This book is about the combinatorial properties of convex sets,
families of convex sets in finite dimensional Euclidean spaces, and
finite points sets related to convexity. This area is classic, with
theorems of Helly, Caratheodory, and Radon that go back more than a
hundred years. At the same time, it is a modern and active field of
research with recent results like Tverberg's theorem, the colourful
versions of Helly and Caratheodory, and the $(p, q)$ theorem of
Alon and Kleitman. As the title indicates, the topic is convexity
and geometry, and is close to discrete mathematics. The questions
considered are frequently of a combinatorial nature, and the proofs
use ideas from geometry and are often combined with graph and
hypergraph theory. The book is intended for students (graduate and
undergraduate alike), but postdocs and research mathematicians will
also find it useful. It can be used as a textbook with short
chapters, each suitable for a one- or two-hour lecture. Not much
background is needed: basic linear algebra and elements of
(hyper)graph theory as well as some mathematical maturity should
suffice.
General
| Imprint: |
American Mathematical Society
|
| Country of origin: |
United States |
| Series: |
University Lecture Series |
| Release date: |
November 2021 |
| Authors: |
Imre Barany
|
| Dimensions: |
254 x 178 x 14mm (L x W x T) |
| Format: |
Paperback
|
| Pages: |
148 |
| ISBN-13: |
978-1-4704-6709-8 |
| Categories: |
Books >
Science & Mathematics >
Mathematics >
Geometry >
General
Promotions
|
| LSN: |
1-4704-6709-7 |
| Barcode: |
9781470467098 |
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