Course overview¶
- Software installation and check: Should be able to start IPython Notebook
from the shell and see an option for a new R notebook when Jupyter starts in the browser
- Introduction to Jupyter Notebook https://jupyter.org/
- Introduction to R in Jupyter
- Mathematical preliminaries
- Matrix algebra
- Linear algebra
- real linear vector spaces
- norms and normed linear spaces
- the triangle inequality
- subspaces
- bases
- orthonormal bases
- the Gram--Schmidt procedure
- Numerical linear algebra
- solving linear equations
- condition number
- matrix inversion versus matrix factorization
- the QR decomposition
- Least squares
- the projection theorem
- closest point in a convex set
- closest point in a subspace
- the least squares principle; Legendre & Gauss
- the Normal equations
- Linear Regression
- Experiments and Observational Studies
- Confounding
- The Method of Comparison
- Stratification and cross-tabulation
- Randomization
- Simulation
- Pseudo-random number generators (PRNGs)
- Simulating non-uniform random variates http://luc.devroye.org/rnbookindex.html
- Generating random permutations: Knuth's method
- Monte Carlo methods
- Resampling methods