| |
| |
Prologue--Why Math? An Historical Overview | |
| |
| |
| |
The Nature Of Problem Solving | |
| |
| |
Problem Solving | |
| |
| |
Inductive and Deductive Reasoning | |
| |
| |
Scientific Notation and Estimation | |
| |
| |
Finite and Infinite | |
| |
| |
| |
The Nature Of Numeration Systems | |
| |
| |
Early Numeration Systems | |
| |
| |
Hindu-Arabic Numeration Systems | |
| |
| |
Different Numeration Systems | |
| |
| |
Binary Numeration Systems | |
| |
| |
History of Calculating Devices | |
| |
| |
| |
The Nature Of Numbers | |
| |
| |
Natural Numbers | |
| |
| |
Prime Numbers | |
| |
| |
Integers | |
| |
| |
Rational Numbers | |
| |
| |
Irrational Numbers | |
| |
| |
Groups, Fields, and Real Numbers | |
| |
| |
Discrete Mathematics | |
| |
| |
Cryptography | |
| |
| |
| |
The Nature Of Algebra | |
| |
| |
Polynomials | |
| |
| |
Factoring | |
| |
| |
Evaluation, Applications, and Spreadsheets | |
| |
| |
Equations | |
| |
| |
Inequalities | |
| |
| |
Algebra in Problem Solving | |
| |
| |
Ratios, Proportions, and Problem Solving | |
| |
| |
Percents | |
| |
| |
Modeling Uncategorized Problems | |
| |
| |
| |
The Nature Of Growth | |
| |
| |
Logarithms and Exponents | |
| |
| |
Exponential Equations | |
| |
| |
Logarithmic Equations | |
| |
| |
Applications of Growth and Decay | |
| |
| |
| |
The Nature Of Sequences, Series And Financial Management | |
| |
| |
Interest | |
| |
| |
Installment Buying | |
| |
| |
Sequences | |
| |
| |
Series | |
| |
| |
Annuities | |
| |
| |
Amortization | |
| |
| |
Summary of Financial Formulas | |
| |
| |
| |
The Nature Of Graphs And Functions | |
| |
| |
Cartesian Coordinates and Graphing Lines | |
| |
| |
Graphing Half-Planes | |
| |
| |
Graphing Curves | |
| |
| |
Conic Sections | |
| |
| |
Functions | |
| |
| |
| |
The Nature Of Mathematical Systems | |
| |
| |
Systems of Linear Equations | |
| |
| |
Problem Solving with Systems | |
| |
| |
Matrix Solution of a System of Equations | |
| |
| |
Inverse Matrices | |
| |
| |
Systems of Inequalities | |
| |
| |
Modeling with Linear Programming | |
| |
| |
| |
The Nature Of Networks And Graph Theory | |
| |
| |
Euler Circuits and Hamiltonian Cycles | |
| |
| |
Trees and Minimum Spanning Trees | |
| |
| |
Topology and Fractals | |
| |
| |
Guest Essay: Chaos | |
| |
| |
| |
The Nature Of Voting And Apportionment | |
| |
| |
Voting | |
| |
| |
Voting Dilemmas | |
| |
| |
Apportionment | |
| |
| |
Apportionment Flaws | |
| |
| |
Epilogue--Why Not Math? Mathematics In The Natural Sciences, Social Sciences, And In The Humanities | |
| |
| |
Appendices | |
| |
| |
| |
Glossary | |
| |
| |
| |
Selected Answers | |
| |
| |
| |
Credits | |
| |
| |
| |
Index | |