The course is aimed at first-year graduate students and advanced undergraduates. The
goal of the course is to collect and present important mathematical tools used in
different areas of computer science. The course will mostly focus on linear algebra
and probability.
We intend to cover the following topics and examples:

- Abstract linear algebra: vector spaces, linear transformations, Hilbert
spaces, inner product, Gram-Schmidt orthogonalization, eigenvalues and eigenvectors,
SVD.
- Least squares, iterative solvers for systems of
linear equations, spectral graph theory, perturbation and stability of
eigenvalues
- Discrete probability: random variables, Markov, Chebyshev and Chernoff-Hoeffding
bounds
- Gaussian variables, concentration inequalities, dimension reduction.
- Spectral partitioning and clustering.
**Additional topics** (to be chosen from based on time and interest):
Martingales, Markov Chains, Random Matrices, Tensors, Chaining Methods

The course will have 5 homeworks (60 percent), a midterm (15 percent), and a final (25 percent).

There is no textbook for this course. Please see the "Resources" and "Recommended
Books" sections below for some useful references.