Mathematics for the Modern World Book

Introduction.
Problem Solving.
Estimation.

1. Sets and Logic.
Sets.
Set Operations.
Sets and Venn Diagrams.
Inductive and Deductive Logic.
Logic Statements.
Compound Statements.
Conditional Statements.
More Conditionals.
Analyzing Logic Arguments.
Logical Circuits.
Review.

2. Finance.
Compound Interest.
Geometric Sequences.
Annuities.
Loans.
Loan Amortization.
Logarithms and Finance.
Review.

3. Geometry.
Length and Area.
Polygons.
Solids: Volume and Surface Area.
Polyhedral.
Rigid Motions.
Symmetry.
Tilings.
Euclidean and Non-Euclidean Geometry.
Fractals.
Review.

4. Graph Theory.
Introduction to Graphs.
Edge Paths.
Edge Cycles.
Vertex Cycles.
The Traveling Salesman Problem.
Approximations to the Traveling Salesman Problem.
Trees.
Instant Insanity.
Review.

5. Probability.
Basic Probability Ideas.
Rules of Probability.
Probabilities of Unions and Intersections.
Conditional Probability and Independence.
Bayes' Formula.
Permutations and Combinations.
Probability and Counting Formulas.
Expected Value.
Binomial Experiments.
Review.

6. Statistics.
What is Statistics?
Organizing Data.
Displaying Data.
Measures of Central Tendency.
Measures of Variability.
Measures of Relative Position.
The Normal Distribution.
Confidence Intervals.
Regression and Correlation.
Review.

7. Decision Theory.
Voting.
More on Voting.
Weighted Voting: Banzhaf Power Index.
Weighted Voting: Shapley-Shubik Power Index.
Fair Division: Continuous Items.
Fair Division: DiscreteItems.
Apportionment.
Apportionment: Divisor Methods.
Review.

Appendix A: Scientific Notation.
Appendix B: Summation Notation.
Appendix C: Spreadsheets.
Appendix D: Tables.
Pascal's Triangle.
Area Under the Standard Normal Curve.
15 Year Amortization Table.
30 Year Amortization Table.