Discrete Mathematics for Computer Science

680 Pages·2017·18.648 MB·English

by  David Liben-Nowell

1
David Liben-Nowell
Department of Computer Science
Carleton College
Discrete Mathematics
for Computer Science
or
(A Bit of) The Math that
Computer Scientists
Need to Know
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ISBN: 978-1-118-06553-2 (PBK)
ISBN: 978-1-119-07073-3 (EVALC)
Library of Congress Cataloging in Publication Data:
Liben-Nowell, David, author.
Title: Discrete mathematics for computer science / by David Liben-Nowell.
Description: Hoboken, NJ : John Wiley & Sons, 2017. | Includes index. |
Identifiers: LCCN 2017025007 (print) | LCCN 2017035974 (ebook) | ISBN
9781119397199 (pdf) | ISBN 9781119397113 (epub) | ISBN 9781118065532 (pbk.)
Subjects: LCSH: Computer science—Mathematics.
Classification: LCC QA76.9.M35 (ebook) | LCC QA76.9.M35 L53 2017 (print) |
DDC 004.01/51—dc23
LC record available at https://lccn.loc.gov/2017025007
The inside back cover will contain printing identification and country of origin if omitted from this page. In
addition, if the ISBN on the back cover differs from the ISBN on this page, the one on the back cover is correct.
To MDSWM, with never-ending appreciation, and
in loving memory of my grandfather, Jay Liben, who
brought more joy, curiosity, and kvetching to this
world than anyone else I know.

Contents
1 On the Point of this Book 101
2 Basic Data Types 201
2.1 Why You MightCare 202
2.2 Booleans, Numbers,and Arithmetic 203
2.3 Sets: UnorderedCollections 222
2.4 Sequences, Vectors,and Matrices: OrderedCollections 237
2.5 Functions 253
2.6 Chapter ataGlance 270
3 Logic 301
3.1 Why You MightCare 302
3.2 An Introduction toPropositional Logic 303
3.3 Propositional Logic: Some Extensions 317
3.4 An Introduction toPredicateLogic 331
3.5 PredicateLogic: NestedQuantifiers 349
3.6 Chapter ataGlance 362
6
4 Proofs 401
4.1 Why You MightCare 402
4.2 Error-CorrectingCodes 403
4.3 Proofs and Proof Techniques 423
4.4 Some Examplesof Proofs 441
4.5 Common ErrorsinProofs 458
4.6 Chapter ataGlance 469
5 Mathematical Induction 501
5.1 Why You MightCare 502
5.2 Proofs by MathematicalInduction 503
5.3 Strong Induction 521
5.4 RecursivelyDefinedStructuresand StructuralInduction 533
5.5 Chapter ataGlance 546
6 Analysis of Algorithms 601
6.1 Why You MightCare 602
6.2 Asymptotics 603
6.3 AsymptoticAnalysisofAlgorithms 617
6.4 RecurrenceRelations: Analyzing RecursiveAlgorithms 631
6.5 RecurrenceRelations: The MasterMethod 647
6.6 Chapter ataGlance 657
7 Number Theory 701
7.1 Why You MightCare 702
7.2 Modular Arithmetic 703
7.3 Primalityand RelativePrimality 717
7.4 MultiplicativeInverses 734
7.5 Cryptography 745
7.6 Chapter ataGlance 756
7
8 Relations 801
8.1 Why You MightCare 802
8.2 Formal Introduction 803
8.3 Propertiesof Relations: Reflexivity,Symmetry,and Transitivity 818
8.4 SpecialRelations: EquivalenceRelations and Partial/TotalOrders 833
8.5 Chapter ataGlance 850
9 Counting 901
9.1 Why You MightCare 902
9.2 Counting Unionsand Sequences 903
9.3 UsingFunctions to Count 926
9.4 Combinations and Permutations 944
9.5 Chapter ataGlance 965
10 Probability 1001
10.1 Why You MightCare 1002
10.2 Probability,Outcomes,and Events 1005
10.3 Independence and Conditional Probability 1021
10.4 Random Variablesand Expectation 1041
10.5 Chapter ataGlance 1067
11 Graphs and Trees 1101
11.1 Why You MightCare 1102
11.2 Formal Introduction 1103
11.3 Paths,Connectivity, and Distances 1129
11.4 Trees 1147
11.5 WeightedGraphs 1164
11.6 Chapter ataGlance 1177
12 Index 1201