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1. LOGIC | |
Deductive vs | |
Inductive Reasoning | |
Symbolic Logic | |
Truth Tables | |
More on Conditionals | |
Analyzing Arguments | |
2. SETS AND COUNTING | |
Sets and Sets Operations | |
Applications of Venn Diagrams | |
Introduction to Combinatronics | |
Permutations and Combinations | |
Voting Systems | |
Infinite Sets | |
3. PROBABILITY | |
History of Probability | |
Basic Terms of Probability | |
Basic Rules of Probability | |
Combinatronics and Probability | |
Expected Value | |
Conditional Probability | |
Independence; Trees in Genetics | |
4. STATISTICS | |
Population, Sample, and Data | |
Measures of Central Tendency | |
Measures of Dispersion | |
The Normal Distribution | |
Polls and Margin of Error | |
Linear Regression | |
5. FINANCE | |
Simple Interest | |
Compound Interest | |
Annuities | |
Amortized Loans | |
Annual Percentage Rate on a Graphing Calculator | |
Payout Annuities | |
6. GEOMETRY | |
Perimeter and Area | |
Volume and Surface Area | |
Egyptian Geometry | |
The Greeks | |
Right Triangle Trigonometry | |
Conic Sections | |
Non-Euclidean Geometry | |
Fractal Geometry | |
The Perimeter and Area of a Fractal | |
7. MATRICES AND MARKOV CHAINS | |
Review of Matrices | |
Markov Chains | |
Systems of Linear Equations | |
Long-Range Predictions with Markov Chains | |
Solving Larger Systems of Equations | |
More on Markov Chains | |
8. LINEAR PROGRAMMING | |
Review of Linear Inequalities | |
The Geometry of Linear Programming | |
Introduction to the Simplex Method | |
The Simplex Method: Complete Problems | |
9. EXPONENTIAL AND LOGARITHMIC FUNCTIONS | |
Review of Exponentials and Logarithms | |
Review of Properties of Logarithms/ Exponential Growth | |
Exponential Decay | |
Logarithmic Scales | |
10. CALCULUS | |
Review of Ratios, Parabolas, and Functions | |
The Antecedents of Calculus | |
Four Problems | |
Newton and Tangent Lines | |
Newton on Falling Objects and the Derivative | |
The Trajectory of a Cannonball | |
Newton and Areas | |
Conclusion | |
Appendix A: Using A Scientific Calculator | |
Appendix B: Using A Graphing Calculator | |
Appendix C: Graphing With A Graphing Calculator | |
Appendix D: Finding Points of Intersection with A Graphing Calculator | |
Appendix E: Dimensional Analysis | |
Appendix F: Body Table for the Standard Normal Distribution | |
Appendix G: Answers To Selected Exercises |