Daniel Walton

Harvey Mudd College Mathematics 2007

Thesis Final Report: A Tiling Approach to Chebyshev Polynomials
Thesis Advisor: Prof. Arthur Benjamin
Second Reader: Prof. Sanjai Gupta

A Tiling Approach to Chebyshev Polynomials

Chebyshev polynomials arise in a variety of continuous settings. They are a sequence of orthogonal polynomials appearing in approximation theory, numerical integration, and differential equations. In my theiss we approach them instead as discrete objects, counting the sum
of weighted tilings. Our combinatorial approach will allow us to prove identites holding for these continuous functions using discrete arguments.