000 06575pam 2201273 a 45’0
001 ocm23383913
005 19910326100324.6
008 910313s1991 enka 001 0 eng H
010 $a91014090
020 $a075030135X
020 $a0750301368 (pbk.)
040 $aDLC$cDLC$dDLC
040 $aDLC$cDLC$dDLC$dOrLoB-B
050 00 $aQA76.9.M35$bG38 1992
092 $a004.0151$bG23
100 1 $aGarnier, Rowan.
245 10 $aDiscrete mathematics for new technology /$cRowan
Garnier, John Taylor.
260 $aBristol :$bA. Hilger,$c1992.
300 $axvii, 678 p. :$bill. ;$c24 cm.
500 $aIncludes index.
520 $aDiscrete Mathematics for New Technology has been
designed to cover the core mathematics requirement for
undergraduate computer science students in the UK and the
USA. This has been approached in a comprehensive way whilst
maintaining an easy to follow progression from the basic
mathematical concepts covered by the GCSE in the UK and by
high-school algebra in the USA, to the more sophisticated
mathematical concepts examined in the latter stages of the
book. The rigorous treatment of theory is punctuated by
frequent use of pertinent examples. This is then reinforced
with exercises to allow the reader to achieve a "feel" for
the subject at hand. Hints and solutions are provided for
these brain-teasers at the end of the book. Although aimed
primarily at computer science students, the structured
development of the mathematics enables this text to be used
by undergraduate mathematicians, scientists and others who
require an understanding of discrete mathematics. The topics
covered include: logic and the nature of mathematical proof
set theory, relations and functions, matrices and systems of
linear equations, algebraic structures, Boolean algebras and
a thorough treatise on graph theory. The authors have
extensive experience of teaching undergraduate mathematics
at colleges and universities in the British and American
systems. They have developed and taught courses for a varied
of non-specialists and have established reputations for
presenting rigorous mathematical concepts in a manner which
is accessible to this audience. Their current research
interests lie in the fields of algebra, topology and
mathematics education. Discrete Mathematics for New
Technology is therefore a rare thing; a readable, friendly
textbook designed for non-mathematicians, presenting
material which is at the foundations of mathematics itself.
It is essential reading.
650 0 $aComputer science$xMathematics.
700 1 $aTaylor, John,$d1957-
970 01 $tPreface
970 01 $tList of Symbols
970 11 $lCh. 1$tLogic$p1
970 12 $l1.1$tPropositions and Truth Values$p1
970 12 $l1.2$tLogical Connectives and Truth Tables$p2
970 12 $l1.3$tTautologies and Contradictions$p13
970 12 $l1.4$tLogical Equivalence and Logical
Implication$pl6
970 12 $l1.5$tThe Algebra of Propositions$p21
970 12 $l1.6$tMore about Conditionals$p24
970 12 $l1.7$tArguments$p25
970 12 $l1.8$tPredicate Logic$p28
970 12 $l1.9$tArguments in Predicate Logic$p37
970 11 $lCh. 2$tMathematical Proof$p41
970 12 $l2.1$tThe Nature of Proof$p41
970 12 $l2.2$tAxioms and Axiom Systems$p42
970 12 $l2.3$tMethods of Proof$p47
970 12 $l2.4$tMathematical Induction$p60
970 11 $lCh. 3$tSets$p70
970 12 $l3.1$tSets and Membership$p70
970 12 $l3.2$tSubsets$p76
970 12 $l3.3$tOperations on Sets$p82
970 12 $l3.4$tCounting Techniques$p89
970 12 $l3.5$tThe Algebra of Sets$p93
970 12 $l3.6$tFamilies of Sets$p99
970 12 $l3.7$tThe Cartesian Product$p107
970 11 $lCh. 4$tRelations$p119
970 12 $l4.1$tRelations and Their Representations$p119
970 12 $l4.2$tProperties of Relations$p127
970 12 $l4.3$tIntersections and Unions of Relations$p133
970 12 $l4.4$tEquivalence Relations and Partitions$p136
970 12 $l4.5$tOrder Relations$p147
970 12 $l4.6$tHasse Diagrams$p156
970 12 $l4.7$tApplication: Relational Databases$p162
970 11 $lCh. 5$tFunctions$p177
970 12 $l5.1$tDefinitions and Examples$p177
970 12 $l5.2$tComposite Functions$p193
970 12 $l5.3$tInjections and Surjections$p199
970 12 $l5.4$tBijections and Inverse Functions$p214
970 12 $l5.5$tMore on Cardinality$p221
970 12 $l5.6$tDatabases: Functional Dependence and Normal
Forms$p228
970 11 $lCh. 6$tMatrix Algebra$p243
970 12 $l6.1$tIntroduction$p243
970 12 $l6.2$tSome Special Matrices$p246
970 12 $l6.3$tOperations on Matrices$p249
970 12 $l6.4$tElementary Matrices$p259
970 12 $l6.5$tThe Inverse of a Matrix$p270
970 11 $lCh. 7$tSystems of Linear Equations$p284
970 12 $l7.1$tIntroduction$p284
970 12 $l7.2$tMatrix Inverse Method$p291
970 12 $l7.3$tGauss-Jordan Elimination$p295
970 12 $l7.4$tGaussian Elimination$p309
970 11 $lCh. 8$tAlgebraic Structures$p315
970 12 $l8.1$tBinary Operations and their Properties$p315
970 12 $l8.2$tAlgebraic Structures$p324
970 12 $l8.3$tMore about Groups$p333
970 12 $l8.4$tSome Families of Groups$p339
970 12 $l8.5$tSubstructures$p349
970 12 $l8.6$tMorphisms$p357
970 12 $l8.7$tGroup Codes$p371
970 11 $lCh. 9$tBoolean Algebra$p391
970 12 $l9.1$tIntroduction$p391
970 12 $l9.2$tProperties of Boolean Algebras$p395
970 12 $l9.3$tBoolean Functions$p402
970 12 $l9.4$tSwitching Circuits$p419
970 12 $l9.5$tLogic Networks$p427
970 12 $l9.6$tMinimization of Boolean Expressions$p435
970 11 $lCh. 10$tGraph Theory$p448
970 12 $l10.1$tDefinitions and Examples$p448
970 12 $l10.2$tPaths and Circuits$p459
970 12 $l10.3$tIsomorphism of Graphs$p471
970 12 $l10.4$tTrees$p477
970 12 $l10.5$tPlanar Graphs$p484
970 12 $l10.6$tDirected Graphs$p491
970 11 $lCh. 11$tApplications of Graph Theory$p499
970 12 $l11.1$tIntroduction$p499
970 12 $l11.2$tRooted Trees$p501
970 12 $l11.3$tSorting$p515
970 12 $l11.4$tSearching Strategies$p532
970 12 $l11.5$tWeighted Graphs$p542
970 12 $l11.6$tThe Shortest Path and Travelling Salesman
Problems$p548
970 12 $l11.7$tNetworks and Flows$p562
970 01 $tReferences and Further Reading$p575
970 01 $tHints and Solutions to Selected Exercises$p581
970 01 $tIndex$p659
997 $boclc
997 $bacas
