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Discrete Mathematics and Its Applications,9780070539655
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Discrete Mathematics and Its Applications

by
Edition:
3rd
ISBN13:

9780070539655

ISBN10:
0070539650
Pub. Date:
1/1/1995
Publisher(s):
MCG

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Table of Contents

Preface xi(10)
To the Student xxi
1 The Foundations: Logic, Sets, and Functions
1(96)
1.1 Logic
1(12)
1.2 Propositional Equivalences
13(8)
1.3 Predicates and Quantifiers
21(16)
1.4 Sets
37(9)
1.5 Set Operations
46(12)
1.6 Functions
58(13)
1.7 Sequences and Summations
71(8)
1.8 The Growth of Functions
79(10)
Key Terms and Results
89(3)
Review Questions
92(1)
Supplementary Exercises
93(2)
Computer Projects
95(1)
Computations and Explorations
95(1)
Writing Projects
96(1)
2 The Fundamentals: Algorithms, the Integers, and Matrices
97(71)
2.1 Algorithms
98(6)
2.2 Complexity of Algorithms
104(7)
2.3 The Integers and Division
111(15)
2.4 Integers and Algorithms
126(10)
2.5 Applications of Number Theory
136(14)
2.6 Matrices
150(12)
Key Terms and Results
162(1)
Review Questions
163(1)
Supplementary Exercises
164(2)
Computer Projects
166(1)
Computations and Explorations
166(1)
Writing Projects
167(1)
3 Mathematical Reasoning
168(63)
3.1 Methods of Proof
169(14)
3.2 Mathematical Induction
183(18)
3.3 Recursive Definitions
201(10)
3.4 Recursive Algorithms
211(6)
3.5 Program Correctness
217(7)
Key Terms and Results
224(1)
Review Questions
225(1)
Supplementary Exercises
226(3)
Computer Projects
229(1)
Computations and Explorations
229(1)
Writing Projects
230(1)
4 Counting
231(76)
4.1 The Basics of Counting
232(11)
4.2 The Pigeonhole Principle
243(7)
4.3 Permutations and Combinations
250(11)
4.4 Discrete Probability
261(7)
4.5 Probability Theory
268(14)
4.6 Generalized Permutations and Combinations
282(11)
4.7 Generating Permutations and Combinations
293(5)
Key Terms and Concepts
298(2)
Review Questions
300(1)
Supplementary Exercises
301(4)
Computer Projects
305(1)
Computations and Explorations
305(1)
Writing Projects
306(1)
5 Advanced Counting Techniques
307(48)
5.1 Recurrence Relations
307(11)
5.2 Solving Recurrence Relations
318(7)
5.3 Divide-and-Conquer Relations
325(7)
5.4 Inclusion-Exclusion
332(7)
5.5 Applications of Inclusion-Exclusion
339(10)
Key Terms and Results
349(1)
Review Questions
350(1)
Supplementary Exercises
351(2)
Computer Projects
353(1)
Computations and Explorations
353(1)
Writing Projects
354(1)
6 Relations
355(74)
6.1 Relations and Their Properties
355(11)
6.2 n-ary Relations and Their Applications
366(7)
6.3 Representing Relations
373(8)
6.4 Closures of Relations
381(12)
6.5 Equivalence Relations
393(9)
6.6 Partial Orderings
402(17)
Key Terms and Results
419(2)
Review Questions
421(1)
Supplementary Exercises
422(4)
Computer Projects
426(1)
Computations and Explorations
427(1)
Writing Projects
427(2)
7 Graphs
429(102)
7.1 Introduction to Graphs
429(8)
7.2 Graph Terminology
437(12)
7.3 Representing Graphs and Graph Isomorphism
449(13)
7.4 Connectivity
462(10)
7.5 Euler and Hamilton Paths
472(16)
7.6 Shortest Path Problems
488(11)
7.7 Planar Graphs
499(10)
7.8 Graph Coloring
509(11)
Key Terms and Results
520(2)
Review Questions
522(1)
Supplementary Exercises
523(5)
Computer Projects
528(1)
Computations and Explorations
529(1)
Writing Projects
529(2)
8 Trees
531(77)
8.1 Introduction to Trees
531(16)
8.2 Applications of Trees
547(7)
8.3 Tree Traversal
554(17)
8.4 Trees and Sorting
571(9)
8.5 Spanning Trees
580(13)
8.6 Minimum Spanning Trees
593(7)
Key Terms and Results
600(2)
Review Questions
602(1)
Supplementary Exercises
603(3)
Computer Projects
606(1)
Computations and Explorations
607(1)
Writing Projects
607(1)
9 Boolean Algebra
608(43)
9.1 Boolean Functions
609(7)
9.2 Representing Boolean Functions
616(5)
9.3 Logic Gates
621(8)
9.4 Minimization of Circuits
629(16)
Key Terms and Results
645(1)
Review Questions
646(1)
Supplementary Exercises
646(3)
Computer Projects
649(1)
Computations and Explorations
649(1)
Writing Projects
650(1)
10 Modeling Computation
651
10.1 Languages and Grammars
652(11)
10.2 Finite-State Machines with Output
663(9)
10.3 Finite-State Machines with No Output
672(10)
10.4 Language Recognition
682(12)
10.5 Turing Machines
694(9)
Key Terms and Results
703(1)
Review Questions
704(1)
Supplementary Exercises
705(3)
Computer Projects
708(1)
Computations and Explorations
709(1)
Writing Projects
709
Appendixes A-0
A.1 Exponential and Logarithmic Functions A-0(3)
A.2 Pseudocode A-3(6)
A.3 Generating Functions A-9
Suggested Readings B-0
Solutions to Odd-Numbered Exercises S-1
Index of Biographies I-0
Index I-1


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