2. Edition - July 2009
115.- Euro
2009. 928 Pages, Hardcover
ISBN-10: 0-470-45793-7
ISBN-13: 978-0-470-45793-1 - John Wiley & Sons






Sample Chapter

Short description
This new edition exposes readers to a wide range of modern and technological applications, emphasizes proof throughout, and provides ample opportunities for practicing the presented concepts through homework exercises and worked examples. Providing examples that are not present in most discrete mathematics books, this second edition covers the deferred acceptance algorithm, the Boyer-Moore algorithm for pattern matching, Sierpinski curves, Persian rugs, adaptive quadrature, the Josephus problem, the five color theorem, and relational databases.

From the contents
Preface.

Acknowledgements.

To The Student.

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; Inclusion-Exclusion.

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-? 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; Finite Projective Planes.

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 A42.

E. Matrices A45.

F. The Greek Alphabet A51.

G. Writing Mathematics A54.

H. Solutions to Selected Exercises A57.

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.

Bibliography.

Index.