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