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Discrete Mathematics with Proof

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ISBN-10: 0470457937

ISBN-13: 9780470457931

Edition: 2nd 2009

Authors: Eric Gossett

List price: $235.95
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Book details

List price: $235.95
Edition: 2nd
Copyright year: 2009
Publisher: John Wiley & Sons, Incorporated
Publication date: 6/8/2009
Binding: Hardcover
Pages: 928
Size: 8.50" wide x 10.25" long x 2.00" tall
Weight: 4.334
Language: English

Preface
Acknowledgements
To The Student
Introduction
What Is Discrete Mathematics?
The Stable Marriage Problem
Other Examples
Exercises
Chapter Review
Sets, Logic, and Boolean Algebras
Sets
Logic in Daily Life
Propositional Logic
Logical Equivalence and Rules of Inference
Boolean Algebras
Predicate Logic
Quick Check Solutions
Chapter Review
Proof
Introduction to Mathematical Proof
Elementary Number Theory: Fuel for Practice
Proof Strategies
Applications of Elementary Number Theory
Mathematical Induction
Creating Proofs: Hints and Suggestions
Quick Check Solutions
Chapter Review
Algorithms
Expressing Algorithms
Measuring Algorithm Efficiency
Pattern Matching
The Halting Problem
Quick Check Solutions
Chapter Review
Counting
Permutations and Combinations
Combinatorial Proofs
Pigeon-Hole Principle
Inclusion-Exclusion
Quick Check Solutions
Chapter Review
Finite Probability Theory
The Language of Probabilities
Conditional Probabilities and Independent Events
Counting and Probability
Expected Value
The Binomial Distribution
Bayes's Theorem
Quick Check Solutions
Recursion
Recursive Algorithms
Recurrence Relations
Big-2and Recursive Algorithms: The Master Theorem
Generating Functions
The Josephus Problem
Quick Check Solutions
Chapter Review
Combinatorics
Partitions, Occupancy Problems, Stirling Numbers
Latin Squares
Finite Projective Planes
Balanced Incomplete Block Designs
The Knapsack Problem
Error-Correcting Codes
Distinct Representatives, Ramsey Numbers
Quick Check Solutions
Chapter Review
Formal Models in Computer Science
Information
Finite-State Machines
Formal Languages
Regular Expressions
The Three Faces of Regular
A Glimpse at More Advanced Topics
Quick Check Solutions
Chapter Review
Graphs
Terminology
Connectivity and Adjacency
Euler and Hamilton
Representation and Isomorphism
The Big Theorems: Planarity, Euler, Polyhedra, Chromatic Number
Directed Graphs and Weighted Graphs
Quick Check Solutions
Chapter Review
Trees
Terminology, Counting
Traversal, Searching, and Sorting
More Applications of Trees
Spanning Trees
Quick Check Solutions
Chapter Review
Functions, Relations, Databases, and Circuits
Functions and Relations
Equivalence Relations, Partially Ordered Sets
n-ary Relations and Relational Databases
Boolean Functions and Boolean Expressions