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Softcover ISBN:  9781470465513 
eBook: ISBN:  9781470463083 
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Softcover ISBN:  9781470465513 
Product Code:  GSM/211.S 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Sale Price:  $55.25 
eBook ISBN:  9781470463083 
EPUB ISBN:  9781470468316 
Product Code:  GSM/211.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Sale Price:  $55.25 
Softcover ISBN:  9781470465513 
eBook ISBN:  9781470463083 
Product Code:  GSM/211.S.B 
List Price:  $170.00 $127.50 
MAA Member Price:  $153.00 $114.75 
AMS Member Price:  $136.00 $102.00 
Sale Price:  $110.50 $82.88 

Book DetailsGraduate Studies in MathematicsVolume: 211; 2021; 226 ppMSC: 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 fastdeveloping 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 onesemester course, and the over 200 exercises will help the readers to deepen their understanding of the subject.
ReadershipGraduate 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


Additional Material

Reviews

This is the book I wish I had read when I was a graduate student...The book fulfills its role as an invitation to the realm of nonlinear algebra, not only for students but also for working mathematicians in other areas, although more advanced arguments naturally require further reading. By browsing this book one can taste the flavour of a growing and developing topic. The strategic choice of the 13 chapters is important in itself. The text is interactive and invites the readers to google some key words to get further information and to experience for themselves several paradigmatic examples with a computer algebra system. Also, several interesting applications are sketched or exemplified.
Alicia Dickenstein and Giorgio Ottaviani, Bulletin of the AMS 61 (2024), 187198 
The text is likely to be an inspiration for the upandcoming graduate student as well as an established mathematician who is looking to widen the scope of their work. By drawing on topics from a wide range of pure and applied mathematics and weaving them into a single narrative, the authors convince us that nonlinear algebra is a discipline to which we should all be introduced.
Anton Dochtermann (Texas State University), MathSciNet Reviews 
... this book provides a highly accessible and very wellwritten 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 selfstudy 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 easytounderstand 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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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 fastdeveloping 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 onesemester course, and the over 200 exercises will help the readers to deepen their understanding of the subject.
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 is the book I wish I had read when I was a graduate student...The book fulfills its role as an invitation to the realm of nonlinear algebra, not only for students but also for working mathematicians in other areas, although more advanced arguments naturally require further reading. By browsing this book one can taste the flavour of a growing and developing topic. The strategic choice of the 13 chapters is important in itself. The text is interactive and invites the readers to google some key words to get further information and to experience for themselves several paradigmatic examples with a computer algebra system. Also, several interesting applications are sketched or exemplified.
Alicia Dickenstein and Giorgio Ottaviani, Bulletin of the AMS 61 (2024), 187198 
The text is likely to be an inspiration for the upandcoming graduate student as well as an established mathematician who is looking to widen the scope of their work. By drawing on topics from a wide range of pure and applied mathematics and weaving them into a single narrative, the authors convince us that nonlinear algebra is a discipline to which we should all be introduced.
Anton Dochtermann (Texas State University), MathSciNet Reviews 
... this book provides a highly accessible and very wellwritten 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 selfstudy 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 easytounderstand 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