Currently:

Descriptive Statistics, Probability, Discrete Probability Distributions, Continuous Probability Distributions, Estimation, Hypothesis Testing: One-Sample Inference, Hypothesis Testing: Two-Sample Inference, Nonparametric Methods, Hypothesis Testing: Categorical Data, Regression and Correlation Methods, Multisample Inference, Design and Analysis Techniques for Epidemiologic Studies, and Hypothesis Testing: Person-Time Data. 

Methods of Point Estimation, Properties of Point Estimators, Sufficiency and Completeness, Confidence Intervals, Testing Statistical Hypotheses, and Likelihood Ratio Tests.

In the past:

Introduction and Overview, Bayesian Network (Directed Models), Template Models for Bayesian Networks, Structured CPDs for Bayesian Networks, Markov Networks (Undirected Models), Decision Making, and Knowledge Engineering & Summary.

Overview of Supervised Learning, Linear Methods for Regression, Linear Methods for Classification, Basis Expansions and Regularization, Kernel Smoothing Methods, Model Assessment and Selection, Model Inference and Averaging, Additive Models, Trees, and Related Methods, 0 Boosting and Additive Trees, 1 Neural Networks, Support Vector Machines and Flexible Discriminants,  Prototype Methods and Nearest-Neighbors, Unsupervised Learning, Random Forests, Ensemble Learning, Undirected Graphical Models, and High-Dimensional Problems: p>>n. 

Kolomogrov axioms, random variables, probability distributions, expectations, conditional independence. Borel-Cantly theorem, characteristic functions, central limit theorem, convergence, Martingale theory, Laws of large numbers, Markov chains.

Simple and multiple regression, multiple and partial correlation,  weighted least squares, testing hypothesis in regression, diagnostic and remedial measures, residual analysis, qualitative independent variables, reduction sum of squares, serial correlation, analysis of covariance, multiple comparison, nonparametric tests, calibration problem, logistic regression, Poisson regression, nonlinear regression, Kruskel-Wallis test, Fredman’s test.

Review of linear algebra including vector and matrix norms and canonical forms. Analysis of numerical methods for linear systems (direct and iterative), conditioned systems. Eigenvalues problems, Interpolation and approximation using polynomials, trigonometric functions and orthogonal polynomials, numerical integration, multiple integrals, and error analysis  of numerical methods for differential equations.

Matrix algebra, determinants, inverses of matrices, Euclidean and unitary spaces, linear transformation, Jordan forms, Calay-Hamilton theorem, matrices:(simple, positive definite, Hermitran, unitary, normal),  and decomposition: (Schur’s, Jordan’s, singular value).

complex numbers, analytic functions, elementary functions, integrals , series, residues and poles, applications of residues, mapping by elementary functions, conformal mapping, applications of conformal mapping, the schwarz-christoffel transforn1ation, integral formulas of the poisson type. 

complex numbers, analytic functions, elementary functions, integrals , series, residues and poles, applications of residues, mapping by elementary functions, conformal mapping, applications of conformal mapping, the schwarz-christoffel transforn1ation, integral formulas of the poisson type.