Nikolas Rauh

Harvey Mudd College Mathematics 2006

Thesis Proposal: Research Proposal: An Treatise on Subtropical Algebra
Midyear Report: Midyear Report: A Treatise on Subtropical Algebra
Thesis: An Exploration in Subtropical Algebra
Poster: An Exploration in Subtropical Algebra Poster
Thesis Advisor: Prof. Francis E. Su
Second Reader: Prof. Arthur T. Benjamin
E-Mail: rauh at math dot hmc dot edu

An Exploration in Subtropical Algebra

Our goal is to understand the workings of min-max arithmetic in an abstracted setting and to use this understanding to produce interesting mathematical objects for further study. We are using Tropical Algebra as the framework for posing questions about min-max algebra. Due to this desire to mimic Tropical results and the similarity of the operations in Tropical Arithmetic and min-max arithmetic, Francis Su and I call this field Subtropical Algebra. What is presented in the first portion of the thesis is a largely failed attempt to construct subtropical polynomials and some basic objects of subtropical geometry. In the second portion, we present a classification of the subtropical endomorphisms in terms of the topologies they induce.