東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Convexity from the geometric point o...

Balestro, Vitor.

Linked to FindBook

Google Book

Amazon

博客來

Convexity from the geometric point of view

Record Type:	Electronic resources : Monograph/item
Title/Author:	Convexity from the geometric point of view/ by Vitor Balestro, Horst Martini, Ralph Teixeira.
Author:	Balestro, Vitor.
other author:	Martini, Horst.
Published:	Cham :Springer International Publishing : : 2024.,
Description:	xix, 1184 p. :ill. (some col.), digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer Nature eBook
Subject:	Convex geometry. -
Online resource:	https://doi.org/10.1007/978-3-031-50507-2
ISBN:	9783031505072

Convexity from the geometric point of view
Balestro, Vitor.

Convexity from the geometric point of view[electronic resource] /by Vitor Balestro, Horst Martini, Ralph Teixeira. - Cham :Springer International Publishing :2024. - xix, 1184 p. :ill. (some col.), digital ;24 cm. - Cornerstones,2197-1838. - Cornerstones..

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.

ISBN: 9783031505072

Standard No.: 10.1007/978-3-031-50507-2doiSubjects--Topical Terms:

567300
Convex geometry.

LC Class. No.: QA639.5

Dewey Class. No.: 516.08

Convexity from the geometric point of view
LDR:03366nmm a2200361 a 4500 001 2374422
003 DE-He213
005 20240714125727.0
006 m d
007 cr nn 008maaau
008 241231s2024 sz s 0 eng d
020 $a 9783031505072 $q (electronic bk.)
020 $a 9783031505065 $q (paper)
024 7 $a 10.1007/978-3-031-50507-2 $2 doi
035 $a 978-3-031-50507-2
040 $a GP $c GP
041 0 $a eng
050 4 $a QA639.5
072 7 $a PBM $2 bicssc
072 7 $a PBD $2 bicssc
072 7 $a MAT012020 $2 bisacsh
072 7 $a PBM $2 thema
072 7 $a PBD $2 thema
082 0 4 $a 516.08 $2 23
090 $a QA639.5 $b .B184 2024
100 1 $a Balestro, Vitor. $3 3723282
245 1 0 $a Convexity from the geometric point of view $h [electronic resource] / $c by Vitor Balestro, Horst Martini, Ralph Teixeira.
260 $a Cham : $b Springer International Publishing : $b Imprint: Birkhäuser, $c 2024.
300 $a xix, 1184 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a Cornerstones, $x 2197-1838
505 0 $a 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.
520 $a 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.
650 0 $a Convex geometry. $3 567300
650 1 4 $a Convex and Discrete Geometry. $3 893686
700 1 $a Martini, Horst. $3 3386935
700 1 $a Teixeira, Ralph Costa. $3 3723283
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Cornerstones. $3 3411035
856 4 0 $u https://doi.org/10.1007/978-3-031-50507-2
950 $a Mathematics and Statistics (SpringerNature-11649)