Mathematics: The Science of Patterns: The Search for Order in Life, Mind and the Universe

232 Pages·2003·13.811 MB·English

by  Keith Devlin

MATHEMATICS
'Patterns
KEITH DEVLIN
Science/Mathematics $32.95
MATHEMATICS
TheScienceofPatterns
TheSearchforOrderinLife,Mind,
andtheUniverse
KeithDevlin
Formostofus,"mathematics"suggestsmea-
suring,counting,andaccounting. Oritrefers
toacollectionoftechniquesforsolvingprob-
lems. Atlevelsbeyondthat,thefieldseems
fartooremoteandimpenetrabletoberele-
vant.
With this fascinating volume, Keith Devlin
provesthattheguidingprinciplesofsomeof
themostmysteriousmathematicaltopicscan
bemadecomprehensible. Writingwithanele-
gantlucidity,Devlinshowsjustwhythedefini-
tion ofmathematicsas "workingwith num-
bers" hasbeenoutofdatefornearly2,500
years. And he demonstrates that far from
beingtoo abstractto matter, mathematics is
instead an essential and uniquely human
endeavor, one that helps us understand the
universeandourselves.
Inthiscenturyalone,therehasbeenaverita-
bleexplosionofmathematicalactivity. Abody
ofknowledgethatin1900mighthavefilled
80 volumes now would require nearly
100,000. Fieldssuchasalgebraandtopology
have grown tremendo.usly, while complexity
theory, dynamical systems theory, and other
newareashavedeveloped. And inthelast
two decades, a common thread running
throughthemanyfacetsofmathematicshas
been recognized: mathematiciansofall kin—ds
nowseetheirworkasthestudyofpatterns
realorimagined,visualormental,arisingfrom
thenatural world orfromwithinthe human
mind.
Devlin usesthisbasicdefinitionashiscentral
.theme, revealingthesearchforpatternsthat
drives the mathematics of counting (natural
numbers), reasoning (language and logic),
(continuedonbackflap)
DATEDUE
OEC 20 1994
FEB'-5 1995
MAR -9 ,Q0C
APR 10 1996
APR,201995
T/Zol/3
IVI'k/n
«C.38-2931
fT
^
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OCT26
£
—
Mathematics:TheScienceofPatterns

Mathematics: The Science ofPatterns
TheSearchforOrderinLife,Mind,andtheUniverse
KeithDevlin
SCIENTIFIC
AMERICAN
LIBRARY
AdivisionofHPHLP
NewYork
LibraryofCongressCataloging-in-PublicationData
Devlin,KeithJ.
Mathematics,thescienceofpatterns:thesearchfororderin
life,mind,andtheuniverse/KeithDevlin.
p. ccmm..
Includesbibliographicalreferencesandindex.
ISBN0-7167-5047-3
1.Mathematics.I.Title.
QA36.D481994 94-11366
510'.1—dc20. CIP
ISSN1040-3213
©1994byScientificAmericanLibrary
Nopartofthisbookmaybereproducedbyanymechanical,
photographic,orelectronicprocess,orintheformofaphono-
graphicrecording,normayitbestoredinaretrievalsystem,
transmitted,orotherwisecopiedforpublicorprivateuse,with-
outwrittenpermissionfromthepublisher.
PrintedintheUnitedStatesofAmerica
ScientificAmericanLibrary
AdivisionofHPHLP
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DistributedbyW.H.FreemanandCompany
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Thisbookisnumber52ofaseries.
Contents
Preface vii
Prologue 1
1 Counting 9
2 ReasoningandCommunicating 37
3 MotionandChange 73
4 Shape 105
5 SymmetryandRegularity 145
6 Position 173
Postscript 208
FurtherReadings 210
SourcesofIllustrations 212
Index 214