Discrete Mathematics and Its Applications
Publisher: Mcgraw-Hill College
Published: March 1995
Language: eng
Number of pages: 832
ISBN-13: 9780070539655
Table of contents: title: Preface
pagenum: xi; title: To the Student
pagenum: xxi; label: 1
title: The Foundations: Logic, Sets, and Functions
pagenum: 1; label: 1.1
title: Logic
pagenum: 1; label: 1.2
title: Propositional Equivalences
pagenum: 13; label: 1.3
title: Predicates and Quantifiers
pagenum: 21; label: 1.4
title: Sets
pagenum: 37; label: 1.5
title: Set Operations
pagenum: 46; label: 1.6
title: Functions
pagenum: 58; label: 1.7
title: Sequences and Summations
pagenum: 71; label: 1.8
title: The Growth of Functions
pagenum: 79; title: Key Terms and Results
pagenum: 89; title: Review Questions
pagenum: 92; title: Supplementary Exercises
pagenum: 93; title: Computer Projects
pagenum: 95; title: Computations and Explorations
pagenum: 95; title: Writing Projects
pagenum: 96; label: 2
title: The Fundamentals: Algorithms, the Integers, and Matrices
pagenum: 97; label: 2.1
title: Algorithms
pagenum: 98; label: 2.2
title: Complexity of Algorithms
pagenum: 104; label: 2.3
title: The Integers and Division
pagenum: 111; label: 2.4
title: Integers and Algorithms
pagenum: 126; label: 2.5
title: Applications of Number Theory
pagenum: 136; label: 2.6
title: Matrices
pagenum: 150; title: Key Terms and Results
pagenum: 162; title: Review Questions
pagenum: 163; title: Supplementary Exercises
pagenum: 164; title: Computer Projects
pagenum: 166; title: Computations and Explorations
pagenum: 166; title: Writing Projects
pagenum: 167; label: 3
title: Mathematical Reasoning
pagenum: 168; label: 3.1
title: Methods of Proof
pagenum: 169; label: 3.2
title: Mathematical Induction
pagenum: 183; label: 3.3
title: Recursive Definitions
pagenum: 201; label: 3.4
title: Recursive Algorithms
pagenum: 211; label: 3.5
title: Program Correctness
pagenum: 217; title: Key Terms and Results
pagenum: 224; title: Review Questions
pagenum: 225; title: Supplementary Exercises
pagenum: 226; title: Computer Projects
pagenum: 229; title: Computations and Explorations
pagenum: 229; title: Writing Projects
pagenum: 230; label: 4
title: Counting
pagenum: 231; label: 4.1
title: The Basics of Counting
pagenum: 232; label: 4.2
title: The Pigeonhole Principle
pagenum: 243; label: 4.3
title: Permutations and Combinations
pagenum: 250; label: 4.4
title: Discrete Probability
pagenum: 261; label: 4.5
title: Probability Theory
pagenum: 268; label: 4.6
title: Generalized Permutations and Combinations
pagenum: 282; label: 4.7
title: Generating Permutations and Combinations
pagenum: 293; title: Key Terms and Concepts
pagenum: 298; title: Review Questions
pagenum: 300; title: Supplementary Exercises
pagenum: 301; title: Computer Projects
pagenum: 305; title: Computations and Explorations
pagenum: 305; title: Writing Projects
pagenum: 306; label: 5
title: Advanced Counting Techniques
pagenum: 307; label: 5.1
title: Recurrence Relations
pagenum: 307; label: 5.2
title: Solving Recurrence Relations
pagenum: 318; label: 5.3
title: Divide-and-Conquer Relations
pagenum: 325; label: 5.4
title: Inclusion-Exclusion
pagenum: 332; label: 5.5
title: Applications of Inclusion-Exclusion
pagenum: 339; title: Key Terms and Results
pagenum: 349; title: Review Questions
pagenum: 350; title: Supplementary Exercises
pagenum: 351; title: Computer Projects
pagenum: 353; title: Computations and Explorations
pagenum: 353; title: Writing Projects
