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Mathematics in Contemporary Society:
A Work in Progress
Elizabeth O’Neil
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Front Matter
Attributions
Note to Students
1
Proportional Reasoning
1.1
Percents
1.1.1
Percents
1.1.2
Converting Between Percents and Decimals
1.1.3
Calculating Percents
1.1.4
Percents over 100%
1.1.5
Absolute and Relative Change
1.1.6
Doubling, Tripling, Etc.
1.1.7
Multiple Percent Changes
1.1.8
Exercises
1.2
Rates, Ratios, and Dimensional Analysis
1.2.1
Unit Rates
1.2.2
Unit Conversions
1.2.3
Proportional Reasoning with Rates and Ratios
1.2.4
Common Unit Conversions
1.2.5
Exercises
1.3
Focus on Dosage Calculations
1.3.1
Calculating Dosages
1.3.2
IV Infusions
1.3.3
Exercises
2
Mathematical Models
2.1
Linear Growth
2.1.1
Linear Growth Models
2.1.2
When Good Models Go Bad
2.1.3
Exercises
2.2
Quadratic Models
2.3
Exponential Growth
2.3.1
Exponential Growth and Decay Models
2.3.2
When Good Models Go Bad
2.3.3
Special Cases
2.3.4
Exercises
2.4
Logarithms and Exponential Equations
2.4.1
The Common Logarithm
2.4.2
Using Common Logarithms to Solve Exponential Equations
2.4.3
Applications
2.5
Natural Growth and Logistic Growth
2.5.1
Natural Growth
2.5.2
Logistic Growth Model
3
Personal Finance
3.1
Introduction to Spreadsheets
3.1.1
Basic Calculations
3.1.2
Cell References
3.1.3
Cell Formatting
3.1.4
Fill-Down Feature
3.1.5
Formulas
3.1.6
Exercises
3.2
Simple Interest
3.2.1
Simple Interest
3.2.2
Future Value
3.2.3
Amortized Loans
3.2.4
Exercises
3.3
Credit Cards
3.3.1
What is a Credit Card?
3.3.2
Credit Card Balances
3.3.3
Finance Charges
3.3.3.1
Unpaid Balance and Average Daily Balance Methods
3.3.3.2
Daily Balance Method
3.3.4
Payoff Balance
3.3.5
Exercises
3.4
Compound Interest
3.4.1
Introduction to Compound Interest
3.4.1.1
Comparing Simple and Compound Interest
3.4.2
Applications of Compound Interest
3.4.3
Continuously Compounded Interest
3.4.4
Annual Percentage Yield (APY)
3.4.5
Using Spreadsheets for Compound Interest Applications
3.4.6
Exercises
3.5
Annuities and Amortized Loans
3.5.1
Savings Annuities
3.5.2
Payout Annuities
3.5.3
Amortized Loans
3.5.4
Formula Derivations
3.5.4.1
Savings Annuity Formulas
3.5.4.2
Payout Annuity and Amortized Loan Formula
4
Statistics
4.1
The Statistical Process
4.1.1
Statistical Process Overview
4.1.2
Statistics Terminology
4.1.2.1
Population and Sample
4.1.2.2
Parameters and Statistics
4.1.2.3
Types of Studies
4.1.3
Sampling and Bias
4.1.3.1
Sampling Methods
4.1.3.2
Sampling Bias
4.1.4
Confounding
4.1.5
Exercises
4.2
Describing Data
4.2.1
Types of Data
4.2.2
Presenting Categorical Data
4.2.3
Frequency Tables
4.2.4
Relative Frequency Tables
4.2.5
Bar graphs
4.2.6
Pie Charts
4.2.7
Using a Spreadsheet to Make Bar Charts and Pie Charts
4.2.8
Misleading Graphs
4.2.9
Perceptual Distortion
4.2.10
Misleading Scale
4.2.11
Stacked Bar Graphs
4.2.12
Presenting Quantitative Data
4.2.13
Histograms
4.2.14
Create Histograms with Technology
4.2.15
The Shape of a Distribution
4.2.16
Modality
4.2.17
Symmetry
4.2.18
Skewness
4.2.19
Skewed to the Left
4.2.20
Skewed to the Right
4.2.21
The Normal Distribution
4.2.22
Outlier
4.2.23
Exercises
4.3
Summary Statistics: Measures of Center
4.3.1
Measures of Center
4.3.2
Mode
4.3.3
Mean
4.3.4
Median
4.3.5
The Relationship Between the Mean and the Median
4.3.6
Exercises
4.4
Summary Statistics: Measures of Variation
4.4.1
Standard Deviation
4.4.2
Range
4.4.3
Quartiles and the Interquartile Range
4.4.4
The Five-Number Summary and Boxplots
4.4.5
Exercises
4.5
The Normal Distribution
4.5.1
Properties of the Normal Distribution
4.5.2
The Empirical Rule
4.5.3
Using the Empirical Rule to Calculate Approximate Probabilities
4.5.4
Z-Scores
4.5.5
Using Technology to Calculate Exact Probabilities
4.5.6
The Standard Normal Distribution and Z-Scores
4.5.7
Confidence Intervals and Margin of Error
4.5.8
Exercises
5
Counting Methods and Probability
5.1
Fundamentals of Probability
5.1.1
Basic Probability
5.1.2
Probability of "And" and "Or" Events
5.1.3
Contingency Tables
5.1.4
Complementary Events
5.1.5
Exercises
5.2
Conditional Probability
5.2.1
Conditional Probability
5.2.2
Independent and Dependent Events
5.2.3
Probability of Sequential Events
5.2.4
Exercises
5.3
Expected Value
5.3.1
Expected Value
5.3.2
Exercises
5.4
Combinatorics
5.4.1
Tree Diagrams and the Fundamental Counting Principle
5.4.2
Factorials
5.4.3
Permutations
5.4.4
Combinations
5.4.5
More Applications Involving Combinations and the Fundamental Counting Principle
5.4.6
Exercises
6
Democracy
6.1
Voting Methods
6.1.1
Ranked Choice Ballots
6.1.2
Preference Schedule
6.1.3
Plurality Method
6.1.4
How Many Votes are Needed to Win?
6.1.5
Insincere Voting
6.1.6
Instant Runoff Method
6.1.7
Borda Count (Point System)
6.1.8
Pairwise Comparison: Copeland’s Method
6.1.9
Which Method is the Most Fair?
6.1.10
Primaries and Sequential Voting
6.1.11
Exercises
6.2
Apportionment
6.2.1
The Problem of Apportionment
6.2.2
Hamilton’s Method
6.3
Apportionment Paradoxes and Problems
6.3.1
The Quota Rule
6.3.2
Paradoxes
6.4
The Popular Vote, Electoral College and Electoral Power
6.4.1
Choosing the U.S. President
6.4.2
How Electoral Votes are Determined
6.4.3
Electoral Power
6.4.4
Exercises
Appendix
A
Answers to Odd-Numbered Exercises
B
Review: Fractions
C
Review: Linear Equations
D
Graphing Technology
D.1
Creating Graphs
D.2
Using Graphs to Solve Problems
Colophon
Colophon
Colophon
This book was authored in PreTeXt.
