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001 978-3-031-50507-2
003 DE-He213
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007 cr nn 008mamaa
008 240714s2024 sz | s |||| 0|eng d
020 _a9783031505072
_9978-3-031-50507-2
024 7 _a10.1007/978-3-031-50507-2
_2doi
050 4 _aQA639.5-640.7
050 4 _aQA640.7-640.77
072 7 _aPBM
_2bicssc
072 7 _aPBD
_2bicssc
072 7 _aMAT012020
_2bisacsh
072 7 _aPBM
_2thema
072 7 _aPBD
_2thema
100 1 _aBalestro, Vitor.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_980551
245 1 0 _aConvexity from the Geometric Point of View
_h[electronic resource] /
_cby Vitor Balestro, Horst Martini, Ralph Teixeira.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Birkhäuser,
_c2024.
300 _aXIX, 1184 p. 86 illus., 13 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aCornerstones,
_x2197-1838
505 0 _aPreface -- 1. Convex functions -- 2. Convex sets -- 3. A first look into polytopes -- 4. Volume and area -- 5. Classical inequalities -- 6. Mixed volumes- 7. Mixed surface area measures -- 8. The Alexandrov-Frechel inequality -- 9. Affine convex geometry Part 1 -- 10. Affine convex geometry Part 2 -- 11. Further selected topics.-12. Historical steps of development of convexity as a field -- A. Measure theory for convex geometers -- References -- Index.
520 _aThis text gives a comprehensive introduction to the “common core” of convex geometry. Basic concepts and tools which are present in all branches of that field are presented with a highly didactic approach. Mainly directed to graduate and advanced undergraduates, the book is self-contained in such a way that it can be read by anyone who has standard undergraduate knowledge of analysis and of linear algebra. Additionally, it can be used as a single reference for a complete introduction to convex geometry, and the content coverage is sufficiently broad that the reader may gain a glimpse of the entire breadth of the field and various subfields. The book is suitable as a primary text for courses in convex geometry and also in discrete geometry (including polytopes). It is also appropriate for survey type courses in Banach space theory, convex analysis, differential geometry, and applications of measure theory. Solutions to all exercises are available to instructors who adopt the text for coursework. Most chapters use the same structure with the first part presenting theory and the next containing a healthy range of exercises. Some of the exercises may even be considered as short introductions to ideas which are not covered in the theory portion. Each chapter has a notes section offering a rich narrative to accompany the theory, illuminating the development of ideas, and providing overviews to the literature concerning the covered topics. In most cases, these notes bring the reader to the research front. The text includes many figures that illustrate concepts and some parts of the proofs, enabling the reader to have a better understanding of the geometric meaning of the ideas. An appendix containing basic (and geometric) measure theory collects useful information for convex geometers.
650 0 _aConvex geometry .
_971929
650 0 _aDiscrete geometry.
_971930
650 1 4 _aConvex and Discrete Geometry.
_971931
700 1 _aMartini, Horst.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_980552
700 1 _aTeixeira, Ralph.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_980553
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031505065
776 0 8 _iPrinted edition:
_z9783031505089
830 0 _aCornerstones,
_x2197-1838
_980554
856 4 0 _uhttps://doi.org/10.1007/978-3-031-50507-2
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c61591
_d61591