rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Metric Algebraic Geometry
  name:
    name part: Breiding, Paul.
    role:
      role term: creator
    role:
      role term: author.
    role:
      role term: aut
    role:
      role term: http://id.loc.gov/vocabulary/relators/aut
  name:
    name part: Kohn, Kathlén.
    role:
      role term: author.
    role:
      role term: aut
    role:
      role term: http://id.loc.gov/vocabulary/relators/aut
  name:
    name part: Sturmfels, Bernd.
    role:
      role term: author.
    role:
      role term: aut
    role:
      role term: http://id.loc.gov/vocabulary/relators/aut
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  genre: Electronic books.
  origin info:
    place:
      place term: sz
    date issued: 2024
    edition: 1st ed. 2024.
    issuance: monographic
  language:
    language term: eng
  physical description:
    reformatting quality: access
    form: remote
    extent: 1 online resource (XIV, 215 pages)
  abstract: Metric algebraic geometry combines concepts from algebraic geometry and differential geometry. Building on classical foundations, it offers practical tools for the 21st century. 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. This is an open access book.
  table of contents: Preface -- Historical Snapshot -- Critical Equations -- Computations -- Polar Degrees -- Wasserstein Distance -- Curvature -- Reach and Offset -- Voronoi Cells -- Condition Numbers -- Machine Learning -- Maximum Likelihood -- Tensors -- Computer Vision -- Volumes of Semialgebraic Sets -- Sampling -- References.
  note: by Paul Breiding, Kathlén Kohn, Bernd Sturmfels.
  note: Open Access
  subject:
    topic: Algebraic geometry
  subject:
    topic: Geometry, Differential
  subject:
    topic: Artificial intelligence
    topic: Data processing
  subject:
    topic: Numerical analysis
  subject:
    topic: Algebraic Geometry
  subject:
    topic: Differential Geometry
  subject:
    topic: Data Science
  subject:
    topic: Numerical Analysis
  classification: QA564-609
  classification: 516.35
  related item:
    title info:
      title: Springer Nature eBook
  related item:
    title info:
      title: Oberwolfach Seminars, 53
  identifier: 9783031514623
  identifier: https://doi.org/10.1007/978-3-031-51462-3
  access condition: Open Access
  record info:
    record creation date: 240227
    record change date: 20240731182814.8
    record identifier: in00004802871