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Convexity from the Geometric Point of View

By Vitor Balestro

Convexity from the Geometric Point of View Mathematics

Convexity from the Geometric Point of View

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Description
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.
Product details
Binding:
Paperback
Number of Pages:
1184
Release Date:
2025-07-15
Publication Date:
2025-07-15
Publisher:
Springer-Verlag GmbH
Languages:
Original: English
ISBN10:
3031505085
ISBN13:
9783031505089
GPSR Manufacturer Reference:
[email protected]
Weight:
2486 g
Height:
180 cm
Width:
254 cm
Thickness:
46 cm
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