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Invitation to Nonlinear Algebra
 
Mateusz Michałek Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany and University of Konstanz, Konstanz, Germany
Bernd Sturmfels Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany
Front Cover for Invitation to Nonlinear Algebra
Available Formats:
Softcover ISBN: 978-1-4704-6551-3
Product Code: GSM/211.S
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Sale Price: $55.25
Electronic ISBN: 978-1-4704-6308-3
Product Code: GSM/211.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Sale Price: $55.25
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $127.50
MAA Member Price: $114.75
AMS Member Price: $102.00
Sale Price: $82.88
Front Cover for Invitation to Nonlinear Algebra
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  • Front Cover for Invitation to Nonlinear Algebra
  • Back Cover for Invitation to Nonlinear Algebra
Invitation to Nonlinear Algebra
Mateusz Michałek Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany and University of Konstanz, Konstanz, Germany
Bernd Sturmfels Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany
Available Formats:
Softcover ISBN:  978-1-4704-6551-3
Product Code:  GSM/211.S
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Sale Price: $55.25
Electronic ISBN:  978-1-4704-6308-3
Product Code:  GSM/211.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Sale Price: $55.25
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $127.50
MAA Member Price: $114.75
AMS Member Price: $102.00
Sale Price: $82.88
  • Book Details
     
     
    Graduate Studies in Mathematics
    Volume: 2112021; 226 pp
    MSC: Primary 05; 13; 14; 15; 20; 52; 90;

    Nonlinear algebra provides modern mathematical tools to address challenges arising in the sciences and engineering. It is useful everywhere, where polynomials appear: in particular, data and computational sciences, statistics, physics, optimization. The book offers an invitation to this broad and fast-developing area. It is not an extensive encyclopedia of known results, but rather a first introduction to the subject, allowing the reader to enter into more advanced topics. It was designed as the next step after linear algebra and well before abstract algebraic geometry. The book presents both classical topics—like the Nullstellensatz and primary decomposition—and more modern ones—like tropical geometry and semidefinite programming. The focus lies on interactions and applications. Each of the thirteen chapters introduces fundamental concepts. The book may be used for a one-semester course, and the over 200 exercises will help the readers to deepen their understanding of the subject.

    Readership

    Graduate students and researchers interested in nonlinear algebra.

  • Table of Contents
     
     
    • Chapters
    • Polynomial rings
    • Varieties
    • Solving and decomposing
    • Mapping and projecting
    • Linear spaces and Grassmannians
    • Nullstellensätze
    • Tropical algebra
    • Toric varieties
    • Tensors
    • Representation theory
    • Invariant theory
    • Semidefinite programming
    • Combinatorics
  • Reviews
     
     
    • … this book provides a highly accessible and very well-written introduction to the vast and exciting field of nonlinear algebra. The chapters are designed so as to be able to serve as a guideline for a graduate course in this field. Nevertheless, one can easily use this book for self-study and it is even usable for advanced undergraduates in mathematics. Given its high quality of writing and abundant examples that illustrate deep concepts in an easy-to-understand manner, I would expect that this book will serve as the classical textbook of this topic for many years to come.

      Fatemeh Mohammadi, Katholieke Universiteit Leuven
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Volume: 2112021; 226 pp
MSC: Primary 05; 13; 14; 15; 20; 52; 90;

Nonlinear algebra provides modern mathematical tools to address challenges arising in the sciences and engineering. It is useful everywhere, where polynomials appear: in particular, data and computational sciences, statistics, physics, optimization. The book offers an invitation to this broad and fast-developing area. It is not an extensive encyclopedia of known results, but rather a first introduction to the subject, allowing the reader to enter into more advanced topics. It was designed as the next step after linear algebra and well before abstract algebraic geometry. The book presents both classical topics—like the Nullstellensatz and primary decomposition—and more modern ones—like tropical geometry and semidefinite programming. The focus lies on interactions and applications. Each of the thirteen chapters introduces fundamental concepts. The book may be used for a one-semester course, and the over 200 exercises will help the readers to deepen their understanding of the subject.

Readership

Graduate students and researchers interested in nonlinear algebra.

  • Chapters
  • Polynomial rings
  • Varieties
  • Solving and decomposing
  • Mapping and projecting
  • Linear spaces and Grassmannians
  • Nullstellensätze
  • Tropical algebra
  • Toric varieties
  • Tensors
  • Representation theory
  • Invariant theory
  • Semidefinite programming
  • Combinatorics
  • … this book provides a highly accessible and very well-written introduction to the vast and exciting field of nonlinear algebra. The chapters are designed so as to be able to serve as a guideline for a graduate course in this field. Nevertheless, one can easily use this book for self-study and it is even usable for advanced undergraduates in mathematics. Given its high quality of writing and abundant examples that illustrate deep concepts in an easy-to-understand manner, I would expect that this book will serve as the classical textbook of this topic for many years to come.

    Fatemeh Mohammadi, Katholieke Universiteit Leuven
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