Mathematics Sampler (eBook)

William P. Berlinghoff is visiting professor of mathematics at Colby College. Kerry E. Grant is professor of mathematics at Southern Connecticut State University. Dale Skrien is professor of computer science at Colby College

Chapter 1 PrefaceChapter 2 To the StudentPart 3 Chapter 1: Problems and SolutionsChapter 4 What Is Mathematics?Chapter 5 Problem SolvingChapter 6 It All Adds UpChapter 7 The Mathematical Way of ThinkingChapter 8 Topics for PapersChapter 9 For Further ReadingPart 10 Chapter 2: Mathematics of Patterns: Number TheoryChapter 11 What Is Number Theory?Chapter 12 DivisibilityChapter 13 Counting DivisorsChapter 14 Summing DivisorsChapter 15 Proper DivisorsChapter 16 Even Perfect NumbersChapter 17 Mersenne PrimesChapter 18 LINK: Number Theory and CryptographyChapter 19 Topics for PapersChapter 20 For Further ReadingPart 21 Chapter 3: Mathematics of Axiom Systems: GeometriesChapter 22 What is Geometry?Chapter 23 Euclidean GeometryChapter 24 Euclid and Parallel LinesChapter 25 Axiom Systems and ModelsChapter 26 Consistency and IndependenceChapter 27 Non-Euclidean GeometriesChapter 28 Axiomatic Geometry and the Real WorldChapter 29 LINK: Axiom Systems and SocietyChapter 30 Topics for PapersChapter 31 For Further ReadingPart 32 Chapter 4: Mathematics of Chance: Probability and StatisticsChapter 33 The GamblersChapter 34 The Language of SetsChapter 35 What Is Probability?Chapter 36 Counting ProcessesChapter 37 LINK: Counting and the Genetic CodeChapter 38 Some Basic Rules of ProbabilityChapter 39 Conditional ProbabilityChapter 40 LINK: Probability and MarketingChapter 41 What Is Statistics?Chapter 42 Central Tendency and SpreadChapter 43 DistributionsChapter 44 Generalization and PredictionChapter 45 LINK: Statistics in the Psychology of LearningChapter 46 Topics for PapersChapter 47 For Further ReadingPart 48 Chapter 5: Mathematics of Infinity: Cantor's Theory of SetsChapter 49 What Is Set Theory?Chapter 50 Infinite SetsChapter 51 The SIze of NChapter 52 Rational and Irrational NumbersChapter 53 A Different SizeChapter 54 Cardinal NumbersChapter 55 Cantor's TheoremChapter 56 The Continuum HypothesisChapter 57 The Foundations of MathematicsChapter 58 LINK: Set Theory and MetaphysicsChapter 59 Topics for PapersChapter 60 For Further ReadingPart 61 Chapter 6: Mathematics of Symmetry: Finite GroupsChapter 62 What Is Group Theory?Chapter 63 OperationsChapter 64 Some Properties of OperationsChapter 65 The Definition of a GroupChapter 66 Some Basic Properties of GroupsChapter 67 SubgroupsChapter 68 Lagrange's TheoremChapter 69 Lagrange's Theorem Proved [Optional]Chapter 70 Groups of SymmetriesChapter 71 LINK: Groups in Music and in ChemistryChapter 72 Topics for PapersChapter 73 For Further ReadingPart 74 Chapter 7: Mathematics of Space and Time: Four-Dimensional GeometryChapter 75 What Is Four-Dimensional Geometry?Chapter 76 One-Dimensional SpaceChapter 77 Two-Dimensional SpaceChapter 78 Three-Dimensional SpaceChapter 79 Four-Dimensional SpaceChapter 80 Cross SectionsChapter 81 Cylinders and Cones [Optional]Chapter 82 LINK: 4-Space in Fiction and in ArtChapter 83 Topics for PapersChapter 84 For Further ReadingPart 85 Chapter 8: Mathematics of Connection : Graph TheoryChapter 86 What Is Graph Theory?Chapter 87 Some Basic TermsChapter 88 Edge PathsChapter 89 Vertex PathsChapter 90 Crossing CurvesChapter 91 Euler's FormulaChapter 92 Looking BackChapter 93 LINK: Diagraphs and Project ManagementChapter 94 Topics for PapersChapter 95 For Further ReadingPart 96 Chapter 9: Mathematics of Machines: Computer AlgorithmsChapter 97 What Is a Computer?Chapter 98 The Traveling Salesman ProblemChapter 99 The Speed of a ComputerChapter 100 Algorithms and SortingChapter 101 Comparing AlgorithmsChapter 102 Complexity AnalysisChapter 103 NP-CompletenessChapter 104 Implications of NP-CompletenessChapter 105 LINK: Algorithms, Abstraction, and Strategic PlanningChapter 106 Topics for PapersChapter 107 For Further ReadingPart 108 APPENDICESPart 109 Appendix A: Basic LogicChapter 110 Statements and Their NegationsChapter 111 Conjunctions and DisjunctionsChapter 112 Conditionals and DeductionChapter 113 Topics for PapersChapter 114 For Further ReadingPart 115 Appendix B: A Brief History of MathematicsChapter 116 Preliminary ThoughtsChapter 117 From the Beginning to 600 B.C.Chapter 118 600 B.C. to A.D. 400Chapter 119 400 to 1400Chapter 123 The Fifteenth and Sixteenth CenturiesChapter 124 The Seventeenth CenturyChapter 125 The Eighteenth CenturyChapter 126 The Nineteenth CenturyChapter 127 The Twentieth CenturyChapter 128 Topics for PapersChapter 129 For Further ReadingPart 130 Appendix C: Literacy in the Language of Mathematics