From tube maps to neural networks: the theory of graphs
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London
RBA
2012
|
| Schriftenreihe: | Everything is mathematical
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | 143 S. Ill., graph. Darst. |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804149694489690112 |
|---|---|
| adam_text | Contents
Preface
........................................................................................................................................................ 11
Chapter l.An Introduction to Graphs
.............................................................................. 13
From
Königsberg
with love
........................................................................................................... 14
The ABC of graph theory
.............................................................................................................. 18
Polygonal and complete graphs
................................................................................................... 23
Planar graphs
............................................................................................................................................ 25
The problem of the wells and the enemy families
.................................................. 26
The trees do let you see the forest
............................................................................................. 28
Graphs in everyday life
...................................................................................................................... 33
Chapter
2.
Graphs and Colours
.............................................................................................. 39
Maps and colours
.................................................................................................................................. 39
Graphs that can be coloured with two or three colours
............................................. 41
Four colours are enough
.................................................................................................................. 43
The chromatic number
..................................................................................................................... 47
Chapter
3.
Graphs, Circuits and Optimisation
........................................................... 51
Eularian circuits
..................................................................................................................................... 51
The Chinese postman problem
................................................................................................... 53
Hamiltonian circuits
............................................................................................................................ 54
The traveller problem
......................................................................................................................... 56
Critical paths
............................................................................................................................................ 58
Graphs and planning: the P.E.R.T. system
............................................................................ 59
Organigram showing the steps of a P.E.R.T.
.............................................................. 60
Chapter
4.
Graphs and Geometry
........................................................................................ 65
Eulers
surprising formula
................................................................................................................ 66
Eulers
formula with just faces and vertices
........................................................................ 69
There is always a triangle, a quadrilateral or a pentagon
............................................. 71
CONTENTS
All the faces different? Impossible!
............................................................................................ 75
Graphs and mosaics
............................................................................................................................. 75
Other geometric problems with graphs
................................................................................. 79
Hamiltonian circuits in polyhedrons
................................................................................ 79
Graphs on non-planar surfaces
............................................................................................. 81
Finite geometries
........................................................................................................................... 82
Chapter
5.
Surprising Applications of Graphs
............................................................ 85
Graphs and the Internet
................................................................................................................... 85
Graphs in chemistry and physics
................................................................................................. 87
Graphs in architecture
........................................................................................................................ 89
Graphs in city planning
..................................................................................................................... 95
Graphs in social networking
.......................................................................................................... 97
Stanley Milgram s small world
............................................................................................ 99
Graphs and timetables
........................................................................................................................ 99
NP-complete problems
............................................................................................................ 101
Recreational graphs
............................................................................................................................. 103
Who will say
20? ........................................................................................................................... 103
The maze in Rouse Ball s garden
....................................................................................... 103
The snake game
.............................................................................................................................. 104
The elegant numbering of a graph
.................................................................................... 104
Towers of Hanoi
............................................................................................................................ 105
The
NIM
game
.............................................................................................................................. 106
Two circuits from Martin Gardner
.................................................................................... 106
The circuit in a rectangle
.................................................................................................. 106
The circuit on a grid
........................................................................................................... 107
Knight routes in chess
................................................................................................................ 108
Lewis Carroll and Eularian graphs
..................................................................................... 109
The four circle problem
............................................................................................................ 110
Magic stars
........................................................................................................................................... 110
The magic hexagram
...........................................................................................................
Ill
Graphs and education
........................................................................................................................ 113
CONTENTS
Graphs and neural networks
.......................................................................................................... 115
Graphs and linear programming
................................................................................................. 118
Epilogue
..................................................................................................................................................... 125
Appendix. Graphs, Sets and Relations
.............................................................................. 127
Equivalence relations
.......................................................................................................................... 130
Ordered relations
................................................................................................................................... 131
Functions
.................................................................................................................................................... 132
Fuzzy sets and graphs
......................................................................................................................... 135
Glossary
...................................................................................................................................................... 137
Bibliography
............................................................................................................................................ 139
Index
............................................................................................................................................................. 141
From Tube Maps to
Neural Networks
The theory of graphs
A graph is an extraordinarily simple construct: a set of points
joined by lines. Graphs include everything from underground
maps to the delivery route taken by a postal worker. In fact,
graphs can describe the multitude of networks that form the
basis of our world. Carefully observing these simple structures
opens our eyes to a universe of links and connections in
which mathematics reigns supreme.
|
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| indexdate | 2024-07-10T00:27:06Z |
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| spelling | Alsina, Claudi 1952- Verfasser (DE-588)143990934 aut From tube maps to neural networks the theory of graphs Claudi Alsina London RBA 2012 143 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Everything is mathematical Graphentheorie (DE-588)4113782-6 gnd rswk-swf Graphentheorie (DE-588)4113782-6 s DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025431255&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025431255&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Alsina, Claudi 1952- From tube maps to neural networks the theory of graphs Graphentheorie (DE-588)4113782-6 gnd |
| subject_GND | (DE-588)4113782-6 |
| title | From tube maps to neural networks the theory of graphs |
| title_auth | From tube maps to neural networks the theory of graphs |
| title_exact_search | From tube maps to neural networks the theory of graphs |
| title_full | From tube maps to neural networks the theory of graphs Claudi Alsina |
| title_fullStr | From tube maps to neural networks the theory of graphs Claudi Alsina |
| title_full_unstemmed | From tube maps to neural networks the theory of graphs Claudi Alsina |
| title_short | From tube maps to neural networks |
| title_sort | from tube maps to neural networks the theory of graphs |
| title_sub | the theory of graphs |
| topic | Graphentheorie (DE-588)4113782-6 gnd |
| topic_facet | Graphentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025431255&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025431255&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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