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Solution Manual for Discrete Mathematics for Computer Scientists Cliff L Stein, Robert Drysdale, Kenneth Bogart

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Product details:

  • ISBN-10 ‏ : ‎ 0132122715
  • ISBN-13 ‏ : ‎ 978-0132122719
  • Author: Clifford Stein

Stein/Drysdale/Bogart’s Discrete Mathematics for Computer Scientists is ideal for computer science students taking the discrete math course.

Written specifically for computer science students, this unique textbook directly addresses their needs by providing a foundation in discrete math while using motivating, relevant CS applications. This text takes an active-learning approach where activities are presented as exercises and the material is then fleshed out through explanations and extensions of the exercises.

Table contents:

  1. CHAPTER 1 Counting
  2. 1.1 Basic Counting
  3. The Sum Principle
  4. Abstraction
  5. Summing Consecutive Integers
  6. The Product Principle
  7. Two-Element Subsets
  8. Important Concepts, Formulas, and Theorems
  9. Problems
  10. 1.2 Counting Lists, Permutations, and Subsets
  11. Using the Sum and Product Principles
  12. Lists and Functions
  13. The Bijection Principle
  14. k-Element Permutations of a Set
  15. Counting Subsets of a Set
  16. Important Concepts, Formulas, and Theorems
  17. Problems
  18. 1.3 Binomial Coeficients
  19. Pascal’s Triangle
  20. A Proof Using the Sum Principle
  21. The Binomial Theorem
  22. Labeling and Trinomial Coeficients
  23. Important Concepts, Formulas, and Theorems
  24. Problems
  25. 1.4 Relations
  26. What Is a Relation?
  27. Functions as Relations
  28. Properties of Relations
  29. Equivalence Relations
  30. Partial and Total Orders
  31. Important Concepts, Formulas, and Theorems
  32. Problems
  33. 1.5 Using Equivalence Relations in Counting
  34. The Symmetry Principle
  35. Equivalence Relations
  36. The Quotient Principle
  37. Equivalence Class Counting
  38. Multisets
  39. The Bookcase Arrangement Problem
  40. The Number of k-Element Multisets of an n-Element Set
  41. Using the Quotient Principle to Explain a Quotient
  42. Important Concepts, Formulas, and Theorems
  43. Problems
  44. CHAPTER 2 Cryptography and Number Theory
  45. 2.1 Cryptography and Modular Arithmetic
  46. Introduction to Cryptography
  47. Private-Key Cryptography
  48. Public-Key Cryptosystems
  49. Arithmetic Modulo n
  50. Cryptography Using Addition mod n
  51. Cryptography Using Multiplication mod n
  52. Important Concepts, Formulas, and Theorems
  53. Problems
  54. 2.2 Inverses and Greatest Common Divisors
  55. Solutions to Equations and Inverses mod n
  56. Inverses mod n
  57. Converting Modular Equations to Normal Equations
  58. Greatest Common Divisors
  59. Euclid’s Division Theorem
  60. Euclid’s GCD Algorithm
  61. Extended GCD Algorithm
  62. Computing Inverses
  63. Important Concepts, Formulas, and Theorems
  64. Problems
  65. 2.3 The RSA Cryptosystem
  66. Exponentiation mod n
  67. The Rules of Exponents
  68. Fermat’s Little Theorem
  69. The RSA Cryptosystem
  70. The Chinese Remainder Theorem
  71. Important Concepts, Formulas, and Theorems
  72. Problems
  73. 2.4 Details of the RSA Cryptosystem
  74. Practical Aspects of Exponentiation mod n
  75. How Long Does It Take to Use the RSA Algorithm?
  76. How Hard Is Factoring?
  77. Finding Large Primes
  78. Important Concepts, Formulas, and Theorems
  79. Problems
  80. CHAPTER 3 Reflections on Logic and Proof
  81. 3.1 Equivalence and Implication
  82. Equivalence of Statements
  83. Truth Tables
  84. DeMorgan’s Laws
  85. Implication
  86. If and Only If
  87. Important Concepts, Formulas, and Theorems
  88. Problems
  89. 3.2 Variables and Quantifiers
  90. Variables and Universes
  91. Quantifiers
  92. Standard Notation for Quantification
  93. Statements about Variables
  94. Rewriting Statements to Encompass Larger Universes
  95. Proving Quantified Statements True or False
  96. Negation of Quantified Statements
  97. Implicit Quantification
  98. Proof of Quantified Statements
  99. Important Concepts, Formulas, and Theorems
  100. Problems
  101. 3.3 Inference
  102. Direct Inference (Modus Ponens) and Proofs
  103. Rules of Inference for Direct Proofs
  104. Contrapositive Rule of Inference
  105. Proof by Contradiction
  106. Important Concepts, Formulas, and Theorems
  107. Problems
  108. CHAPTER 4 Induction, Recursion, and Recurrences
  109. 4.1 Mathematical Induction
  110. Smallest Counterexamples
  111. The Principle of Mathematical Induction
  112. Strong Induction
  113. Induction in General
  114. A Recursive View of Induction
  115. Structural Induction
  116. Important Concepts, Formulas, and Theorems
  117. Problems
  118. 4.2 Recursion, Recurrences, and Induction
  119. Recursion
  120. Examples of First-Order Linear Recurrences
  121. Iterating a Recurrence
  122. Geometric Series
