Helm, David, doctor of mathematics2012-02-012017-05-112012-02-012017-05-112011-12December 2http://hdl.handle.net/2152/ETD-UT-2011-12-4777textHurwitz numbers are a weighted count of degree d ramified covers of curves with specified ramification profiles at marked points on the codomain curve. Isomorphism classes of these covers can be included as a dense open set in a moduli space, called a Hurwitz space. The Hurwitz space has a forgetful morphism to the moduli space of marked, stable curves, and this morphism encodes the Hurwitz numbers. Mikhalkin has constructed a moduli space of tropical marked, stable curves, and this space is a tropical variety. In this paper, I construct a tropical analogue of the Hurwitz space in the sense that it is a connected, polyhedral complex with a morphism to the tropical moduli space of curves such that the degree of the morphism encodes the Hurwitz numbers.application/pdfengTropical geometryAlgebraic geometrythesis2012-02-012152/ETD-UT-2011-12-4777