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Prologue: Why Math? | |

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A Historical Overview | |

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The Nature Of Problem Solving | |

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The Nature of Problem Solving | |

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Problem Solving | |

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Inductive and Deductive Reasoning | |

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Scientific Notation and Estimation | |

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Summary | |

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The Nature Of Sets | |

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Sets, Subsets, and Venn Diagrams | |

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Operations with Sets | |

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Applications of Sets | |

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Finite and Infinite Sets | |

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Summary | |

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The Nature Of Logic | |

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Deductive Reasoning | |

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Truth Tables and the Conditional | |

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Operators and Laws of Logic | |

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The Nature of Proof | |

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Problem Solving Using Logic | |

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Logic Circuits (Optional) | |

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Summary | |

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The Nature Of Numeration Systems | |

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Early Numeration Systems | |

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Hindu-Arabic Numeration System | |

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Different Numeration Systems | |

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Binary Numeration System | |

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History of Calculating Devices (Optional) | |

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Summary | |

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The Nature Of Numbers | |

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Natural Numbers | |

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Prime Numbers | |

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Integers | |

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Rational Numbers | |

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Irrational Numbers | |

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Groups, Fields, and Real Numbers | |

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Discrete Mathematics | |

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Cryptography (Optional) | |

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Summary | |

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The Nature Of Algebra | |

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Polynomials | |

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Factoring | |

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Evaluation, Applications, and Spreadsheets | |

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Equations | |

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Guest Essay: "Chaos" | |

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Inequalities | |

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Algebra in Problem Solving | |

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Ratios, Proportions, and Problem Solving | |

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Percents | |

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Modeling Uncategorized Problems | |

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Summary | |

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The Nature Of Geometry | |

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Geometry | |

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Polygons and Angles | |

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Triangles | |

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Similar Triangles | |

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Right Triangle Trigonometry (Optional) | |

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Mathematics, Art, and Non-Euclidean Geometries (Optional Sections) | |

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Summary | |

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The Nature Of Networks And Graph Theory | |

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Euler Circuits and Hamiltonian Cycles | |

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Trees and Minimum Spanning Trees | |

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Topology and Fractals | |

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Guest Essay: "What Good Are Fractals?" | |

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Summary | |

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The Nature Of Measurement | |

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Perimeter | |

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Area | |

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Surface Area, Volume and Capacity | |

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Miscellaneous Measurements (Optional) | |

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U.S.-Metric Conversions | |

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Summary | |

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The Nature Of Growth | |

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Exponential Equations | |

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Logarithmic Equations | |

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Applications of Growth and Decay | |

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Summary | |

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The Nature Of Sequences, Series, And Financial Management | |

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IntereSt. Installment Buying | |

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Sequences | |

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Series | |

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Annuities | |

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Amortization | |

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Summary of Financial Formulas | |

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Summary | |

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The Nature Of Counting | |

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Permutations | |

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Combinations | |

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Counting without Counting | |

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Rubik's Cube and Instant Insanity (Optional) | |

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Summary | |

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The Nature Of Probability | |

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Introduction to Probability | |

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Mathematical Expectation | |

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Probability Models | |

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Calculated Probabilities | |

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The Binomial Distribution (Optional) | |

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Guest Essay: "Extrasensory Perception" | |

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Summary | |

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The Nature Of Statistics | |

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Frequency Distributions and Graphs | |

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Descriptive Statistics | |

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The Normal Curve | |

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Correlation and Regression | |

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Sampling (Optional) | |

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Summary | |

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The Nature Of Graphs And Functions | |

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Cartesian Coordinates and Graphing Lines | |

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Graphing Half-Planes | |

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Graphing Curves | |

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Conic Sections | |

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Functions | |

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Summary | |

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The Nature Of Mathematical Systems | |

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Systems of Linear Equations | |

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Problem Solving with Systems | |

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Matrix Solution of a System of Equations | |

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Inverse Matrices | |

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Modeling with Linear Programming (Optional) | |

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Summary | |

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The Nature Of Voting And Apportionment | |

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Voting | |

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Voting Dilemmas | |

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Apportionment | |

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Apportionment Flaws | |

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Summary | |

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The Nature Of Calculus (Optional) | |

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What Is Calculus? | |

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Limits | |

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Derivatives | |

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Integrals | |

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Summary | |

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Epilogue: Why Not Math? | |

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Mathematics in the Natural Sciences, Social Sciences, and in the Humanities | |

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Appendices | |

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Glossary | |

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Selected Answers | |

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Index | |