On this site, I collect brief notes about various topics in mathematics of interest to me.

Much of the material is not original. Some may be. I hope that itโs all well-written and interesting.

## Acceptance-rejection sampling

## Algebra of sets

## Almost sure convergence

## Arctangent at infinity

## Bayesian statistics

## Binomial coefficients

## Binomial series

## Bohr-Mollerup theorem

## Borel-Cantelli lemma

## Brownian motion

## Cadlag property

## Caratheodory measurable

## Caratheodory outer measure

## Caratheodory's extension theorem

## Cauchy's formula for repeated anti-differentiation

## Central limit theorem

## Characteristic functions

## Condorcet breakdown

## Convergence in distribution

## Convergence in probability

## Diffusion

## Duverger's law

## Equilibrium renewal processes

## Error function

## Euler's product representation of the gamma function

## Euler-Mascheroni constant

## Expected value

## Exponential integral

## Extendability condition for finitely additive measures

## Extension of measures from finite additivity to countable additivity

## Extreme value theory

## Finitely additive measure

## First passage time

## Fourier transform

## Fractional calculus

## Frechet distributions

## Gamma function

## Gumbel distribution

## Hegselmann-Krause model

## Infinite products

## Kermack-McKendrick model

## Laplace transform

## Laplace's rule of succession

## Law of exponents

## Lebesgue-Stieltjes measure

## Left-right model of election outcomes

## Linear algebra

## Majority judgment

## Multivariate Gaussian

## Opinion dynamics

## Pairwise comparison diagram

## Pi-lambda theorem

## Portmanteau theorem

## Preference schedule

## Range voting

## Renewal processes

## Riemann-Liouville fractional anti-derivative

## Sampling from prescribed distributions

## Shannon entropy

## Single winner election methods

- Condorcet breakdown in plurality voting and instant runoff (๐)
- Duverger's law (๐)
- Left-right model of election outcomes (๐)
- Left-right model with prejudiced voters (๐)
- Pairwise comparison diagrams and preference schedules
- Polarization and Condorcet breakdown for three candidates (๐)
- Range voting and majority judgment

## Smooth, compactly supported functions are dense in L1

## Special relativity

## Stieltjes length of intervals

## Tauber's theorem

## Uniform convergence of distribution functions

## Voting methods

- Condorcet breakdown in plurality voting and instant runoff (๐)
- Duverger's law (๐)
- Left-right model of election outcomes (๐)
- Left-right model with prejudiced voters (๐)
- Pairwise comparison diagrams and preference schedules
- Polarization and Condorcet breakdown for three candidates (๐)
- Range voting and majority judgment