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Metric Algebraic Geometry by Paul Breiding, K Kohn, B. Sturmfels



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About this book :-
This text combines algebraic geometry and differential geometry to solve real-world problems. It focuses on understanding shapes and spaces defined by polynomial equations, which is useful in areas like data science, machine learning, and computer vision. Many applied problems center around metric questions, such as optimization with respect to distances. After a short dive into 19th-century geometry of plane curves, we turn to problems expressed by polynomial equations over the real numbers. The solution sets are real algebraic varieties. Many of our metric problems arise in data science, optimization and statistics. These include minimizing Wasserstein distances in machine learning, maximum likelihood estimation, computing curvature, or minimizing the Euclidean distance to a variety. This book addresses a wide audience of researchers and students and can be used for a one-semester course at the graduate level. The key prerequisite is a solid foundation in undergraduate mathematics, especially in algebra and geometry. Metric Algebraic Geometry aims to join methods and ideas of (metric) differential geometry with its (real) algebraic counterpart, with a common goal a variety of practical applications in optimization, modeling and analyzing statistical data, machine learning and computer vision. An ambitious goal indeed. The motivating observation is that many problems in those applications can be approached using polynomial equations in several variables and with coefficients in the field of real numbers.

Book Detail :-
This book has following details information.
Title: Metric Algebraic Geometry by Paul Breiding, K Kohn, B. Sturmfels by NA
Publisher: Birkhäuser
Series: freeCompBooks
Year: 2024
Pages: 232
Type: PDF
Language: English
ISBN-10 #: 3031514610
ISBN-13 #: 978-3031514616
Country: Pakistan
License: N\A
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About Author :-
The author NA NA

Book Contents :-
conver the following topics.
1. Historical Snapshot 2. Critical Equations 3. Computations 4. Polar Degrees 5. Wasserstein Distance 6. Curvature 7. Reach and Ofset 8. Voronoi Cells 9. Condition Numbers 10. Machine Learning 11. Maximum Likelihood 12. Tensors 13. Computer Vision 14. Volumes of Semi Algebraic Sets 15. Sampling

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