Graduation Year

2006

Document Type

Open Access Senior Thesis

Degree Name

Bachelor of Science

Department

Mathematics

Reader 1

Francis Edward Su

Reader 2

Michael Orrison

Abstract

This paper explores some properties of subtropical arithmetic, which is the extended real line R = R ∪ {−∞, ∞} considered under the binary operations min(·, ·) and max(·, ·). We begin by examining some results in tropical polynomials. We then consider subtropical polynomials and subtropical geometry, drawing on tropical geometry for motivation. Last, we derive a complete classification of subtropical endomorphisms up to equivalence with respect to the coarsest topologies making these endomorphisms continuous.

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