TTIC 31150/CMSC 31150 - Mathematical Toolkit (Spring 2021)

Lectures: Tue/Thu 4:20-5:40pm, Online (See Canvas page for zoom link)

Discussion: Wed 6:00-7:00, Online

Instructor: Avrim Blum (Office hours: Mon 1:00-2:00)

TAs: Han Shao (Office hours: Mon 6:00-7:00) and Tushant Mittal (Office hours: Wed 11:00-12:00)

Course description: 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:

Coursework: 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 "Recommended test/readings" section below for some useful references.


Lecture Notes

  1. 03/30: Fields and vector spaces. Linear independence and bases.
  2. 04/01: Vector space applications and linear transformations.
  3. 04/06: Eigenvalues and eigenvectors.
  4. 04/08: Orthogonality and adjoints.
  5. 04/13: The Real Spectral Theorem.
  6. 04/15: Singular Value Decomposition.
  7. 04/20: SVD for Matrices.

Recommended texts/readings: