Károly Bezdek

Classical Topics in Discrete Geometry (eBook, PDF)

• Format: PDF

Produktbeschreibung

About the author: Karoly Bezdek received his Dr.rer.nat.(1980) and Habilitation (1997) degrees in mathematics from the Eötvös Loránd University, in Budapest and his Candidate of Mathematical Sciences (1985) and Doctor of Mathematical Sciences (1994) degrees from the Hungarian Academy of Sciences. He is the author of more than 100 research papers and currently he is professor and Canada Research Chair of mathematics at the University of Calgary. About the book: This multipurpose book can serve as a textbook for a semester long graduate level course giving a brief introduction to Discrete Geometry. It also can serve as a research monograph that leads the reader to the frontiers of the most recent research developments in the classical core part of discrete geometry. Finally, the forty-some selected research problems offer a great chance to use the book as a short problem book aimed at advanced undergraduate and graduate students as well as researchers. The text is centered around four major and by now classical problems in discrete geometry. The first is the problem of densest sphere packings, which has more than 100 years of mathematically rich history. The second major problem is typically quoted under the approximately 50 years old illumination conjecture of V. Boltyanski and H. Hadwiger. The third topic is on covering by planks and cylinders with emphases on the affine invariant version of Tarski's plank problem, which was raised by T. Bang more than 50 years ago. The fourth topic is centered around the Kneser-Poulsen Conjecture, which also is approximately 50 years old. All four topics witnessed very recent breakthrough results, explaining their major role in this book.

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Produktdetails

• Verlag: Springer US
• Seitenzahl: 166
• Erscheinungstermin: 23. Juni 2010
• Englisch
• ISBN-13: 9781441906007
• Artikelnr.: 43727922

Inhaltsangabe

Classical Topics Revisited.- Sphere Packings.- Finite Packings by Translates of Convex Bodies.- Coverings by Homothetic Bodies - Illumination and Related Topics.- Coverings by Planks and Cylinders.- On the Volume of Finite Arrangements of Spheres.- Ball-Polyhedra as Intersections of Congruent Balls.- Selected Proofs.- Selected Proofs on Sphere Packings.- Selected Proofs on Finite Packings of Translates of Convex Bodies.- Selected Proofs on Illumination and Related Topics.- Selected Proofs on Coverings by Planks and Cylinders.- Selected Proofs on the Kneser-Poulsen Conjecture.- Selected Proofs on Ball-Polyhedra.

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Classical Topics Revisited.- Sphere Packings.- Finite Packings by Translates of Convex Bodies.- Coverings by Homothetic Bodies - Illumination and Related Topics.- Coverings by Planks and Cylinders.- On the Volume of Finite Arrangements of Spheres.- Ball-Polyhedra as Intersections of Congruent Balls.- Selected Proofs.- Selected Proofs on Sphere Packings.- Selected Proofs on Finite Packings of Translates of Convex Bodies.- Selected Proofs on Illumination and Related Topics.- Selected Proofs on Coverings by Planks and Cylinders.- Selected Proofs on the Kneser Poulsen Conjecture.- Selected Proofs on Ball-Polyhedra.

Rezensionen

From the reviews:

"The present volume actually surveys packing and covering problems in Euclidean space and close cousins. ... Bezdek ... surveys the state of the art, best results, and outstanding conjectures for a host of problems. ... Summing Up: Recommended. Academic audiences, upper-division undergraduates through researchers/faculty." (D. V. Feldman, Choice, Vol. 48 (5), January, 2011)

"The book is intended for graduate students interested in discrete geometry. The book provides a road map to the state-of-the-art of several topics in discrete geometry. It can also serve as a textbook for a graduate level course or a seminar. Additionally, the book is extremely current, with many references to as late as 2009-2010 publications." (Alex Bogomolny, The Mathematical Association of America, August, 2010)

"This very interesting monograph contains a selection of topics in discrete geometry, mainly those on which the author and his collaborators have worked. ... The many conjectures and problems to be found throughout the text will serve as an inspiration to many discrete geometers." (Konrad Swanepoel, Zentralblatt MATH, Vol. 1207, 2011)