{"product_id":"combinatorics-9781118404362","title":"Combinatorics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eBridges combinatorics and probability and uniquely includes detailed formulas and proofs to promote mathematical thinking\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003ci\u003eCombinatorics: An Introduction\u003c\/i\u003e introduces readers to counting combinatorics, offers examples that feature unique approaches and ideas, and presents case-by-case methods for solving problems.\u003c\/p\u003e \u003cp\u003eDetailing how combinatorial problems arise in many areas of pure mathematics, most notably in algebra, probability theory, topology, and geometry, this book provides discussion on logic and paradoxes; sets and set notations; power sets and their cardinality; Venn diagrams; the multiplication principal; and permutations, combinations, and problems combining the multiplication principal. Additional features of this enlightening introduction include:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eWorked examples, proofs, and exercises in every chapter\u003c\/li\u003e \u003cli\u003eDetailed explanations of formulas to promote fundamental understanding\u003c\/li\u003e \u003cli\u003ePromotion of mathematical thinking by examinin\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface xiii\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Logic 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Formal Logic 1\u003c\/p\u003e \u003cp\u003e1.2 Basic Logical Strategies 6\u003c\/p\u003e \u003cp\u003e1.3 The Direct Argument 10\u003c\/p\u003e \u003cp\u003e1.4 More Argument Forms 12\u003c\/p\u003e \u003cp\u003e1.5 Proof By Contradiction 15\u003c\/p\u003e \u003cp\u003e1.6 Exercises 23\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Sets 25\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Set Notation 25\u003c\/p\u003e \u003cp\u003e2.2 Predicates 26\u003c\/p\u003e \u003cp\u003e2.3 Subsets 28\u003c\/p\u003e \u003cp\u003e2.4 Union and Intersection 30\u003c\/p\u003e \u003cp\u003e2.5 Exercises 32\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Venn Diagrams 35\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Inclusion\/Exclusion Principle 35\u003c\/p\u003e \u003cp\u003e3.2 Two Circle Venn Diagrams 37\u003c\/p\u003e \u003cp\u003e3.3 Three Square Venn Diagrams 42\u003c\/p\u003e \u003cp\u003e3.4 Exercises 50\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Multiplication Principle 55\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 What is the Principle? 55\u003c\/p\u003e \u003cp\u003e4.2 Exercises 60\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Permutations 63\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Some Special Numbers 64\u003c\/p\u003e \u003cp\u003e5.2 Permutations Problems 65\u003c\/p\u003e \u003cp\u003e5.3 Exercises 68\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Combinations 69\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Some Special Numbers 69\u003c\/p\u003e \u003cp\u003e6.2 Combination Problems 70\u003c\/p\u003e \u003cp\u003e6.3 Exercises 74\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Problems Combining Techniques 77\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Significant Order 77\u003c\/p\u003e \u003cp\u003e7.2 Order Not Significant 78\u003c\/p\u003e \u003cp\u003e7.3 Exercises 83\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Arrangement Problems 85\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Examples of Arrangements 86\u003c\/p\u003e \u003cp\u003e8.2 Exercises 91\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 At Least, At Most, and Or 93\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Counting With Or 93\u003c\/p\u003e \u003cp\u003e9.2 At Least, At Most 98\u003c\/p\u003e \u003cp\u003e9.3 Exercises 102\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Complement Counting 103\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 The Complement Formula 103\u003c\/p\u003e \u003cp\u003e10.2 A New View of ?At Least? 