Invitation to Nonlinear Algebra
Seiten
2021
American Mathematical Society (Verlag)
978-1-4704-5367-1 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-5367-1 (ISBN)
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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. This book offers an invitation to this broad and fast-developing area.
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.
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.
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.
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
| Erscheinungsdatum | 15.01.2021 |
|---|---|
| Reihe/Serie | Graduate Studies in Mathematics |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie | |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 1-4704-5367-3 / 1470453673 |
| ISBN-13 | 978-1-4704-5367-1 / 9781470453671 |
| Zustand | Neuware |
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Buch | Softcover (2022)
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CHF 55,95
