Date of Final Oral Examination (Defense)


Type of Culminating Activity


Degree Title

Master of Science in Mathematics



Major Advisor

Andres E. Caicedo, Ph.D.


This thesis considers several coloring problems all of which have a combinatorial flavor. We review some results on the chromatic number of the plane, and improve a bound on the value of regressive Ramsey numbers. The main work of this thesis considers the problem of whether given any n ≥ 1; one can color Z+ in such a way that for all a ϵ Z+ the numbers a, 2a, 3a, ..., na are assigned different colors. Such colorings are referred to as satisfactory. We provide a sufficient condition for guaranteeing the existence of satisfactory colorings and analyze the resulting structure. Explicit constructions are given for n ≤ 54: The thesis concludes with some suggestions towards a general argument.