Discrete Mathematics: for New Technology

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ISBN: 9780750301350 | 075030135X
Cover: Nonspecific Binding
Copyright: 5/1/1992

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This title sets out to cover the core mathematics required for undergraduate computer science students. The subject comprehensively covered with an easy to follow progression from the basic mathematical concepts acquired at high school level. More sophisticated mathematical concepts are examined in the latter stages of the book.

Preface
List of Symbols
Logic	p. 1
Propositions and Truth Values	p. 1
Logical Connectives and Truth Tables	p. 2
Tautologies and Contradictions	p. 13
Logical Equivalence and Logical Implication	p. l6
The Algebra of Propositions	p. 21
More about Conditionals	p. 24
Arguments	p. 25
Predicate Logic	p. 28
Arguments in Predicate Logic	p. 37
Mathematical Proof	p. 41
The Nature of Proof	p. 41
Axioms and Axiom Systems	p. 42
Methods of Proof	p. 47
Mathematical Induction	p. 60
Sets	p. 70
Sets and Membership	p. 70
Subsets	p. 76
Operations on Sets	p. 82
Counting Techniques	p. 89
The Algebra of Sets	p. 93
Families of Sets	p. 99
The Cartesian Product	p. 107
Relations	p. 119
Relations and Their Representations	p. 119
Properties of Relations	p. 127
Intersections and Unions of Relations	p. 133
Equivalence Relations and Partitions	p. 136
Order Relations	p. 147
Hasse Diagrams	p. 156
Application: Relational Databases	p. 162
Functions	p. 177
Definitions and Examples	p. 177
Composite Functions	p. 193
Injections and Surjections	p. 199
Bijections and Inverse Functions	p. 214
More on Cardinality	p. 221
Databases: Functional Dependence and Normal Forms	p. 228
Matrix Algebra	p. 243
Introduction	p. 243
Some Special Matrices	p. 246
Operations on Matrices	p. 249
Elementary Matrices	p. 259
The Inverse of a Matrix	p. 270
Systems of Linear Equations	p. 284
Introduction	p. 284
Matrix Inverse Method	p. 291
Gauss-Jordan Elimination	p. 295
Gaussian Elimination	p. 309
Algebraic Structures	p. 315
Binary Operations and their Properties	p. 315
Algebraic Structures	p. 324
More about Groups	p. 333
Some Families of Groups	p. 339
Substructures	p. 349
Morphisms	p. 357
Group Codes	p. 371
Boolean Algebra	p. 391
Introduction	p. 391
Properties of Boolean Algebras	p. 395
Boolean Functions	p. 402
Switching Circuits	p. 419
Logic Networks	p. 427
Minimization of Boolean Expressions	p. 435
Graph Theory	p. 448
Definitions and Examples	p. 448
Paths and Circuits	p. 459
Isomorphism of Graphs	p. 471
Trees	p. 477
Planar Graphs	p. 484
Directed Graphs	p. 491
Applications of Graph Theory	p. 499
Introduction	p. 499
Rooted Trees	p. 501
Sorting	p. 515
Searching Strategies	p. 532
Weighted Graphs	p. 542
The Shortest Path and Travelling Salesman Problems	p. 548
Networks and Flows	p. 562
References and Further Reading	p. 575
Hints and Solutions to Selected Exercises	p. 581
Index	p. 659
Table of Contents provided by Blackwell. All Rights Reserved.

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Discrete Mathematics: for New Technology

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