Geometric Etudes in Combinatorial Mathematics
Springer-Verlag New York Inc.
978-0-387-75469-7 (ISBN)
Geometric Etudes in Combinatorial Mathematics is not only educational, it is inspirational. This distinguished mathematician captivates the young readers, propelling them to search for solutions of life’s problems—problems that previously seemed hopeless.
Review from the first edition:
The etudes presented here are not simply those of Czerny, but are better compared to the etudes of Chopin, not only technically demanding and addressed to a variety of specific skills, but at the same time possessing an exceptional beauty that characterizes the best of art...Keep this book at hand as you plan your next problem solving seminar.
—The American Mathematical Monthly
-Forewords to the Second Edition.-Forewords to the First Edition.-Preface to the Second Edition.-Preface to the First Edition.-Part I. Original Etudes.-1. Tiling a Checker Rectangle.- 1.1 Introduction.-1.2 Tiling Rectangles by Trominoes.- 1.3 Tetrominoes and 'Color' Reasoning.-1.4Tiling by Linear Polyominoes.- 1.5 Polyominoes and Rotational.-1.6 Symmetries.-1.7 Tiling on Other Surfaces.- 2. Proofs of Existence.- 2.1 The Pigeonhole Principle in Geometry.- 2.2 An Infinite Flock of Pigeons.-3. A Word About Graphs.-3.1 Combinatorics of Acquaintance, or
Introduction to Graph Theory. -3.2 More About Graphs.-3.3 Planarity.-3.4 The Intersection Index and the Jordan Curve Theorem.-4. Ideas of Combinatorial Geometry.-4.1 What are Convex Figures?.-4.2 Decomposition of Figures Into Parts of Smaller Diameters.-4.3 Figures of Constant Width.-4.4 Solution of the Borsuk Problem for Figures in the Plane.-4.5 Illumination of Convex Figures.-4.6 Theorems of Helly and Szökefalvi-Nagy.-Part II. New Landscape or the View 18 Years Later.-5. Mitya Karabash and a Tiling Conjecture.-6. Norton Starr’s 3-Dimensional Tromino Tiling.-7. Large Progress in Small Ramsey Numbers.-8. The Borsuk Problem Conquered.-9. Etude on the Chromatic Number of the Plane.-10. Farewell to the Reader.-References.-Notation.-Index.
Erscheint lt. Verlag | 15.6.2010 |
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Zusatzinfo | 332 Illustrations, black and white; XXXVI, 264 p. 332 illus. |
Verlagsort | New York, NY |
Sprache | englisch |
Maße | 155 x 235 mm |
Gewicht | 940 g |
Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
Mathematik / Informatik ► Mathematik ► Graphentheorie | |
Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
ISBN-10 | 0-387-75469-5 / 0387754695 |
ISBN-13 | 978-0-387-75469-7 / 9780387754697 |
Zustand | Neuware |
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