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1. Pure Mathematics
Introduction; Euclidean Geometry as Pure Mathematics; Games; Why Study Pure Mathematics?; What's Coming; Suggested Reading
2. Graphs
Introduction; Sets; Paradox; Graphs; Graph diagrams; Cautions; Common Graphs; Discovery; Complements and Subgraphs; Isomorphism; Recognizing Isomorphic Graphs; Semantics
The Number of Graphs Having a Given nu; Exercises; Suggested Reading
3. Planar Graphs
Introduction; UG, K subscript 5, and the Jordan Curve Theorem; Are there More Nonplanar Graphs?; Expansions;
Kuratowski's Theorem; Determining Whether a Graph is Planar or Nonplanar; Exercises; Suggested Reading
4. Euler's Formula
Introduction; Mathematical Induction; Proof of Euler's Formula; Some Consequences of Euler's Formula; Algebraic Topology; Exercises; Suggested Reading
5. Platonic Graphs
Introduction; Proof of the Theorem; History; Exercises; Suggested Reading
6. Coloring
Chromatic Number; Coloring Planar Graphs; Proof of the Five Color Theorem; Coloring Maps; Exercises; Suggested Reading
7. The Genus of a Graph
Introduction; The Genus of a Graph; Euler's Second Formula; Some Consequences; Estimating the Genus of a Connected Graph; g-Platonic Graphs; The Heawood Coloring Theorem; Exercises; Suggested Reading
8. Euler Walks and Hamilton Walks
Introduction; Euler Walks; Hamilton Walks; Multigraphs; The Königsberg Bridge Problem; Exercises; Suggested Reading
Afterword
Solutions to Selected Exercises
Index
Special symbols
| Erscheinungsjahr: | 1994 |
|---|---|
| Fachbereich: | Arithmetik & Algebra |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Inhalt: | Kartoniert / Broschiert |
| ISBN-13: | 9780486678702 |
| ISBN-10: | 0486678709 |
| UPC: | 800759678709 |
| EAN: | 0800759678709 |
| Sprache: | Englisch |
| Einband: | Kartoniert / Broschiert |
| Autor: | Trudeau, Richard J |
| Auflage: | 2nd Revised edition |
| Hersteller: | Dover Publications |
| Maße: | 215 x 137 x 11 mm |
| Von/Mit: | Richard J Trudeau |
| Erscheinungsdatum: | 09.02.1994 |
| Gewicht: | 0,231 kg |
1. Pure Mathematics
Introduction; Euclidean Geometry as Pure Mathematics; Games; Why Study Pure Mathematics?; What's Coming; Suggested Reading
2. Graphs
Introduction; Sets; Paradox; Graphs; Graph diagrams; Cautions; Common Graphs; Discovery; Complements and Subgraphs; Isomorphism; Recognizing Isomorphic Graphs; Semantics
The Number of Graphs Having a Given nu; Exercises; Suggested Reading
3. Planar Graphs
Introduction; UG, K subscript 5, and the Jordan Curve Theorem; Are there More Nonplanar Graphs?; Expansions;
Kuratowski's Theorem; Determining Whether a Graph is Planar or Nonplanar; Exercises; Suggested Reading
4. Euler's Formula
Introduction; Mathematical Induction; Proof of Euler's Formula; Some Consequences of Euler's Formula; Algebraic Topology; Exercises; Suggested Reading
5. Platonic Graphs
Introduction; Proof of the Theorem; History; Exercises; Suggested Reading
6. Coloring
Chromatic Number; Coloring Planar Graphs; Proof of the Five Color Theorem; Coloring Maps; Exercises; Suggested Reading
7. The Genus of a Graph
Introduction; The Genus of a Graph; Euler's Second Formula; Some Consequences; Estimating the Genus of a Connected Graph; g-Platonic Graphs; The Heawood Coloring Theorem; Exercises; Suggested Reading
8. Euler Walks and Hamilton Walks
Introduction; Euler Walks; Hamilton Walks; Multigraphs; The Königsberg Bridge Problem; Exercises; Suggested Reading
Afterword
Solutions to Selected Exercises
Index
Special symbols
| Erscheinungsjahr: | 1994 |
|---|---|
| Fachbereich: | Arithmetik & Algebra |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Inhalt: | Kartoniert / Broschiert |
| ISBN-13: | 9780486678702 |
| ISBN-10: | 0486678709 |
| UPC: | 800759678709 |
| EAN: | 0800759678709 |
| Sprache: | Englisch |
| Einband: | Kartoniert / Broschiert |
| Autor: | Trudeau, Richard J |
| Auflage: | 2nd Revised edition |
| Hersteller: | Dover Publications |
| Maße: | 215 x 137 x 11 mm |
| Von/Mit: | Richard J Trudeau |
| Erscheinungsdatum: | 09.02.1994 |
| Gewicht: | 0,231 kg |
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