Invitation to Nonlinear Algebra

Mateusz Michalek, Bernd Sturmfels (Autoren)

Buch | Softcover

226 Seiten

2021
American Mathematical Society (Verlag)
978-1-4704-6551-3 (ISBN)

Artikel merken

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	19.07.2021
Reihe/Serie	Graduate Studies in Mathematics
Verlagsort	Providence
Sprache	englisch
Gewicht	428 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	1-4704-6551-5 / 1470465515
ISBN-13	978-1-4704-6551-3 / 9781470465513
Zustand	Neuware