Outline

1. Math and basic statistics
   1. Linear algebra
   2. Basic differential equations
   3. Probability theory
   4. Basic statistics
      1. Sampling, distributions, variance, central tendency
      2. Standardization, z-scores, standard errors
      3. Statistical significance, effect size, confidence intervals, correlation
      4. t-tests, F-tests, ANOVA, chi-squared
      5. Monte Carlo methods and Markov chains
      6. Basics of Bayesian statistics
2. Coding (recommend: Python)
   1. Data types
   2. Logic and control: iteration, conditionals
   3. Functions, classes, and objects
   4. Modularity, abstraction, encapsulation, algorithms
3. Data prep
   1. Wrangling, cleaning, and processing
   2. Exploratory analysis and data visualization
4. Regression analysis
   1. Linear regression
      1. OLS, simple regression, multiple regression
      2. Variable selection, Variable transformation, weighted least squares
      3. Regression diagnostics, autocorrelation, multicollinearity
      4. Multi-level modeling
      5. Ridge regression and LASSO
   2. Poisson and negative binomial regression
   3. Path analysis, structural equation modeling, and causal models
5. Machine learning and data mining
   1. Supervised learning classifiers
      1. Logistic regression
      2. Support vector machines
      3. Decision trees and random forests
      4. k-nearest neighbors and kernel density estimation
      5. Perceptron
      6. Naïve Bayes
   2. Clustering
      1. Hierarchical
      2. k-means
      3. DBSCAN
      4. OPTICS
   3. Dimensionality reduction
      1. Factor analysis
      2. Linear discriminant analysis
      3. Principal components analysis
      4. Multidimensional scaling
   4. Neural networks
      1. Back-propagation
      2. Recurrent neural network
      3. Self-organizing maps
      4. Deep learning
   5. Natural language processing
6. Network analysis
7. Tools
   1. Python libraries (NLTK, scikit-learn, scipy, statsmodels, numpy, pandas, networkx, matplotlib)
   2. Apache Spark, Hadoop, MapReduce
   3. TensorFlow and Theano