Combinatorics: An Introduction

Preface xiii1 Logic 11.1 Formal Logic 11.2 Basic Logical Strategies 61.3 The Direct Argument 101.4 More Argument Forms 121.5 Proof By Contradiction 151.6 Exercises 232 Sets 252.1 Set Notation 252.2 Predicates 262.3 Subsets 282.4 Union and Intersection 302.5 Exercises 323 Venn Diagrams 353.1 Inclusion/Exclusion Principle 353.2 Two Circle Venn Diagrams 373.3 Three Square Venn Diagrams 423.4 Exercises 504 Multiplication Principle 554.1 What is the Principle? 554.2 Exercises 605 Permutations 635.1 Some Special Numbers 645.2 Permutations Problems 655.3 Exercises 686 Combinations 696.1 Some Special Numbers 696.2 Combination Problems 706.3 Exercises 747 Problems Combining Techniques 777.1 Significant Order 777.2 Order Not Significant 787.3 Exercises 838 Arrangement Problems 858.1 Examples of Arrangements 868.2 Exercises 919 At Least, At Most, and Or 939.1 Counting With Or 939.2 At Least, At Most 989.3 Exercises 10210 Complement Counting 10310.1 The Complement Formula 10310.2 A New View of ?At Least? 10510.3 Exercises 10911 Advanced Permutations 11111.1 Venn Diagrams and Permutations 11111.2 Exercises 12012 Advanced Combinations 12512.1 Venn Diagrams and Combinations 12512.2 Exercises 13113 Poker and Counting 13313.1 Warm Up Problems 13313.2 Poker Hands 13513.3 Jacks or Better 14113.4 Exercises 14314 Advanced Counting 14514.1 Indistinguishable Objects 14514.2 Circular Permutations 14814.3 Bracelets 15114.4 Exercises 15515 Algebra and Counting 15715.1 The Binomial Theorem 15715.2 Identities 16015.3 Exercises 16516 Derangements 16716.1 Fixed Point Theorems 16816.2 His Own Coat 17316.3 Exercises 17417 Probability Vocabulary 17517.1 Vocabulary 17518 Equally Likely Outcomes 18118.1 Exercises 18819 Probability Trees 18919.1 Tree Diagrams 18919.2 Exercises 19820 Independent Events 19920.1 Independence 19920.2 Logical Consequences of Influence 20220.3 Exercises 20621 Sequences and Probability 20921.1 Sequences of Events 20921.2 Exercises 21522 Conditional Probability 21722.1 What Does Conditional Mean? 21722.2 Exercises 22323 Bayes? Theorem 22523.1 The Theorem 22523.2 Exercises 23024 Statistics 23124.1 Introduction 23124.2 Probability is not Statistics 23124.3 Conversational Probability 23224.4 Conditional Statistics 23924.5 The Mean 24124.6 Median 24224.7 Randomness 24425 Linear Programming 24925.1 Continuous Variables 24925.2 Discrete Variables 25425.3 Incorrectly Applied Rules 25826 Subjective Truth 261Bibliography 267Index 269