Discrete Mathematics: Essentials and Applications offers a comprehensive survey of the area, particularly concentrating on the basic principles and applications of Discrete Mathematics. This up-to-date text provides proofs of significance, keeping the focus on numerous relevant examples and many pertinent applications. Written in a simple and clear tone, the title features insightful descriptions and intuitive explanations of all complex concepts and ensures a thorough understanding of the subject matter.
1. Discrete Mathematics - p. ii 2. Cover - p. ii 3. Title Page - p. ii 4. Copyright - p. iv 5. Table of Contents - p. iv 6. Dedication - p. v 7. Preface - p. vii 8. Acknowledgments - p. ix 9. Chapter 1 Propositional Logic - p. 1 10. Chapter 2 Predicate Logic - p. 21 11. Chapter 3 Rules of Inference - p. 37 12. Chapter 4 Proof Methods - p. 55 13. Chapter 5 Sets - p. 67 14. 5.1: Definitions and Notation - p. 68 15. 5.2: Set Operations - p. 73 16. 5.3: Set Identities and Methods of Proof - p. 77 17. 5.4: Cardinality of Sets - p. 80 18. 5.5: Computer Representation of Sets - p. 84 19. 5.6: Multisets - p. 85 20. 5.7: Fuzzy Sets - p. 87 21. 5.8: Paradoxes in Set Theory - p. 88 22. Chapter 6 Matrices - p. 93 23. Chapter 7 Functions - p. 113 24. Chapter 8 Boolean Algebra - p. 131 25. Chapter 9 Relations - p. 155 26. 9.1: Relations on Sets - p. 156 27. 9.2: Properties of Relations - p. 156 28. 9.3: Representations of Relations - p. 160 29. 9.4: Operations on Relations - p. 165 30. 9.5: Closure Properties - p. 167 31. 9.6: Equivalence Relations - p. 169 32. 9.7: Partial Orderings - p. 171 33. 9.8: Relational Databases - p. 172 34. Chapter 10 Number Theory - p. 177 35. Chapter 11 Cryptography - p. 197 36. Chapter 12 Algorithms - p. 211 37. Chapter 13 Induction - p. 231 38. Chapter 14 Recursion - p. 249 39. Chapter 15 Counting Methods - p. 271 40. Chapter 16 Discrete Probability - p. 285 41. Chapter 17 Discrete Random Variables - p. 307 42. Chapter 18 Graphs - p. 327 43. Chapter 19 Trees - p. 351 44. Chapter 20 Finite-State Machines - p. 373 45. List of Symbols - p. 389 46. Bibliography - p. 407 47. Answers/Hints to Exercises - p. 409 48. Index - p. 441
Discrete Mathematics: Essentials and Applications offers a comprehensive survey of the area, particularly concentrating on the basic principles and applications of Discrete Mathematics. This up-to-date text provides proofs of significance, keeping the focus on numerous relevant examples and many pertinent applications. Written in a simple and clear tone, the title features insightful descriptions and intuitive explanations of all complex concepts and ensures a thorough understanding of the subject matter.
1. Discrete Mathematics - p. ii 2. Cover - p. ii 3. Title Page - p. ii 4. Copyright - p. iv 5. Table of Contents - p. iv 6. Dedication - p. v 7. Preface - p. vii 8. Acknowledgments - p. ix 9. Chapter 1 Propositional Logic - p. 1 10. Chapter 2 Predicate Logic - p. 21 11. Chapter 3 Rules of Inference - p. 37 12. Chapter 4 Proof Methods - p. 55 13. Chapter 5 Sets - p. 67 14. 5.1: Definitions and Notation - p. 68 15. 5.2: Set Operations - p. 73 16. 5.3: Set Identities and Methods of Proof - p. 77 17. 5.4: Cardinality of Sets - p. 80 18. 5.5: Computer Representation of Sets - p. 84 19. 5.6: Multisets - p. 85 20. 5.7: Fuzzy Sets - p. 87 21. 5.8: Paradoxes in Set Theory - p. 88 22. Chapter 6 Matrices - p. 93 23. Chapter 7 Functions - p. 113 24. Chapter 8 Boolean Algebra - p. 131 25. Chapter 9 Relations - p. 155 26. 9.1: Relations on Sets - p. 156 27. 9.2: Properties of Relations - p. 156 28. 9.3: Representations of Relations - p. 160 29. 9.4: Operations on Relations - p. 165 30. 9.5: Closure Properties - p. 167 31. 9.6: Equivalence Relations - p. 169 32. 9.7: Partial Orderings - p. 171 33. 9.8: Relational Databases - p. 172 34. Chapter 10 Number Theory - p. 177 35. Chapter 11 Cryptography - p. 197 36. Chapter 12 Algorithms - p. 211 37. Chapter 13 Induction - p. 231 38. Chapter 14 Recursion - p. 249 39. Chapter 15 Counting Methods - p. 271 40. Chapter 16 Discrete Probability - p. 285 41. Chapter 17 Discrete Random Variables - p. 307 42. Chapter 18 Graphs - p. 327 43. Chapter 19 Trees - p. 351 44. Chapter 20 Finite-State Machines - p. 373 45. List of Symbols - p. 389 46. Bibliography - p. 407 47. Answers/Hints to Exercises - p. 409 48. Index - p. 441
