Polynomials and applications

Time: Wednesdays, 1130-1300 and Fridays, 0930-1100

Place: Online, as of now. YouTube playlist.

Lecture notes/transcripts

Brief description

This will be a “short” (a total of 20-25 hours of lectures over the semester) 2-credit course.

Tentative list of topics

  1. Tools for analyzing the locations of roots of polynomials: rule of signs, Rolle’s theorem, Gauss- Lucas lemma.

  2. Stability theory of polynomials, and closure properties of stable polynomials.

  3. Connections between stability and computer science: negative association. The method of interlacing polynomials, and its use in the Marcus-Spielman-Srivastava Ramanujan graph construction.

  4. Polynomial interpolation with errors, and a brief review of its applications in computer science, including quantum computation.

Prerequisites

The prerequisites for the course are minimal (basic calculus/analysis and Class 12 level complex numbers). Having taken one of the two Mathematical Foundations courses offered by the department would be helpful.

Evaluation

Evaluation will be based on 2-3 homework assignments (60-70% of the final grade) and a final exam (30-40% of the final grade).