000 | 03397nam a22005895i 4500 | ||
---|---|---|---|
001 | 978-3-031-51462-3 | ||
003 | DE-He213 | ||
005 | 20240508090327.0 | ||
007 | cr nn 008mamaa | ||
008 | 240227s2024 sz | s |||| 0|eng d | ||
020 |
_a9783031514623 _9978-3-031-51462-3 |
||
024 | 7 |
_a10.1007/978-3-031-51462-3 _2doi |
|
050 | 4 | _aQA564-609 | |
072 | 7 |
_aPBMW _2bicssc |
|
072 | 7 |
_aMAT012010 _2bisacsh |
|
072 | 7 |
_aPBMW _2thema |
|
082 | 0 | 4 |
_a516.35 _223 |
100 | 1 |
_aBreiding, Paul. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
|
245 | 1 | 0 |
_aMetric Algebraic Geometry _h[electronic resource] / _cby Paul Breiding, Kathlén Kohn, Bernd Sturmfels. |
250 | _a1st ed. 2024. | ||
264 | 1 |
_aCham : _bSpringer Nature Switzerland : _bImprint: Birkhäuser, _c2024. |
|
300 |
_aXIV, 215 p. _bonline resource. |
||
336 |
_atext _btxt _2rdacontent |
||
337 |
_acomputer _bc _2rdamedia |
||
338 |
_aonline resource _bcr _2rdacarrier |
||
347 |
_atext file _bPDF _2rda |
||
490 | 1 |
_aOberwolfach Seminars, _x2296-5041 ; _v53 |
|
505 | 0 | _aPreface -- 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. | |
506 | 0 | _aOpen Access | |
520 | _aMetric 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. | ||
650 | 0 | _aAlgebraic geometry. | |
650 | 0 | _aGeometry, Differential. | |
650 | 0 |
_aArtificial intelligence _xData processing. |
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650 | 0 | _aNumerical analysis. | |
650 | 1 | 4 | _aAlgebraic Geometry. |
650 | 2 | 4 | _aDifferential Geometry. |
650 | 2 | 4 | _aData Science. |
650 | 2 | 4 | _aNumerical Analysis. |
700 | 1 |
_aKohn, Kathlén. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
|
700 | 1 |
_aSturmfels, Bernd. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
|
710 | 2 | _aSpringerLink (Online service) | |
773 | 0 | _tSpringer Nature eBook | |
776 | 0 | 8 |
_iPrinted edition: _z9783031514616 |
776 | 0 | 8 |
_iPrinted edition: _z9783031514630 |
830 | 0 |
_aOberwolfach Seminars, _x2296-5041 ; _v53 |
|
856 | 4 | 0 | _uhttps://doi.org/10.1007/978-3-031-51462-3 |
912 | _aZDB-2-SMA | ||
912 | _aZDB-2-SXMS | ||
912 | _aZDB-2-SOB | ||
999 |
_c37782 _d37782 |