Tropical geometry is a combinatorial shadow of algebraic geometry,
offering new polyhedral tools to compute invariants of algebraic
varieties. It is based on tropical algebra, where the sum of two
numbers is their minimum and the product is their sum. This turns
polynomials into piecewise-linear functions, and their zero sets
into polyhedral complexes. These tropical varieties retain a
surprising amount of information about their classical
counterparts. Tropical geometry is a young subject that has
undergone a rapid development since the beginning of the 21st
century. While establishing itself as an area in its own right,
deep connections have been made to many branches of pure and
applied mathematics. This book offers a self-contained introduction
to tropical geometry, suitable as a course text for beginning
graduate students. Proofs are provided for the main results, such
as the Fundamental Theorem and the Structure Theorem. Numerous
examples and explicit computations illustrate the main concepts.
Each of the six chapters concludes with problems that will help the
readers to practice their tropical skills, and to gain access to
the research literature.
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