Master’s thesis

October 6, 2011

My student

Thomas Chartier

will be will defending his Master’s thesis for a Mathematics degree, titled

Coloring Problems


Abstract: We consider two coloring problems which have a combinatorial flavor. The chromatic number of the plane, \chi, is the least number of colors necessary to color {\mathbb R}^2 in such a way that no two points at a unit distance apart receive the same color. It is well known that 4\le\chi\le 7. We begin by discussing the arguments that give these bounds.

The main point the talk considers the problem of whether given any n\in{\mathbb Z}^+, one can color the positive integers in such a way that for all a\in{\mathbb Z}^+, the numbers a,2a,3a,\dots,na are assigned different colors. Such colorings are referred to as satisfactory. We begin with an example which provides insight into the underlying structure inherent in all satisfactory colorings, present a sufficient condition for guaranteeing the existence of satisfactory colorings, and analyze the resulting structure.


The defense will be held Thursday, October 13, 2011, 2:40-3:30 pm, in Room MP-201. Refreshments will be served in the math lounge at 2:15 pm.

187 – Selected solutions from Chapter 2

October 6, 2011

Professor Warren Esty, has made available a list of solutions to some of the problems from Chapter 2. As before, please let him (or me) know if you find errors or typos, or if you have suggestions for alternative solutions or different approaches.

Solutions (Chapter 2)