The course covers fundamental topics in linear algebra and probability theory. In the linear algebra part, concepts such as linear dependence, linear function, matrix, matrix multiplication, inverse matrix, determinant, eigenvalue, eigenvector, definiteness, idempotent matrix, projection matrix, and orthogonal projection matrix are defined. Results such as the Fundamental Theorem of Linear Algebra, Cramer’s rule, and the Spectral Theorem are discussed.
In the probability part concepts such as sample space, conditional probability, independence, expected value, variance, and moment-generating function are introduced. The most common discrete and continuous distributions are covered, including the bivariate normal distribution. Finally, various forms of convergence, the central limit theorem, the law of large numbers, the delta method, and maximum likelihood estimation are discussed.