Discrete Mathematical Structures

✍ Scribed by Bernard Kolman; Robert C. Busby; Sharon Cutler Ross

• Publisher: Prentice Hall
• Year: 2008
• Tongue: English
• Leaves: 552
• Edition: 6 ed.
• Category: Library

✦ Synopsis

Key Message: Discrete Mathematical Structures, Sixth Edition, offers a clear and concise presentation of the fundamental concepts of discrete mathematics. This introductory book contains more genuine computer science applications than any other text in the field, and will be especially helpful for readers interested in computer science. This book is written at an appropriate level for a wide variety of readers, and assumes a college algebra course as the only prerequisite. Key Topics: Fundamentals; Logic; Counting; Relations and Digraphs; Functions; Order Relations and Structures; Trees; Topics in Graph Theory; Semigroups and Groups; Languages and Finite-State Machines; Groups and Coding Market: For all readers interested in discrete mathematics.

✦ Table of Contents

Cover
Title Page
Copyright Page
Acknowledgments
Contents
Preface
A Word to Students
1 Fundamentals
1.1 Sets and Subsets
1.2 Operations on Sets
1.3 Sequences
1.4 Properties of the Integers
1.5 Matrices
1.6 Mathematical Structures
2 Logic
2.1 Propositions and Logical Operations
2.2 Conditional Statements
2.3 Methods of Proof
2.4 Mathematical Induction
2.5 Mathematical Statements
2.6 Logic and Problem Solving
3 Counting
3.1 Permutations
3.2 Combinations
3.3 Pigeonhole Principle
3.4 Elements of Probability
3.5 Recurrence Relations
4 Relations and Digraphs
4.1 Product Sets and Partitions
4.2 Relations and Digraphs
4.3 Paths in Relations and Digraphs
4.4 Properties of Relations
4.5 Equivalence Relations
4.6 Data Structures for Relations and Digraphs
4.7 Operations on Relations
4.8 Transitive Closure and Warshall’s Algorithm
5 Functions
5.1 Functions
5.2 Functions for Computer Science
5.3 Growth of Functions
5.4 Permutation Functions
6 Order Relations and Structures
6.1 Partially Ordered Sets
6.2 Extremal Elements of Partially Ordered Sets
6.3 Lattices
6.4 Finite Boolean Algebras
6.5 Functions on Boolean Algebras
6.6 Circuit Design
7 Trees
7.1 Trees
7.2 Labeled Trees
7.3 Tree Searching
7.4 Undirected Trees
7.5 Minimal Spanning Trees
8 Topics in Graph Theory
8.1 Graphs
8.2 Euler Paths and Circuits
8.3 Hamiltonian Paths and Circuits
8.4 Transport Networks
8.5 Matching Problems
8.6 Coloring Graphs
9 Semigroups and Groups
9.1 Binary Operations Revisited
9.2 Semigroups
9.3 Products and Quotients of Semigroups
9.4 Groups
9.5 Products and Quotients of Groups
9.6 Other Mathematical Structures
10 Languages and Finite-State Machines
10.1 Languages
10.2 Representations of Special Grammars and Languages
10.3 Finite-State Machines
10.4 Monoids, Machines, and Languages
10.5 Machines and Regular Languages
10.6 Simpli.cation of Machines
11 Groups and Coding
11.1 Coding of Binary Information and Error Detection
11.2 Decoding and Error Correction
11.3 Public Key Cryptology
Appendix A: Algorithms and Pseudocode
Appendix B: Additional Experiments in Discrete Mathematics
Appendix C: Coding Exercises
Answers to Odd-Numbered Exercises
Answers to Chapter Self-Tests
Glossary
Index
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
Z
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