## Essentials of Discrete MathematicsEssentials of Discrete Mathematics, Second Edition is the ideal text for a one-term discrete mathematics course to serve computer science majors as well as students from a wide range of other disciplines. It introduces students to the mathematical way of thinking, and also to many important modern applications. The material is organized around five types of thinking: logical, relational, recursive, quantitative, and analytical. This presentation results in a coherent outline that steadily builds upon mathematical sophistication. Graphs are introduced early and referred to throughout the text, providing a richer context for examples and applications. Students will encounter algorithms near the end of the text, after they have acquired the skills and experience needed to analyze them. The final chapter contains in-depth case studies from a variety of fields, including biology, sociology, linguistics, economics, and music. Clear and concise, Essentials of Discrete Mathematics presents a unified and complete picture of discrete mathematics that instructors can cover in a single semester. |

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### Contents

Chapter 1 Logical Thinking | 1 |

Chapter 2 Relational Thinking | 65 |

Chapter 3 Recursive Thinking | 149 |

Chapter 4 Quantitative Thinking | 215 |

Chapter 5 Analytical Thinking | 291 |

Chapter 6 Thinking Through Applications | 373 |

Hints Answers and Solutions to Selected Exercises | 431 |

Selected References | 475 |

479 | |

487 | |

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### Common terms and phrases

actors array Axiom binary search tree binary tree bubble sort calculation called closed-form solution color comparisons Compute connected Consider the following contains count the number decision tree digits domain elements equation equivalence classes equivalence relation Euler Euler path Example Exercise Explain Figure Find following algorithm following recurrence relation following statement formula fractal function f Give given Hasse diagram inductive hypothesis inductive step integers language line map log2 logically equivalent loop invariant mathematical merge sort natural numbers negation nodes notation number of edges one-to-one correspondence pair partial ordering path poset possible Postconditions Preconditions predicate logic problem Proof Induction proof sequence Prove pseudocode real numbers recurrence relation recursive definition represent sentence signed graph simple SList social network string subset Suppose as inductive symbols Theorem tone row total number true truth table undirected graph variables vertex vertices words Write