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Tropical geometry. (English) Zbl 1441.14208
Harris, Pamela E. (ed.) et al., A project-based guide to undergraduate research in mathematics. Starting and sustaining accessible undergraduate research. Cham: Birkhäuser. Found. Undergrad. Res. Math., 63-105 (2020).
Summary: 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.
For the entire collection see [Zbl 1454.00004].
MSC:
14Txx Tropical geometry
14-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry
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