Prologue: Why Math? | |

A Historical Overview | |

The Nature Of Problem Solving | |

The Nature of Problem Solving | |

Problem Solving | |

Inductive and Deductive Reasoning | |

Scientific Notation and Estimation | |

Summary | |

The Nature Of Sets | |

Sets, Subsets, and Venn Diagrams | |

Operations with Sets | |

Applications of Sets | |

Finite and Infinite Sets | |

Summary | |

The Nature Of Logic | |

Deductive Reasoning | |

Truth Tables and the Conditional | |

Operators and Laws of Logic | |

The Nature of Proof | |

Problem Solving Using Logic | |

Logic Circuits (Optional) | |

Summary | |

The Nature Of Numeration Systems | |

Early Numeration Systems | |

Hindu-Arabic Numeration System | |

Different Numeration Systems | |

Binary Numeration System | |

History of Calculating Devices (Optional) | |

Summary | |

The Nature Of Numbers | |

Natural Numbers | |

Prime Numbers | |

Integers | |

Rational Numbers | |

Irrational Numbers | |

Groups, Fields, and Real Numbers | |

Discrete Mathematics | |

Cryptography (Optional) | |

Summary | |

The Nature Of Algebra | |

Polynomials | |

Factoring | |

Evaluation, Applications, and Spreadsheets | |

Equations | |

Guest Essay: "Chaos" | |

Inequalities | |

Algebra in Problem Solving | |

Ratios, Proportions, and Problem Solving | |

Percents | |

Modeling Uncategorized Problems | |

Summary | |

The Nature Of Geometry | |

Geometry | |

Polygons and Angles | |

Triangles | |

Similar Triangles | |

Right Triangle Trigonometry (Optional) | |

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

Summary | |

The Nature Of Networks And Graph Theory | |

Euler Circuits and Hamiltonian Cycles | |

Trees and Minimum Spanning Trees | |

Topology and Fractals | |

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

Summary | |

The Nature Of Measurement | |

Perimeter | |

Area | |

Surface Area, Volume and Capacity | |

Miscellaneous Measurements (Optional) | |

U.S.-Metric Conversions | |

Summary | |

The Nature Of Growth | |

Exponential Equations | |

Logarithmic Equations | |

Applications of Growth and Decay | |

Summary | |

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

IntereSt. Installment Buying | |

Sequences | |

Series | |

Annuities | |

Amortization | |

Summary of Financial Formulas | |

Summary | |

The Nature Of Counting | |

Permutations | |

Combinations | |

Counting without Counting | |

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

Summary | |

The Nature Of Probability | |

Introduction to Probability | |

Mathematical Expectation | |

Probability Models | |

Calculated Probabilities | |

The Binomial Distribution (Optional) | |

Guest Essay: "Extrasensory Perception" | |

Summary | |

The Nature Of Statistics | |

Frequency Distributions and Graphs | |

Descriptive Statistics | |

The Normal Curve | |

Correlation and Regression | |

Sampling (Optional) | |

Summary | |

The Nature Of Graphs And Functions | |

Cartesian Coordinates and Graphing Lines | |

Graphing Half-Planes | |

Graphing Curves | |

Conic Sections | |

Functions | |

Summary | |

The Nature Of Mathematical Systems | |

Systems of Linear Equations | |

Problem Solving with Systems | |

Matrix Solution of a System of Equations | |

Inverse Matrices | |

Modeling with Linear Programming (Optional) | |

Summary | |

The Nature Of Voting And Apportionment | |

Voting | |

Voting Dilemmas | |

Apportionment | |

Apportionment Flaws | |

Summary | |

The Nature Of Calculus (Optional) | |

What Is Calculus? | |

Limits | |

Derivatives | |

Integrals | |

Summary | |

Epilogue: Why Not Math? | |

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

Appendices | |

Glossary | |

Selected Answers | |

Index | |

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