105\u003c\/p\u003e \u003cp\u003e10.3 Exercises 109\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Advanced Permutations 111\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Venn Diagrams and Permutations 111\u003c\/p\u003e \u003cp\u003e11.2 Exercises 120\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Advanced Combinations 125\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Venn Diagrams and Combinations 125\u003c\/p\u003e \u003cp\u003e12.2 Exercises 131\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Poker and Counting 133\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Warm Up Problems 133\u003c\/p\u003e \u003cp\u003e13.2 Poker Hands 135\u003c\/p\u003e \u003cp\u003e13.3 Jacks or Better 141\u003c\/p\u003e \u003cp\u003e13.4 Exercises 143\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Advanced Counting 145\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Indistinguishable Objects 145\u003c\/p\u003e \u003cp\u003e14.2 Circular Permutations 148\u003c\/p\u003e \u003cp\u003e14.3 Bracelets 151\u003c\/p\u003e \u003cp\u003e14.4 Exercises 155\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Algebra and Counting 157\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e15.1 The Binomial Theorem 157\u003c\/p\u003e \u003cp\u003e15.2 Identities 160\u003c\/p\u003e \u003cp\u003e15.3 Exercises 165\u003c\/p\u003e \u003cp\u003e\u003cb\u003e16 Derangements 167\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e16.1 Fixed Point Theorems 168\u003c\/p\u003e \u003cp\u003e16.2 His Own Coat 173\u003c\/p\u003e \u003cp\u003e16.3 Exercises 174\u003c\/p\u003e \u003cp\u003e\u003cb\u003e17 Probability Vocabulary 175\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e17.1 Vocabulary 175\u003c\/p\u003e \u003cp\u003e\u003cb\u003e18 Equally Likely Outcomes 181\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e18.1 Exercises 188\u003c\/p\u003e \u003cp\u003e\u003cb\u003e19 Probability Trees 189\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e19.1 Tree Diagrams 189\u003c\/p\u003e \u003cp\u003e19.2 Exercises 198\u003c\/p\u003e \u003cp\u003e\u003cb\u003e20 Independent Events 199\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e20.1 Independence 199\u003c\/p\u003e \u003cp\u003e20.2 Logical Consequences of Influence 202\u003c\/p\u003e \u003cp\u003e20.3 Exercises 206\u003c\/p\u003e \u003cp\u003e\u003cb\u003e21 Sequences and Probability 209\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e21.1 Sequences of Events 209\u003c\/p\u003e \u003cp\u003e21.2 Exercises 215\u003c\/p\u003e \u003cp\u003e\u003cb\u003e22 Conditional Probability 217\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e22.1 What Does Conditional Mean? 217\u003c\/p\u003e \u003cp\u003e22.2 Exercises 223\u003c\/p\u003e \u003cp\u003e\u003cb\u003e23 Bayes? Theorem 225\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e23.1 The Theorem 225\u003c\/p\u003e \u003cp\u003e23.2 Exercises 230\u003c\/p\u003e \u003cp\u003e\u003cb\u003e24 Statistics 231\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e24.1 Introduction 231\u003c\/p\u003e \u003cp\u003e24.2 Probability is not Statistics 231\u003c\/p\u003e \u003cp\u003e24.3 Conversational Probability 232\u003c\/p\u003e \u003cp\u003e24.4 Conditional Statistics 239\u003c\/p\u003e \u003cp\u003e24.5 The Mean 241\u003c\/p\u003e \u003cp\u003e24.6 Median 242\u003c\/p\u003e \u003cp\u003e24.7 Randomness 244\u003c\/p\u003e \u003cp\u003e\u003cb\u003e25 Linear Programming 249\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e25.1 Continuous Variables 249\u003c\/p\u003e \u003cp\u003e25.2 Discrete Variables 254\u003c\/p\u003e \u003cp\u003e25.3 Incorrectly Applied Rules 258\u003c\/p\u003e \u003cp\u003e\u003cb\u003e26 Subjective Truth 261\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eBibliography 267\u003c\/p\u003e \u003cp\u003eIndex 269\u003c\/p\u003e\n\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"Wiley-Blackwell","offers":[{"title":"Default Title","offer_id":51039262638423,"sku":"9781118404362","price":74.05,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781118404362.jpg?v=1750943090","url":"https:\/\/bookcurl.com\/products\/combinatorics-9781118404362","provider":"Book Curl","version":"1.0","type":"link"}