CHAPTER 5 Induction and Recursion 115 51 Mathematical Induction 115 52 Strong

Chapter 5 induction and recursion 115 51 mathematical

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CHAPTER 5Induction and Recursion1155.1Mathematical Induction1155.2Strong Induction and Well-Ordering1245.3Recursive Definitions and Structural Induction1305.4Recursive Algorithms1365.5Program Correctness140Supplementary Exercises for Chapter 5141CHAPTER 6Counting1526.1The Basics of Counting1526.2The Pigeonhole Principle1586.3Permutations and Combinations1616.4Binomial Coefficients and Identities1646.5Generalized Permutations and Combinations1676.6Generating Permutations and Combinations172Supplementary Exercises for Chapter 6173CHAPTER 7Discrete Probability1787.1An Introduction to Discrete Probability1787.2Probability Theory1807.3Bayes’ Theorem1857.4Expected Value and Variance187Supplementary Exercises for Chapter 7192CHAPTER 8Advanced Counting Techniques1968.1Applications of Recurrence Relations1968.2Solving Linear Recurrence Relations2038.3Divide-and-Conquer Algorithmsand Recurrence Relations2098.4Generating Functions2138.5Inclusion–Exclusion2248.6Applications of Inclusion–Exclusion226Supplementary Exercises for Chapter 8227CHAPTER 9Relations2319.1Relations and Their Properties2319.2n-ary Relations and Their Applications2369.3Representing Relations2389.4Closures of Relations2419.5Equivalence Relations2449.6Partial Orderings

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