Linear Algebra I (1/6/2022)
Course goals and logistics. Vectors, linear combinations, span, matrices as linear transformations, matrix multiplication, determinants, matrix inverse, range, nullspace.
Programming basics (Optional) (1/13/2022)
Programming basics. Introduction to Colab notebooks and Python syntax. NumPy.
Linear Algebra II (1/20/2022)
Change of basis, eigenvalues and eigenvectors, principal components analysis (PCA).
Probability and Statistics I (2/3/2022)
Introduction to basic probability theory & useful distributions (normal, binomial, poisson)
Probability and Statistics II (2/17/2022)
Applied statistics. Significance testing using formal methods (e.g. T-test, ANOVA) vs. resampling techniques (bootstrapping & permutation testing). Model selection using cross validation.
Differential Equations (3/3/2022)
Introduction to ODEs and methods for solving. Linear dynamical systems. Leaky integrate-and-fire model neuron.