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Discrete mathematics with proof / Eric Gossett.

By: Material type: TextTextPublisher: Hoboken, N.J. : Wiley, [2009]Copyright date: ©2009Edition: Second editionDescription: xxiii, 806, 98 pages : illustrations ; 26 cmContent type:
  • text
Media type:
  • unmediated
Carrier type:
  • volume
ISBN:
  • 0470457937
  • 9780470457931
Subject(s): DDC classification:
  • 510 22
LOC classification:
  • QA39.3 .G68 2009
Contents:
1. Introduction -- 1.1. What Is Discrete Mathematics? -- 1.2. The Stable Marriage Problem -- 1.3. Other Examples -- 1.4. Exercises -- 1.5. Chapter Review -- 2. Sets, Logic, and Boolean Algebras -- 2.1. Sets -- 2.2. Logic in Daily Life -- 2.3. Propositional Logic -- 2.4. Logical Equivalence and Rules of Inference -- 2.5. Boolean Algebras -- 2.6. Predicate Logic -- 2.7. Quick Check Solutions -- 2.8. Chapter Review -- 3. Proof -- 3.1. Introduction to Mathematical Proof -- 3.2. Elementary Number Theory: Fuel for Practice -- 3.3. Proof Strategies -- 3.4. Applications of Elementary Number Theory -- 3.5. Mathematical Induction -- 3.6. Creating Proofs: Hints and Suggestions -- 3.7. Quick Check Solutions -- 3.8. Chapter Review -- 4. Algorithms -- 4.1. Expressing Algorithms -- 4.2. Measuring Algorithm Efficiency -- 4.3. Pattern Matching -- 4.4. The Halting Problem -- 4.5. Quick Check Solutions -- 4.6. Chapter Review -- 5. Counting -- 5.1. Permutations and Combinations -- 5.2. Combinatorial Proofs -- 5.3. Pigeon-Hole Principle -- 5.4. Quick Check Solutions -- 5.5. Chapter Review -- 6. Finite Probability Theory -- 6.1. The Language of Probabilities -- 6.2. Conditional Probabilities and Independent Events -- 6.3. Counting and Probability -- 6.4. Expected Value -- 6.5. The Binomial Distribution -- 6.6. Bayes's Theorem -- 6.7. Quick Check Solutions -- 7. Recursion -- 7.1. Recursive Algorithms -- 7.2. Recurrence Relations -- 7.3. Big-T and Recursive Algorithms: The Master Theorem -- 7.4. Generating Functions -- 7.5. The Josephus Problem -- 7.6. Quick Check Solutions -- 7.7. Chapter Review -- 8. Combinatorics -- 8.1. Partitions, Occupancy Problems, Stirling Numbers -- 8.2. Latin Squares -- 8.3. Balanced Incomplete Block Designs -- 8.4. The Knapsack Problem -- 8.5. Error-Correcting Codes -- 8.6. Distinct Representatives, Ramsey Numbers -- 8.7. Quick Check Solutions -- 8.8. Chapter Review -- 9. Formal Models in Computer Science -- 9.1. Information -- 9.2. Finite-State Machines -- 9.3. Formal Languages -- 9.4. Regular Expressions -- 9.5. The Three Faces of Regular -- 9.6. A Glimpse at More Advanced Topics -- 9.7. Quick Check Solutions -- 9.8. Chapter Review -- 10. Graphs -- 10.1. Terminology -- 10.2. Connectivity and Adjacency -- 10.3. Euler and Hamilton -- 10.4. Representation and Isomorphism -- 10.5. The Big Theorems: Planarity, Euler, Polyhedra, Chromatic Number -- 10.6. Directed Graphs and Weighted Graphs -- 10.7. Quick Check Solutions -- 10.8. Chapter Review -- 11. Trees -- 11.1. Terminology, Counting -- 11.2. Traversal, Searching, and Sorting -- 11.3. More Applications of Trees -- 11.4. Spanning Trees -- 11.5. Quick Check Solutions -- 11.6. Chapter Review -- 12. Functions, Relations, Databases, and Circuits -- 12.1. Functions and Relations -- 12.2. Equivalence Relations, Partially Ordered Sets -- 12.3. n-ary Relations and Relational Databases -- 12.4. Boolean Functions and Boolean Expressions -- 12.5. Combinatorial Circuits -- 12.6. Quick Check Solutions -- 12.7. Chapter Review -- A. Number Systems -- A.1. The Natural Numbers -- A.2. The Integers -- A.3. The Rational Numbers -- A.4. The Real Numbers -- A.5. The Complex Numbers -- A.6. Other Number Systems -- A.7. Representation of Numbers -- B. Summation Notation -- C. Logic Puzzles and Analyzing Claims -- C.1. Logic Puzzles -- C.2. Analyzing Claims -- C.3. Quick Check Solutions -- D. The Golden Ratio -- E. Matrices -- F. The Greek Alphabet -- G. Writing Mathematics -- H. Solutions to Selected Exercises -- H.1. Introduction -- H.2. Sets, Logic, and Boolean Algebras -- H.3. Proof -- H.4. Algorithms -- H.5. Counting -- H.6. Finite Probability Theory -- H.7. Recursion -- H.8. Combinatorics -- H.9. Formal Models in Computer Science -- H.10. Graphs -- H.11. Trees -- H.12. Functions, Relations, Databases, and Circuits -- H.13. Appendices.
Summary: "Discrete mathematics has become increasingly popular in recent years due to its growing applications in the field of computer science. Discrete Mathematics with Proof, Second Edition continues to facilitate an up-to-date understanding of this important topic, exposing readers to a wide range of modern and technological applications."--Publisher's website.
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Includes bibliographical references and index.

