Mathematics

1. LOGIC. Deductive versus Inductive Reasoning. Symbolic Logic. Truth Tables. More on Conditionals. Analyzing Arguments. Deductive Proof of Validity. 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; Medical Tests and 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 with a TI-Calculator's TVM Application. Payout Annuities. 6. VOTING AND APPORTIONMENT. Voting Systems. Methods of Apportionment. Flaws of Apportionment. 7. NUMBER SYSTEMS AND NUMBER THEORY. Place Systems. Addition and Subtraction in Different Bases. Multiplication and Division in Different Bases. Prime Numbers and Perfect Numbers. Fibonacci Numbers and the Golden Ratio. 8. GEOMETRY. Perimeter and Area. Volume and Surface Area. Egyptian Geometry. The Greeks. Right Triangle Trigonometry. Linear Perspective. Conic Sections and Analytic Geometry. Non-Euclidean Geometry. Fractal Geometry. The Perimeter and Area of a Fractal. 9. GRAPH THEORY. A Walk through Koningsberg. Graphs and Euler Trails. 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. MARKOV CHAINS. Review of Matrices. Review of Systems of Linear Equations. Markov Chains and Tree Diagrams. Markov Chains and Matrices. Long-Range Predictions with Markov Chains. Solving Larger Systems of Equations. More on Markov Chains. 12. LINEAR PROGRAMMING. Review of Linear Inequalities. The Geometry of Linear Programming. Introduction to the Simplex Model.[online section only] The Simplex Method: Complete Problems. [online section only] 13. THE CONCEPTS AND HISTORY OF CALCULUS. [online chapter only] 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. APPENDICES. A. Using a Scientific Calculator. B. Using a Graphing Calculator. C. Graphing with a Graphing Calculator. D. Finding Points of Intersection with a Graphing Calculator. E. Dimensional Analysis. F. Body Table for the Standard Normal Distribution. G. Answers.