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Tropical Geometry

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Part of the Foundations for Undergraduate Research in Mathematics book series (FURM)

Abstract

Tropical mathematics redefines the rules of arithmetic by replacing addition with taking a maximum, and by replacing multiplication with addition. After briefly discussing a tropical version of linear algebra, we study polynomials built with these new operations. These equations define piecewise-linear geometric objects called tropical varieties. We explore these tropical varieties in two and three dimensions, building up discrete tools for studying them and determining their geometric properties. We then discuss the relationship between tropical geometry and algebraic geometry, which considers shapes defined by usual polynomial equations.

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Williams CollegeWilliamstownUSA

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