Essential Discrete Mathematics for Computer Science

403 Pages·2019·26.999 MB·English

by  Harry Lewis , Rachel zax

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ESSENTIAL DISCRETE
MATHEMATICS FOR
COMPUTER SCIENCE
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ESSENTIAL DISCRETE
MATHEMATICS FOR
COMPUTER SCIENCE
Harry Lewis and Rachel Zax
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To Alexandra, Stella, Elizabeth, and Annie
and
to David, Marcia, Ben, and Aryeh
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Anengineerissaidtobeamanwhoknowsagreatdealaboutavery
little,andwhogoesaroundknowingmoreandmore,aboutlessand
less,untilfinally,hepracticallyknowseverythingaboutnothing;
whereas,aSalesman,ontheotherhand,isamanwhoknowsavery
littleaboutagreatdeal,andkeepsonknowinglessandlessaboutmore
andmoreuntilfinallyheknowspracticallynothing,abouteverything.
VanNuys,California,News,June26,1933
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CONTENTS
Preface
xi
1
ThePigeonholePrinciple 1
2
BasicProofTechniques 11
3
ProofbyMathematicalInduction 25
4
StrongInduction 39
5
Sets 49
6
RelationsandFunctions 59
7
CountableandUncountableSets 69
8
StructuralInduction 79
9
PropositionalLogic 89
10
NormalForms 101
11
LogicandComputers 111
12
QuantificationalLogic 119
13
DirectedGraphs 133
14
DigraphsandRelations 141
15
StatesandInvariants 151
16
UndirectedGraphs 161
17
Connectivity 173
18
Coloring 179
19
FiniteAutomata 187
20
RegularLanguages 201
21
OrderNotation 211
22
Counting 233
23
CountingSubsets 243 −
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