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Essentials of Tropical Combinatorics
 
Michael Joswig Technische Universität Berlin, Berlin, Germany and Max-Planck Institut für Mathematik in den Naturwissenschaften, Leipzig, Germany
Essentials of Tropical Combinatorics
Softcover ISBN:  978-1-4704-6741-8
Product Code:  GSM/219.S
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
eBook ISBN:  978-1-4704-6740-1
EPUB ISBN:  978-1-4704-7234-4
Product Code:  GSM/219.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Softcover ISBN:  978-1-4704-6741-8
eBook: ISBN:  978-1-4704-6740-1
Product Code:  GSM/219.S.B
List Price: $170.00 $127.50
MAA Member Price: $153.00 $114.75
AMS Member Price: $136.00 $102.00
Please Note: Purchasing the eBook version includes access to both a PDF and EPUB version
Essentials of Tropical Combinatorics
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Essentials of Tropical Combinatorics
Michael Joswig Technische Universität Berlin, Berlin, Germany and Max-Planck Institut für Mathematik in den Naturwissenschaften, Leipzig, Germany
Softcover ISBN:  978-1-4704-6741-8
Product Code:  GSM/219.S
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
eBook ISBN:  978-1-4704-6740-1
EPUB ISBN:  978-1-4704-7234-4
Product Code:  GSM/219.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Softcover ISBN:  978-1-4704-6741-8
eBook ISBN:  978-1-4704-6740-1
Product Code:  GSM/219.S.B
List Price: $170.00 $127.50
MAA Member Price: $153.00 $114.75
AMS Member Price: $136.00 $102.00
Please Note: Purchasing the eBook version includes access to both a PDF and EPUB version
  • Book Details
     
     
    Graduate Studies in Mathematics
    Volume: 2192021; 398 pp
    MSC: Primary 14; 52; 90;

    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 \(\texttt{polymake}\).

    Readership

    Graduate students and researchers interested in combinatorial, polyhedral, and optimization aspects (as opposed to algebraic geometry aspects) of tropical geometry.

  • Table of Contents
     
     
    • Chapters
    • Tropical hypersurfaces
    • Fields of power series and tropicalization
    • Graph algorithms and polyhedra
    • Products of tropical polynomials and the Cayley trick
    • Tropical convexity
    • Combinatorics of tropical polytopes
    • Tropical half-spaces
    • Tropical linear programming
    • Feasibility and mean payoffs
    • Matroids and tropical linear spaces
    • Geometric combinatorics
    • Computational complexity
    • Using $\texttt {polymake}$
    • Hints to selected problems
  • Reviews
     
     
    • The expository style is remarkably friendly to newcomers, while the content includes several topics that a practitioner of tropical geometry may find new or refreshing. No knowledge of algebraic geometry is required throughout the textbook. An exposure to polyhedral geometry and computational complexity is helpful, for which Appendices A and B provide a suitable introduction. Each chapter includes numerous exercises and some open problems for future research, along with Appendix D which discusses them further. The textbook will become an indispensable reference for the interaction between tropical geometry and optimization.

      Christopher Eur (Harvard Department of Mathematics), MathSciNet
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2192021; 398 pp
MSC: Primary 14; 52; 90;

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 \(\texttt{polymake}\).

Readership

Graduate students and researchers interested in combinatorial, polyhedral, and optimization aspects (as opposed to algebraic geometry aspects) of tropical geometry.

  • Chapters
  • Tropical hypersurfaces
  • Fields of power series and tropicalization
  • Graph algorithms and polyhedra
  • Products of tropical polynomials and the Cayley trick
  • Tropical convexity
  • Combinatorics of tropical polytopes
  • Tropical half-spaces
  • Tropical linear programming
  • Feasibility and mean payoffs
  • Matroids and tropical linear spaces
  • Geometric combinatorics
  • Computational complexity
  • Using $\texttt {polymake}$
  • Hints to selected problems
  • The expository style is remarkably friendly to newcomers, while the content includes several topics that a practitioner of tropical geometry may find new or refreshing. No knowledge of algebraic geometry is required throughout the textbook. An exposure to polyhedral geometry and computational complexity is helpful, for which Appendices A and B provide a suitable introduction. Each chapter includes numerous exercises and some open problems for future research, along with Appendix D which discusses them further. The textbook will become an indispensable reference for the interaction between tropical geometry and optimization.

    Christopher Eur (Harvard Department of Mathematics), MathSciNet
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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