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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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