Linear algebra: Vector spaces, linear transformations, change of basis, inner products, orthogonalization, least squares approximation, QR factorization, determinants, eigenvalues and eigenvectors, diagonalization, Jordan forms, matrix exponentials and applications to systems of differential equations, other applications of linear algebra.
Probability and statistics: Sample spaces, probability, random variables and probability distributions, standard discrete and continuous distributions, multivariate distributions, Central Limit Theorem, statistical inference, confidence intervals and hypothesis testing, linear regression, inference in the linear model. Matlab will be used in this course.