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Discrete Math (4th Ed)

ISBN: 9780135182420 | 0135182425
Edition: 4th
Format: Hardcover
Publisher: PRENTICE HALL PTR
Pub. Date: 7/1/1996

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SummaryTable of Contents
Mild revision of top selling text. This text has the best coverage of topics in computer science. New edition features new Mathematician's Corner which is found in each chapter and shows students how to do proofs.
1 LOGIC AND PROOFS
1(62)
1.1 Propositions
2(6)
1.2 Conditional Propositions and Logical Equivalence
... MORE		8(10)
1.3 Quantifiers
18(16)
1.4 Proofs
34(8)
1.5 Resolution Proofs
42(4)
1.6 Mathematical Induction
46(10)
Problem-Solving Corner: Mathematical Induction
56(3)
Notes
59(1)
Chapter Review
59(2)
Chapter Self-Test
61(2)
2 THE LANGUAGE OF MATHEMATICS
63(79)
2.1 Sets
64(9)
2.2 Sequences and Strings
73(11)
2.3 Number Systems
84(7)
2.4 Relations
91(13)
Problem-Solving Corner: Relations
102(2)
2.5 Equivalence Relations
104(10)
Problem-Solving Corner: Equivalence Relations
111(3)
2.6 Matrices of Relations
114(4)
2.7 Relational Databases
118(7)
2.8 Functions
125(11)
Notes
136(1)
Chapter Review
137(2)
Chapter Self-Test
139(3)
3 ALGORITHMS
142(55)
3.1 Introduction
143(1)
3.2 Notation for Algorithms
144(7)
3.3 The Euclidean Algorithms
151(6)
3.4 Recursive Algorithms
157(9)
3.5 Complexity of Algorithms
166(20)
Problem-Solving Corner: Design and Analysis of an Algorithm
182(4)
3.6 Analysis of the Euclidean Algorithm
186(3)
3.7 The RSA Public-Key Cryptosystem
189(4)
Notes
193(1)
Chapter Review
193(1)
Chapter Self-Test
194(3)
4 COUNTING METHODS AND THE PIGEONHOLE PRINCIPLE
197(59)
4.1 Basic Principles
197(13)
Problem-Solving Corner: Counting
207(3)
4.2 Permutations and Combinations
210(18)
Problem-Solving Corner: Combinations
225(3)
4.3 Algorithms for Generating Permutations and Combinations
228(7)
4.4 Generalized Permutations and Combinations
235(7)
4.5 Binomial Coefficients and Combinatorial Identities
242(6)
4.6 The Pigeonhole Principle
248(5)
Notes
253(1)
Chapter Review
253(1)
Chapter Self-Test
254(2)
5 RECURRENCE RELATIONS
256(48)
5.1 Introduction
256(14)
5.2 Solving Recurrence Relations
270(17)
Problem-Solving Corner: Recurrence Relations
284(3)
5.3 Applications to the Analysis of Algorithms
287(15)
Notes
302(1)
Chapter Review
302(1)
Chapter Self-Test
302(2)
6 GRAPH THEORY
304(72)
6.1 Introduction
305(11)
6.2 Paths and Cycles
316(15)
Problem-Solving Corner: Graphs
330(1)
6.3 Hamiltonian Cycles and the Traveling Salesperson Problem
331(7)
6.4 A Shortest-Path Algorithm
338(6)
6.5 Representations of Graphs
344(6)
6.6 Isomorphisms of Graphs
350(9)
6.7 Planar Graphs
359(7)
6.8 Instant Insanity
366(5)
Notes
371(1)
Chapter Review
371(1)
Chapter Self-Test
372(4)
7 TREES
376(79)
7.1 Introduction
377(8)
7.2 Terminology and Characterizations of Trees
385(7)
Problem-Solving Corner: Trees
390(2)
7.3 Spanning Trees
392(8)
7.4 Minimal Spanning Trees
400(8)
7.5 Binary Trees
408(7)
7.6 Tree Traversals
415(7)
7.7 Decision Trees and the Minimum Time for Sorting
422(7)
7.8 Isomorphisms of Trees
429(11)
7.9 Game Trees
440(10)
Notes
450(1)
Chapter Review
450(1)
Chapter Self-Test
451(4)
8 NETWORK MODELS AND PETRI NETS
455(45)
8.1 Network Models
456(6)
8.2 A Maximal Flow Algorithm
462(11)
8.3 The Max Flow, Min Cut Theorem
473(5)
8.4 Matching
478(8)
Problem-Solving Corner: Matching
484(2)
8.5 Petri Nets
486(10)
Notes
496(1)
Chapter Review
497(1)
Chapter Self-Test
498(2)
9 BOOLEAN ALGEBRAS AND COMBINATORIAL CIRCUITS
500(46)
9.1 Combinatorial Circuits
500(9)
9.2 Properties of Combinatorial Circuits
509(7)
9.3 Boolean Algebras
516(8)
Problem-Solving Corner: Boolean Algebras
522(2)
9.4 Boolean Functions and Synthesis of Circuits
524(7)
9.5 Applications
531(11)
Notes
542(1)
Chapter Review
542(1)
Chapter Self-Test
543(3)
10 AUTOMATA, GRAMMARS, AND LANGUAGES
546(47)
10.1 Sequential Circuits and Finite-State Machines
546(8)
10.2 Finite-State Automata
554(8)
10.3 Languages and Grammars
562(11)
10.4 Nondeterministic Finite-State Automata
573(9)
10.5 Relationships Between Languages and Automata
582(7)
Notes
589(1)
Chapter Review
590(1)
Chapter Self-Test
590(3)
11 COMPUTATIONAL GEOMETRY
593(17)
11.1 The Closest-Pair Problem
593(5)
11.2 A Lower Bound for the Closest-Pair Problem
598(3)
11.3 An Algorithm to Compute the Convex Hull
601(7)
Notes
608(1)
Chapter Review
609(1)
Chapter Self-Test
609(1)
APPENDIX: MATRICES610(5)
REFERENCES615(6)
HINTS AND SOLUTIONS TO SELECTED EXERCISES621(66)
INDEX687

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