Math and Human Society

1 Modeling
1.1 Scientific Notation
1.1.2 Exercises
1.2 Percents
1.2.2 Markup, markdown, and sale price
1.2.3 Sales tax
1.2.4 Exercises
1.3 Introduction to Modeling
1.3.1 Definition of function
1.3.2 First models
1.4 Linear Models
1.4.1 Definition of linear function
1.4.2 Slope of a line
1.4.3 y-intercept
1.4.4 Equation of a line
1.4.5 Exercises
1.5 Quadratic Models
1.5.1 Definition of quadratic function
1.5.2 Finding the vertex of a parabola
1.5.3 Sketching parabolas
1.5.4 Finding the x-intercepts of a parabola
1.5.5 Exercises
1.6 Exponential Models
1.6.1 Definition of exponential function
1.6.2 Exercises
1.7 Logarithmic models
1.7.1 Logarithms of numbers
1.7.2 Common and natural logarithms
1.7.3 A magical property of logarithms
1.7.4 Logarithm functions
1.7.5 Exercises
1.8 Review Problems

2 Financial Mathematics
2.1 Simple Interest
2.1.2 Future value
2.1.3 Exercises
2.2 Introduction to Microsoft Excel
2.2.1 Getting started
2.2.2 Formulas
2.2.3 Copying formulas
2.2.4 Forcing Excel to use the cell you want
2.2.5 Exercises
2.3 Credit Card Debt
2.3.2 Exercises
2.4 Compound Interest
2.4.1 Computations
2.4.2 Nominal versus effective interest rate
2.4.3 Back to the future
2.4.4 Exercises
2.5 Present Value
2.5.1 The idea of present value
2.5.2 Application of present value to bonds
2.5.3 Exercises
2.6 Annuities and Mortgages
2.6.2 Principal and interest in amortized loans
2.6.3 Exercises
2.7 Review Problems

3 Descriptive Statistics
3.1 Introduction to Statistics
3.1.1 Population and sample
3.1.2 Parameter and statistic
3.1.3 Sampling
3.1.4 Categorical and numerical data
3.1.5 Exercises
3.2 Graphing Categorical Data: Bar Graphs and Pie Charts
3.2.1 Introduction
3.2.2 Bar graphs
3.2.3 Pie charts
3.2.4 Exercises
3.3 Line Graphs
3.3.2 Exercises
3.4 Making Graphs in Excel
3.4.1 Bar graphs
3.4.2 Pie charts
3.4.3 Line graphs
3.4.4 Exercises
3.5 Averages: Measures of Central Tendency
3.5.1 Mean
3.5.2 Median
3.5.3 Mode
3.5.4 Use of mean, median, and mode
3.5.5 Exercises
3.6 Variability
3.6.1 Range
3.6.2 Sample variance
3.6.3 Sample standard deviation
3.6.4 Exercises
3.7 Descriptive Statistics in Excel
3.7.1 Using Excel’s built-in functions
3.7.2 Exercises
3.8 Graphing Numerical Data: Stem-and-Leaf Diagrams
3.8.2 Exercises
3.9 Graphing Numerical Data: Frequency Tables and Histograms
3.9.1 Frequency tables
3.9.2 Histograms
3.9.3 Calculating descriptive statistics from a frequency table
3.9.4 Exercises
3.10 Lying with Statistics
3.10.2 Exercises
3.11 Review Problems

4 Voting and Apportionment
4.1 Voting
4.1.1 Majority rule
4.1.2 Plurality
4.1.3 Hare
4.1.4 Borda count
4.1.5 Pairwise comparison
4.1.6 Approval
4.1.7 True majority rule
4.1.8 Condorcet’s Jury Theorem
4.1.9 Exercises
4.2 Voting Problems
4.2.2 Fairness in voting
4.2.3 Arrow’s Impossibility Theorem
4.2.4 Gaming voting systems
4.2.5 The agenda effect
4.2.6 Exercises
4.3 Apportionment
4.3.1 A bit of history
4.3.2 Adams’ method
4.3.3 Jefferson’s method
4.3.4 Hamilton’s method
4.3.5 Webster’s method
4.3.6 The Huntington-Hill method
4.3.7 Exercises
4.4 Review Problems

Appendix A. In-Class Exercises
Appendix B. Answers to (Almost) All the Exercises
Index