pagenum: 354; label: 6
title: Relations
pagenum: 355; label: 6.1
title: Relations and Their Properties
pagenum: 355; label: 6.2
title: n-ary Relations and Their Applications
pagenum: 366; label: 6.3
title: Representing Relations
pagenum: 373; label: 6.4
title: Closures of Relations
pagenum: 381; label: 6.5
title: Equivalence Relations
pagenum: 393; label: 6.6
title: Partial Orderings
pagenum: 402; title: Key Terms and Results
pagenum: 419; title: Review Questions
pagenum: 421; title: Supplementary Exercises
pagenum: 422; title: Computer Projects
pagenum: 426; title: Computations and Explorations
pagenum: 427; title: Writing Projects
pagenum: 427; label: 7
title: Graphs
pagenum: 429; label: 7.1
title: Introduction to Graphs
pagenum: 429; label: 7.2
title: Graph Terminology
pagenum: 437; label: 7.3
title: Representing Graphs and Graph Isomorphism
pagenum: 449; label: 7.4
title: Connectivity
pagenum: 462; label: 7.5
title: Euler and Hamilton Paths
pagenum: 472; label: 7.6
title: Shortest Path Problems
pagenum: 488; label: 7.7
title: Planar Graphs
pagenum: 499; label: 7.8
title: Graph Coloring
pagenum: 509; title: Key Terms and Results
pagenum: 520; title: Review Questions
pagenum: 522; title: Supplementary Exercises
pagenum: 523; title: Computer Projects
pagenum: 528; title: Computations and Explorations
pagenum: 529; title: Writing Projects
pagenum: 529; label: 8
title: Trees
pagenum: 531; label: 8.1
title: Introduction to Trees
pagenum: 531; label: 8.2
title: Applications of Trees
pagenum: 547; label: 8.3
title: Tree Traversal
pagenum: 554; label: 8.4
title: Trees and Sorting
pagenum: 571; label: 8.5
title: Spanning Trees
pagenum: 580; label: 8.6
title: Minimum Spanning Trees
pagenum: 593; title: Key Terms and Results
pagenum: 600; title: Review Questions
pagenum: 602; title: Supplementary Exercises
pagenum: 603; title: Computer Projects
pagenum: 606; title: Computations and Explorations
pagenum: 607; title: Writing Projects
pagenum: 607; label: 9
title: Boolean Algebra
pagenum: 608; label: 9.1
title: Boolean Functions
pagenum: 609; label: 9.2
title: Representing Boolean Functions
pagenum: 616; label: 9.3
title: Logic Gates
pagenum: 621; label: 9.4
title: Minimization of Circuits
pagenum: 629; title: Key Terms and Results
pagenum: 645; title: Review Questions
pagenum: 646; title: Supplementary Exercises
pagenum: 646; title: Computer Projects
pagenum: 649; title: Computations and Explorations
pagenum: 649; title: Writing Projects
pagenum: 650; label: 10
title: Modeling Computation
pagenum: 651; label: 10.1
title: Languages and Grammars
pagenum: 652; label: 10.2
title: Finite-State Machines with Output
pagenum: 663; label: 10.3
title: Finite-State Machines with No Output
pagenum: 672; label: 10.4
title: Language Recognition
pagenum: 682; label: 10.5
title: Turing Machines
pagenum: 694; title: Key Terms and Results
pagenum: 703; title: Review Questions
pagenum: 704; title: Supplementary Exercises
pagenum: 705; title: Computer Projects
pagenum: 708; title: Computations and Explorations
pagenum: 709; title: Writing Projects
pagenum: 709; title: Appendixes
pagenum: A-0; label: A.1
title: Exponential and Logarithmic Functions
pagenum: A-0; label: A.2
title: Pseudocode
pagenum: A-3; label: A.3
title: Generating Functions
pagenum: A-9; title: Suggested Readings
pagenum: B-0; title: Solutions to Odd-Numbered Exercises
pagenum: S-1; title: Index of Biographies
pagenum: I-0; title: Index
pagenum: I-1