9780073229720

Discrete Mathematics and Its Applications

by
  • ISBN13:

    9780073229720

  • ISBN10:

    0073229725

  • Edition: 6th
  • Format: Hardcover
  • Copyright: 7/26/2006
  • Publisher: McGraw-Hill Education
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Summary

Discrete Mathematics and its Applications, Sixth Edition, is intended for one- or two-term introductory discrete mathematics courses taken by students from a wide variety of majors, including computer science, mathematics, and engineering. This renowned best-selling text, which has been used at over 500 institutions around the world, gives a focused introduction to the primary themes in a discrete mathematics course and demonstrates the relevance and practicality of discrete mathematics to a wide a wide variety of real-world applications...from computer science to data networking, to psychology, to chemistry, to engineering, to linguistics, to biology, to business, and to many other important fields.

Table of Contents

Preface
The MathZone Companion Website To the Student
The Foundations: Logic and Proofs
Propositional Logic
Propositional Equivalences
Predicates and Quantifiers
Nested Quantifiers
Rules of Inference
Introduction to Proofs
Proof Methods and Strategy End-of-Chapter Material
Basic Structures: Sets, Functions, Sequences and Sums
Sets
Set Operations
Functions
Sequences and Summations End-of-Chapter Material
The Fundamentals: Algorithms, the Integers, and Matrices
Algorithms
The Growth of Functions
Complexity of Algorithms
The Integers and Division
Primes and Greatest Common Divisors
Integers and Algorithms
Applications of Number Theory
Matrices End-of-Chapter Material
Induction and Recursion
Mathematical Induction
Strong Induction and Well-Ordering
Recursive Definitions and Structural Induction
Recursive Algorithms
Program Correctness End-of-Chapter Material
Counting
The Basics of Counting
The Pigeonhole Principle
Permutations and Combinations
Binomial Coefficients
Generalized Permutations and Combinations
Generating Permutations and Combinations End-of-Chapter Material
Discrete Probability
An Introduction to Discrete Probability
Probability Theory
Bayes’ Theorem
Expected Value and Variance End-of-Chapter Material
Advanced Counting Techniques
Recurrence Relations
Solving Linear Recurrence Relations
Divide-and-Conquer Algorithms and Recurrence elations
Generating Functions
Inclusion-Exclusion
Applications of Inclusion-Exclusion End-of-Chapter Material
Relations
Relations and Their Properties
n-ary Relations and Their Applications
Representing Relations
Closures of Relations
Equivalence Relations
Partial Orderings End-of-Chapter Material
Graphs
Graphs and Graph Models
Graph Terminology and Special Types of Graphs
Representing Graphs and Graph Isomorphism
Connectivity
Euler and Hamilton Paths
Shortest-Path Problems
Planar Graphs
Graph Coloring End-of-Chapter Material
Trees
Introduction to Trees
Applications of Trees
Tree Traversal
Spanning Trees
Minimum Spanning Trees End-of-Chapter Material
Boolean Algebra
Boolean Functions
Representing Boolean Functions
Logic Gates
Minimization of Circuits End-of-Chapter Material
Modeling Computation
Languages and Grammars
Finite-State Machines with Output
Finite-State Machines with No Output
Language Recognition
Turing Machines End-of-Chapter Material
Appendixes
Axioms for the Real Numbers and the Positive Integers
Exponential and Logarithmic Functions
Pseudocode Suggested Readings
Answers to Odd-Numbered Exercises
Photo Credits
Index of Biographies
Index
Table of Contents provided by Publisher. All Rights Reserved.

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