1. Introduction -- 1.1. What Is Discrete Mathematics? -- 1.2. The Stable Marriage Problem -- 1.3. Other Examples -- 1.4. Exercises -- 1.5. Chapter Review -- 2. Sets, Logic, and Boolean Algebras -- 2.1. Sets -- 2.2. Logic in Daily Life -- 2.3. Propositional Logic -- 2.4. Logical Equivalence and Rules of Inference -- 2.5. Boolean Algebras -- 2.6. Predicate Logic -- 2.7. Quick Check Solutions -- 2.8. Chapter Review -- 3. Proof -- 3.1. Introduction to Mathematical Proof -- 3.2. Elementary Number Theory: Fuel for Practice -- 3.3. Proof Strategies -- 3.4. Applications of Elementary Number Theory -- 3.5. Mathematical Induction -- 3.6. Creating Proofs: Hints and Suggestions -- 3.7. Quick Check Solutions -- 3.8. Chapter Review -- 4. Algorithms -- 4.1. Expressing Algorithms -- 4.2. Measuring Algorithm Efficiency -- 4.3. Pattern Matching -- 4.4. The Halting Problem -- 4.5. Quick Check Solutions -- 4.6. Chapter Review -- 5. Counting -- 5.1. Permutations and Combinations -- 5.2. Combinatorial Proofs -- 5.3. Pigeon-Hole Principle -- 5.4. Quick Check Solutions -- 5.5. Chapter Review -- 6. Finite Probability Theory -- 6.1. The Language of Probabilities -- 6.2. Conditional Probabilities and Independent Events -- 6.3. Counting and Probability -- 6.4. Expected Value -- 6.5. The Binomial Distribution -- 6.6. Bayes's Theorem -- 6.7. Quick Check Solutions -- 7. Recursion -- 7.1. Recursive Algorithms -- 7.2. Recurrence Relations -- 7.3. Big-T and Recursive Algorithms: The Master Theorem -- 7.4. Generating Functions -- 7.5. The Josephus Problem -- 7.6. Quick Check Solutions -- 7.7. Chapter Review -- 8. Combinatorics -- 8.1. Partitions, Occupancy Problems, Stirling Numbers -- 8.2. Latin Squares -- 8.3. Balanced Incomplete Block Designs -- 8.4. The Knapsack Problem -- 8.5. Error-Correcting Codes -- 8.6. Distinct Representatives, Ramsey Numbers -- 8.7. Quick Check Solutions -- 8.8. Chapter Review -- 9. Formal Models in Computer Science -- 9.1. Information -- 9.2. Finite-State Machines -- 9.3. Formal Languages -- 9.4. Regular Expressions -- 9.5. The Three Faces of Regular -- 9.6. A Glimpse at More Advanced Topics -- 9.7. Quick Check Solutions -- 9.8. Chapter Review -- 10. Graphs -- 10.1. Terminology -- 10.2. Connectivity and Adjacency -- 10.3. Euler and Hamilton -- 10.4. Representation and Isomorphism -- 10.5. The Big Theorems: Planarity, Euler, Polyhedra, Chromatic Number -- 10.6. Directed Graphs and Weighted Graphs -- 10.7. Quick Check Solutions -- 10.8. Chapter Review -- 11. Trees -- 11.1. Terminology, Counting -- 11.2. Traversal, Searching, and Sorting -- 11.3. More Applications of Trees -- 11.4. Spanning Trees -- 11.5. Quick Check Solutions -- 11.6. Chapter Review -- 12. Functions, Relations, Databases, and Circuits -- 12.1. Functions and Relations -- 12.2. Equivalence Relations, Partially Ordered Sets -- 12.3. n-ary Relations and Relational Databases -- 12.4. Boolean Functions and Boolean Expressions -- 12.5. Combinatorial Circuits -- 12.6. Quick Check Solutions -- 12.7. Chapter Review -- A. Number Systems -- A.1. The Natural Numbers -- A.2. The Integers -- A.3. The Rational Numbers -- A.4. The Real Numbers -- A.5. The Complex Numbers -- A.6. Other Number Systems -- A.7. Representation of Numbers -- B. Summation Notation -- C. Logic Puzzles and Analyzing Claims -- C.1. Logic Puzzles -- C.2. Analyzing Claims -- C.3. Quick Check Solutions -- D. The Golden Ratio -- E. Matrices -- F. The Greek Alphabet -- G. Writing Mathematics -- H. Solutions to Selected Exercises -- H.1. Introduction -- H.2. Sets, Logic, and Boolean Algebras -- H.3. Proof -- H.4. Algorithms -- H.5. Counting -- H.6. Finite Probability Theory -- H.7. Recursion -- H.8. Combinatorics -- H.9. Formal Models in Computer Science -- H.10. Graphs -- H.11. Trees -- H.12. Functions, Relations, Databases, and Circuits -- H.13. Appendices.

"Discrete mathematics has become increasingly popular in recent years due to its growing applications in the field of computer science. Discrete Mathematics with Proof, Second Edition continues to facilitate an up-to-date understanding of this important topic, exposing readers to a wide range of modern and technological applications."--Publisher's website.

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