Probability
Basics of Probability
Addition and multiplication rules, conditional probability, and Bayes' theorem.
Discrete Random Variables
Bernoulli, Binomial, Poisson, Categorical and Multinomial distributions.
Probability Densities
Gaussian, Uniform, Exponential distributions. Transformation of densities.
Multivariate Gaussian Distribution
Conditionals, marginals, Bayes updates, maximum likelihood estimation
Transformations of Densities
Change of variables, Jacobians.
Multivariate Calculus
Functions of Multiple Variables
Graphical representations of multivariate functions. Limits and continuity
Partial Derivatives
Understanding change in multiple dimensions.
Chain Rule
Generalizing the chain rule for multivariate functions.
Directional Derivatives
Rates of change in any direction. Opimal direction of change.
Differentials and Jacobians
Linear approximations, differentials, and Jacobians.
Optimization
Optimization of multivariate functions.
Multivariate Integration
Integration of multivariate functions.