04333nam a22005535i 4500 978-3-031-50507-2 DE-He213 20251030112628.0 cr nn 008mamaa 240714s2024 sz | s |||| 0|eng d 9783031505072 978-3-031-50507-2 10.1007/978-3-031-50507-2 doi QA639.5-640.7 QA640.7-640.77 PBM bicssc PBD bicssc MAT012020 bisacsh PBM thema PBD thema Balestro, Vitor. author. aut http://id.loc.gov/vocabulary/relators/aut 80551 Convexity from the Geometric Point of View [electronic resource] / by Vitor Balestro, Horst Martini, Ralph Teixeira. 1st ed. 2024. Cham : Springer International Publishing : Imprint: Birkhäuser, 2024. XIX, 1184 p. 86 illus., 13 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Cornerstones, 2197-1838 Preface -- 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. This 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. Convex geometry . 71929 Discrete geometry. 71930 Convex and Discrete Geometry. 71931 Martini, Horst. author. aut http://id.loc.gov/vocabulary/relators/aut 80552 Teixeira, Ralph. author. aut http://id.loc.gov/vocabulary/relators/aut 80553 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031505065 Printed edition: 9783031505089 Cornerstones, 2197-1838 80554 https://doi.org/10.1007/978-3-031-50507-2 ZDB-2-SMA ZDB-2-SXMS 61591 61591