Probability
See also:

Discrete math / combinatorics
Graphical Models
https://en.wikipedia.org/wiki/Bayesian_network bayesian networks directed edges express conditional rpobablity. Hopefully acyclic. https://en.wikipedia.org/wiki/Graphical_model graphical models https://en.wikipedia.org/wiki/Markov_random_field
Statistics
I should have more to say here? Probability Experimental design Hypothesis testing Goodness of fit metrices Bayes rules Regularization Bayes rule and regularization can be seen to be related. Regularization corresponds to a prior that the values of your parameters arenâ€™t going to be ridiculous. A Gaussian prior and guassian distrubtion of error
\(e^{ \frac{\eps^2}{\sigma^2} }\) \(y_j = \eps_j + \sum a_i f_i(x_j)\)
Machine learning
Cumulants Paradoxes
Measure theory stochastic calculus
Combinatorics
Markov decision processes Monte carlo algos las vegas algos
Bayesian
bayesian vs freqeuntist Priors as regularization
Distributions
Gaussian Poisson Binomial
Mathematical
https://en.wikipedia.org/wiki/Cox%27s_theorem
from z3 import *
E = Sort("Event")
P = Function("P", E, RealSort())
# Proof system for probability theory?
https://en.wikipedia.org/wiki/Probability_axioms Kolmogorov axioms
Sets and probability. You need to know an ambient space X to be working in.
https://en.wikipedia.org/wiki/Probabilistic_logic
Law of Total Probability $P(A) = \sum P(A \cap B_i) = \sum P(A  B_i) P(B_i)$ if $B_i$ is a partition of the sample space
https://en.wikipedia.org/wiki/Law_of_total_expectation
Central limit theorem
Markov bound Chernoff bound