  123. First-Order Linear Recurrences
  124. Important Concepts, Formulas, and Theorems
  125. Problems
  126. 4.3 Growth Rates of Solutions to Recurrences
  127. Divide and Conquer Algorithms
  128. Recursion Trees
  129. Three Different Behaviors
  130. Important Concepts, Formulas, and Theorems
  131. Problems
  132. 4.4 The Master Theorem
  133. Master Theorem
  134. Solving More General Kinds of Recurrences
  135. Extending the Master Theorem
  136. Important Concepts, Formulas, and Theorems
  137. Problems
  138. 4.5 More General Kinds of Recurrences
  139. Recurrence Inequalities
  140. The Master Theorem for Inequalities
  141. A Wrinkle with Induction
  142. Further Wrinkles in Induction Proofs
  143. Dealing with Functions Other Than n[sup(c)]
  144. Important Concepts, Formulas, and Theorems
  145. Problems
  146. 4.6 Recurrences and Selection
  147. The Idea of Selection
  148. A Recursive Selection Algorithm
  149. Selection without Knowing the Median in Advance
  150. An Algorithm to Find an Element in the Middle Half
  151. An Analysis of the Revised Selection Algorithm
  152. Uneven Divisions
  153. Important Concepts, Formulas, and Theorems
  154. Problems
  155. CHAPTER 5 Probability
  156. 5.1 Introduction to Probability
  157. Why Study Probability?
  158. Some Examples of Probability Computations
  159. Complementary Probabilities
  160. Probability and Hashing
  161. The Uniform Probability Distribution
  162. Important Concepts, Formulas, and Theorems
  163. Problems
  164. 5.2 Unions and Intersections
  165. The Probability of a Union of Events
  166. Principle of Inclusion and Exclusion for Probability
  167. The Principle of Inclusion and Exclusion for Counting
  168. Important Concepts, Formulas, and Theorems
  169. Problems
  170. 5.3 Conditional Probability and Independence
  171. Conditional Probability
  172. Bayes’ Theorem
  173. Independence
  174. Independent Trials Processes
  175. Tree Diagrams
  176. Primality Testing
  177. Important Concepts, Formulas, and Theorems
  178. Problems
  179. 5.4 Random Variables
  180. What Are Random Variables?
  181. Binomial Probabilities
  182. A Taste of Generating Functions
  183. Expected Value
  184. Expected Values of Sums and Numerical Multiples
  185. Indicator Random Variables
  186. The Number of Trials until the First Success
  187. Important Concepts, Formulas, and Theorems
  188. Problems
  189. 5.5 Probability Calculations in Hashing
  190. Expected Number of Items per Location
  191. Expected Number of Empty Locations
  192. Expected Number of Collisions
  193. Expected Maximum Number of Elements in a Location of a Hash Table
  194. Important Concepts, Formulas, and Theorems
  195. Problems
  196. 5.6 Conditional Expectations, Recurrences, and Algorithms
  197. When Running Times Depend on More than Size of Inputs
  198. Conditional Expected Values
  199. Randomized Algorithms
  200. Selection Revisited
  201. QuickSort
  202. A More Careful Analysis of RandomSelect
  203. Important Concepts, Formulas, and Theorems
  204. Problems
  205. 5.7 Probability Distributions and Variance
  206. Distributions of Random Variables
  207. Variance
  208. Important Concepts, Formulas, and Theorems
  209. Problems
  210. CHAPTER 6 Graphs
  211. 6.1 Graphs
  212. The Degree of a Vertex
  213. Connectivity
  214. Cycles
  215. Trees
  216. Other Properties of Trees
  217. Important Concepts, Formulas, and Theorems
  218. Problems
  219. 6.2 Spanning Trees and Rooted Trees
  220. Spanning Trees
  221. Breadth-First Search
  222. Rooted Trees
  223. Important Concepts, Formulas, and Theorems
  224. Problems
  225. 6.3 Eulerian and Hamiltonian Graphs
  226. Eulerian Tours and Trails
  227. Finding Eulerian Tours
  228. Hamiltonian Paths and Cycles
  229. NP-Complete Problems
  230. Proving That Problems Are NP-Complete
  231. Important Concepts, Formulas, and Theorems
  232. Problems
  233. 6.4 Matching Theory
  234. The Idea of a Matching
  235. Making Matchings Bigger
  236. Matching in Bipartite Graphs
  237. Searching for Augmenting Paths in Bipartite Graphs
  238. The Augmentation-Cover Algorithm
  239. Efficient Algorithms
  240. Important Concepts, Formulas, and Theorems
  241. Problems
  242. 6.5 Coloring and Planarity
  243. The Idea of Coloring
  244. Interval Graphs
  245. Planarity
  246. The Faces of a Planar Drawing
  247. The Five-Color Theorem
  248. Important Concepts, Formulas, and Theorems
  249. Problems
  250. APPENDIX A: Derivation of the More General Master Theorem
  251. More General Recurrences
  252. Recurrences for General n
  253. Removing Floors and Ceilings
  254. Floors and Ceilings in the Stronger Version of the Master Theorem
  255. Proofs of Theorems
  256. Important Concepts, Formulas, and Theorems
  257. Problems
  258. APPENDIX B: Answers and Hints to Selected Problems
  259. Bibliography
  260. Index

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