Convexity from the Geometric Point of View: Exercises and Solutions / by Vitor Balestro, Horst Martini, Ralph Teixeira.

Format:

Book

Author/Creator:

Balestro, Vitor.

Contributor:

Martini, Horst.

Teixeira, Ralph.

Series:

Cornerstones, 2197-1838

Language:

English

Subjects (All):

Convex geometry.

Discrete geometry.

Convex and Discrete Geometry.

Local Subjects:

Convex and Discrete Geometry.

Physical Description:

1 online resource (594 pages)

Edition:

1st ed. 2025.

Place of Publication:

Cham : Springer Nature Switzerland : Imprint: Birkhäuser, 2025.

Summary:

This book provides the solutions to all 347 exercises contained in the text Convexity from the Geometric Point of View, published in the same Cornerstones series. All these exercises are restated and numbered analogously to those in the original text. The corresponding solutions follow each exercise. Besides the discussion of all solutions, some additional facts about the main text are sprinkled throughout. Sections of further reading are posted to the ends of each chapter supplying the reader with background literature to selected notions and tools that play a role in the exercises and/or solutions to the chapter. The original text gives a comprehensive introduction to the “common core” of convex geometry and is suitable as a primary text for courses in convex geometry and in discrete geometry (including polytopes). Additionally, it can be used as a single reference for a complete introduction to convex geometry. The content coverage is sufficiently broad that the reader may gain a glimpse of the entire breadth of the field, various subfields, and interesting connections to neighboring disciplines. Mainly directed to graduate and advanced undergraduates, the original text 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. The same is true for this book of solutions.

Contents:

Exercises & Solutions Convex functions

Exercises & Solutions Convex sets

Exercises & Solutions A first look into polytopes

Exercises & Solutions Volume and area

Exercises & Solutions Classical inequalities

Exercises & Solutions Mixed volumes

Exercises & Solutions Mixed surface area measures

Exercises & Solutions The Alexandrov-Fenchel inequality

Exercises & Solutions Affine convex geometry I

Exercises & Solutions Affine convex geometry II

Exercises & Solutions Further selected topics

Exercises & Solutions Historical steps of development of convexity as a field.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

3-031-83937-4

OCLC:

1527724113