Metric Algebraic Geometry by Breiding, Kohn, Sturmfels
Metric Algebraic Geometry - Table of Contents
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
What You Will Learn in Metric Algebraic Geometry
"Metric Algebraic Geometry" by Paul Breiding, Kathlén Kohn, and Bernd Sturmfels is a modern mathematics book that connects "algebraic geometry" with "metric geometry" in a clear and application-driven way. The book focuses on geometric objects defined by polynomial equations and studies them using distances, angles, and optimization concepts. Rather than treating geometry as purely abstract, it emphasizes measurable and computable properties of algebraic varieties.
A key strength of the book is its strong link to real-world applications. Topics such as "Euclidean distance", "optimization", "curvature", and "critical points" are developed with examples coming from "data science", statistics, and machine learning. The authors show how classical geometry interacts with modern computational tools, making the subject relevant for both pure mathematicians and applied researchers.
Written at a graduate level, the book is suitable for advanced students with background knowledge in algebra and geometry. Its structured approach, combined with examples and exercises, makes it useful for self-study and seminars. Overall, "Metric Algebraic Geometry" provides a fresh and practical perspective on how "algebraic geometry", "distance problems", "real varieties", "optimization", and "applications" come together in contemporary mathematics.
Book Details & Specifications
Title:
Metric Algebraic Geometry by Breiding, Kohn, Sturmfels
Publisher:
Birkhäuser
Year:
2024
Pages:
232
Type:
PDF
Language:
English
ISBN-10 #:
3031514610
ISBN-13 #:
978-3031514616
License:
CC BY-NC-ND 4.0
Amazon:
Amazon
About the Author: Paul Breiding, K Kohn, B. Sturmfels
The author
Paul Breiding, K Kohn, B. Sturmfels
are leading researchers in "algebraic geometry", "computational mathematics", and "data-driven geometry". Paul Breiding works on numerical and probabilistic methods in geometry with applications to "optimization" and data science. Kathlén Kohn focuses on geometric techniques for "computer vision", machine learning, and statistics, connecting theory with real-world problems. Bernd Sturmfels is a globally recognized mathematician known for foundational work in "algebraic geometry", combinatorics, and applied mathematics. Together, the authors combine deep theory, computation, and applications, making "Metric Algebraic Geometry" a modern and influential contribution to "algebraic geometry", "optimization", "real varieties", "data science", and "metric geometry".
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