The Cube: A Window to Convex and Discrete Geometry (Hardcover)

Chuanming Zong

ISBN 10: 0521855357 / ISBN 13: 9780521855358

Verlag: Cambridge University Press, Cambridge, 2006

Beschreibung

Hardcover. This tract has two purposes: to show what is known about the n-dimensional unit cubes and to demonstrate how Analysis, Algebra, Combinatorics, Graph Theory, Hyperbolic Geometry, Number Theory, can be applied to the study of them. The unit cubes, from any point of view, are among the most important and fascinating objects in an n-dimensional Euclidean space. However, our knowledge about them is still quite limited and many basic problems remain unsolved. In this Tract eight topics about the unit cubes are introduced: cross sections, projections, inscribed simplices, triangulations, 0/1 polytopes, Minkowski's conjecture, Furtwangler's conjecture, and Keller's conjecture. In particular the author demonstrates how deep analysis like log concave measure and the Brascamp-Lieb inequality can deal with the cross section problem, how Hyperbolic Geometry helps with the triangulation problem, how group rings can deal with Minkowski's conjecture and Furtwangler's conjecture, and how Graph Theory handles Keller's conjecture. Eight topics about the unit cubes are introduced within this textbook: cross sections, projections, inscribed simplices, triangulations, 0/1 polytopes, Minkowski's conjecture, Furtwangler's conjecture, and Keller's conjecture. In particular Chuanming Zong demonstrates how deep analysis like log concave measure and the Brascamp-Lieb inequality can deal with the cross section problem, how Hyperbolic Geometry helps with the triangulation problem, how group rings can deal with Minkowski's conjecture and Furtwangler's conjecture, and how Graph Theory handles Keller's conjecture. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Bestandsnummer des Verkäufers 9780521855358

Bibliografische Details

Titel: The Cube: A Window to Convex and Discrete ...

Verlag: Cambridge University Press, Cambridge

Erscheinungsdatum: 2006

Einband: Hardcover

Zustand: new

Über diesen Titel

Inhaltsangabe:

This tract has two purposes: to show what is known about the n-dimensional unit cubes and to demonstrate how Analysis, Algebra, Combinatorics, Graph Theory, Hyperbolic Geometry, Number Theory, can be applied to the study of them.

Críticas:

"Because this book is a love letter to the unity of mathematics, readers can hardly but come to share Zong's undisguised enthusiasm...Highly recommended." -- Choice