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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 | |