| 1. LOGIC. Deductive vs. Inductive Reasoning. Symbolic Logic. Truth Tables. More on Conditionals. Analyzing Arguments. 2. SETS AND COUNTING. Sets and Set Operations. Applications of Venn Diagrams. Introduction to Combinatorics. Permutations and Combinations. Infinite Sets. 3. PROBABILITY. History of Probability. Basic Terms of Probability. Basic Rules of Probability. Combinatorics 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. VOTING AND APPORTIONMENT. Voting Systems. Methods of Apportionment. Flaws of Apportionment. 7. NUMBER SYSTEMS AND NUMBER THEORY. Place Systems. Arithmetic in Different Bases. Primes and Perfect Numbers. The Fibonacci Sequence and the Golden Ratio. 8. GEOMETRY. Perimeter and Area. Volume and Surface Area. Egyptian Geometry. The Greeks. Right Triangle Trigonometry. Conic Sections and Analytic Geometry. Non-Euclidean Geometry. Fractal Geometry. The Perimeter and Area of a Fractal. 9. GRAPH THEORY. A Walk Through Konigsberg. Graphs and Euler Paths. Hamilton Circuits. Networks. Scheduling. 10. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Review of Exponentials and Logarithms. Review of Properties of Logarithms. Exponential Growth. Exponential Decay. Logarithmic Scales. 11. MATRICES AND MARKOV CHAINS. Review of Matrices. Introduction to Markov Chains. Systems of Linear Equations. Long-Range Predictions. Solving Larger Systems of Equations. More on Markov Chains. 12. LINEAR PROGRAMMING. Review of Linear Inequalities. The Geometry of Linear Programming. Appendices: Using a Scientific Calculator. Using a Graphing Calculator. Graphing with a Graphing Calculator. Finding Points of Intersection with a Graphing Calculator. Dimensional Analysis. Body Table for the Standard Normal Distribution. Answers to Selected Exercises. AVAILABLE ON THE WEB: LINEAR PROGRAMMING. Introduction to the Simplex Method. The Simplex Method: Complete Problems. THE CONCEPTS AND HISTORY OF CALCULUS. The 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. |
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