This summer school will introduce graduate students to sketching-based approaches to computational linear and multi-linear algebra. Sketching here refers to a set of techniques for compressing a matrix, to one with fewer rows, or columns, or entries, usually via various kinds of random linear maps. We will discuss matrix computations, tensor algebras, and such sketching techniques, together with their applications and analysis.
There will be two lectures per day. There will be a problem session in the morning after Lecture 1, and one in the afternoon after Lecture 2. The problem sessions will generally be led by the Teaching Assistants, though the Lecturers will be involved to observe or lead discussion as well. The purpose of the sessions is to reinforce and deepen students’ understanding of the material from the lectures by working on problems and in certain cases, to discuss material relevant to future lectures. This will be done by discussion, question-and-answer, and problem-solving from problem sets. Activities may include presentation of solutions to problems assigned based on lectures, student or TA presentation of material relevant to lecture, or exercises and presentation of relevant background material.