Discrete and Combinatorial Mathematics

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  • Edition: 5th
  • Format: Paperback
  • Copyright: 2003-07-17
  • Publisher: Pearson
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This fifth edition continues to improve on the features that have made it the market leader. The text offers a flexible organization, enabling instructors to adapt the book to their particular courses. The book is both complete and careful, and it continues to maintain its emphasis on algorithms and applications. Excellent exercise sets allow students to perfect skills as they practice. This new edition continues to feature numerous computer science applications-making this the ideal text for preparing students for advanced study.

Table of Contents

Fundamentals of Discrete Mathematics
Fundamental Principles of Counting
The Rules of Sum and Product
Combinations: The Binomial Theorem
Combinations with Repetition
The Catalan Numbers (Optional)
Summary and Historical Review
Fundamentals of Logic
Basic Connectives and Truth Tables
Logical Equivalence: The Laws of Logic
Logical Implication: Rules of Inference
The Use of Quantifiers
Quantifiers, Definitions, and the Proofs of Theorems
Summary and Historical Review
Set Theory
Sets and Subsets
Set Operations and the Laws of Set Theory
Counting and Venn Diagrams
A First Word on Probability
The Axioms of Probability (Optional)
Conditional Probability: Independence (Optional)
Discrete Random Variables (Optional)
Summary and Historical Review
Properties of the Integers: Mathematical Induction
The Well-Ordering Principle: Mathematical Induction
Recursive Definitions
The Division Algorithm: Prime Numbers
The Greatest Common Divisor: The Euclidean Algorithm
The Fundamental Theorem of Arithmetic
Summary and Historical Review
Relations and Functions
Cartesian Products and Relations
Functions: Plain and One-to-One
Onto Functions: Stirling Numbers of the Second Kind
Special Functions
The Pigeonhole Principle
Function Composition and Inverse Functions
Computational Complexity
Analysis of Algorithms
Summary and Historical Review
Languages: Finite State Machines
Language: The Set Theory of Strings
Finite State Machines: A First Encounter
Finite State Machines: A Second Encounter
Summary and Historical Review
Relations: The Second Time Around
Relations Revisited: Properties of Relations
Computer Recognition: Zero-One Matrices and Directed Graphs
Partial Orders
Table of Contents provided by Publisher. All Rights Reserved.

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