Essentials of Tropical Combinatorics

Released on by Michael Joswig
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  • Essentials of Tropical Combinatorics Book Detail

  • Author : Michael Joswig
  • Release Date : 2021-12-08
  • Publisher : American Mathematical Society
  • Genre : Mathematics
  • Pages : 398
  • ISBN 13 : 1470466538
  • File Size : 72,72 MB
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Essentials of Tropical Combinatorics by Michael Joswig PDF Summary

Book Description: The goal of this book is to explain, at the graduate student level, connections between tropical geometry and optimization. Building bridges between these two subject areas is fruitful in two ways. Through tropical geometry optimization algorithms become applicable to questions in algebraic geometry. Conversely, looking at topics in optimization through the tropical geometry lens adds an additional layer of structure. The author covers contemporary research topics that are relevant for applications such as phylogenetics, neural networks, combinatorial auctions, game theory, and computational complexity. This self-contained book grew out of several courses given at Technische Universität Berlin and elsewhere, and the main prerequisite for the reader is a basic knowledge in polytope theory. It contains a good number of exercises, many examples, beautiful figures, as well as explicit tools for computations using $texttt{polymake}$.

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