, and proof of Projection Theorem. Might also talk about general Banach spaces but probably mostly Hilbert spaces.
property testing "Direct Sum Testing"
[05-20-24]
Suppose you had a function that was a direct product. Could you tell? Yup.
pi^2/6
[08-25-23]
The fact \sum 1/n^2 = \pi^2/6 is well known and celebrated. In this note we present the simple fourier-analytic proof of this fact.
Lambert-W function Inverse
[08-31-23]
The lambert-W function $x\mapsto xe^{x}$ turns up surprisingly often. For some reason I always have had a hard time approximating it. Today I finally found the "inequalities" section of the wikipedia page for Lambert-W function, and will share it here.