
Invitation to Nonlinear Algebra
American Mathematical Society (Publisher)
Will be published approx. on 30. July 2021
Book
Paperback/Softback
226 pages
978-1-4704-6551-3 (ISBN)
Description
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.
More details
Series
Language
English
Place of publication
Providence
United States
Target group
Professional and scholarly
Weight
428 gr
ISBN-13
978-1-4704-6551-3 (9781470465513)
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Schweitzer Classification
Persons
Mateusz Michalek, Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany, and University of Konstanz, Germany.
Bernd Sturmfels, Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany.
Bernd Sturmfels, Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany.
Content
Polynomial rings
Varieties
Solving and decomposing
Mapping and projecting
Linear spaces and Grassmannians
Nullstellensatze
Tropical algebra
Toric varieties
Tensors
Representation theory
Invariant theory
Semidefinite programming
Combinatorics
Bibliography
Index
Varieties
Solving and decomposing
Mapping and projecting
Linear spaces and Grassmannians
Nullstellensatze
Tropical algebra
Toric varieties
Tensors
Representation theory
Invariant theory
Semidefinite programming
Combinatorics
Bibliography
Index