Volume: 211; 2021; 226 pp; Softcover
MSC: Primary 05; 13; 14; 15; 20; 52; 90;
Print ISBN: 978-1-4704-6551-3
Product Code: GSM/211.S
List Price: $85.00
AMS Member Price: $68.00
MAA Member Price: $76.50
Electronic ISBN: 978-1-4704-6308-3
Product Code: GSM/211.E
List Price: $85.00
AMS Member Price: $68.00
MAA Member Price: $76.50
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Supplemental Materials
Invitation to Nonlinear Algebra
Share this pageMateusz Michałek; Bernd Sturmfels
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
Table of Contents
Invitation to Nonlinear Algebra
- Cover Cover11
- Title page iii4
- Preface xi12
- Acknowledgments xiii14
- Chapter 1. Polynomial Rings 116
- Chapter 2. Varieties 1934
- Chapter 3. Solving and Decomposing 3954
- Chapter 4. Mapping and Projecting 5772
- Chapter 5. Linear Spaces and Grassmannians 7388
- Chapter 6. Nullstellensätze 87102
- Chapter 7. Tropical Algebra 99114
- Chapter 8. Toric Varieties 115130
- Chapter 9. Tensors 133148
- Chapter 10. Representation Theory 151166
- Chapter 11. Invariant Theory 171186
- Chapter 12. Semidefinite Programming 187202
- Chapter 13. Combinatorics 201216
- Bibliography 219234
- Index 223238
- Back Cover Back Cover1243