- Probability Spaces and Random Variables
- Distribution and Density functions
- Law of large numbers
- Univariate and multivariate distributions
- Expected Values and Higher Order Moments
- Multivariate Theory (Covariance, Independence, Conditional Expectation)
- Market Models and simple Portfolio Optimization
- Discrete Market Models and Derivatives Pricing using Risk Neutral Probability measures
- Stochastic Processes and martingales

- Data ETL, statistics and plotting
- Linear Regression including Regularization techniques
- Variables Selection - For Regressions, PCA, Correlated Variables AIC and CV use
- Model Selection, Test/Train CV, Caret and scikit-learn. AIC, BIC, Bias Variance tradeoff, Use of test/train split and CV use
- Classification Techniques
- Ensemble Models: Trees, Random Forest, Gradient Boosting. Variable selection with ensemble techniques
- Support Vector Machine
- Practicum Analysis of a data set

- Stationarity
- ARMA, ARIMA and GARCH models
- Introduction to Spectrum
- GMM
- Introduction to VARs
- Factor Models
- Empirical Processes
- Unit Roots
- Cointegration
- Filtering, State Space Models
- Kalman Filter

- Analysis, Interpretation and Visualization of data
- Confidence Intervals and Significance tests
- Design of Experiments and Hypothesis Testing
- Analysis of variance
- Multiple Regression models

- Introduction to Deep Learning Principles, Tensor Flow and Keras
- Convolutional Neural Networks
- Hidden Markov Models
- Recurrent Neural Networks
- Deep Autoencoders
- Reinforcement Learning

- Linear and Non Linear Equations
- Interpolation and Optimization
- Finite Difference Method
- Monte Carlo Simulations
- Variance Reduction Techniques
- Principal Component Analysis

All our data science courses require Linear Algebra and Advance Calculus as pre-requisite. We encourage students to take foundation courses in Linear Algebra and Calculus before diving into **advanced** data science courses