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Math in Society:
Mathematics for liberal arts majors
Portland Community College Math Department
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Front Matter
Colophon
Dedication
Attributions
Project Notes
Resources
Link to 2nd Edition
Introduction to this Book
1
Logic and Sets
1.1
The Language and Rules of Logic
1.1.1
Logic
1.1.2
Propositions
1.1.3
Negation (not)
1.1.4
Negation of All and None
1.1.5
Multiple Negations
1.1.6
Logical Connectors:
and
and
or
1.1.7
Exclusive vs. Inclusive
Or
1.1.8
Conditional Statements (if, then)
1.1.9
Basic Truth Tables
1.1.10
Conditional Truth Tables
1.1.11
Truth Tables for Complex Statements
1.1.12
Truth Tables with Three Propositions
1.1.13
Exercises
1.2
Sets and Venn Diagrams
1.2.1
Sets
1.2.2
Set Notation
1.2.3
Universal Set
1.2.4
The Null Set
1.2.5
Intersection, Union, and Complement (And, Or, Not)
1.2.6
Venn Diagrams
1.2.7
Illustrating Data
1.2.8
Qualified Propositions
1.2.9
Overlapping Sets
1.2.10
Disjoint Sets
1.2.11
Subsets
1.2.12
Exercises
1.3
Describing and Critiquing Arguments
1.3.1
Logical Arguments
1.3.2
Inductive and Deductive Arguments
1.3.3
Evaluating Arguments
1.3.4
Evaluating Deductive Arguments Using Sets
1.3.5
Exercises
1.4
Logical Fallacies
1.4.1
Logical Fallacies
1.4.2
Common Logical Fallacies
1.4.3
Personal Attack (Ad hominem)
1.4.4
Appeal to Ignorance
1.4.5
Appeal to Authority
1.4.6
False Dilemma
1.4.7
Straw Man (or Straw Person)
1.4.8
Post Hoc
1.4.9
Exercises
1.5
Chapter 1 Review
2
Financial Math
2.1
Introduction to Spreadsheets
2.1.1
Basic Calculations
2.1.2
Cell References
2.1.3
Cell Formatting
2.1.4
Fill-Down Feature
2.1.5
Formulas
2.1.6
Exercises
2.2
Simple and Compound Interest
2.2.1
Simple Interest
2.2.2
APR – Annual Percentage Rate
2.2.3
Compound Interest
2.2.4
The Future Value Spreadsheet Formula
2.2.5
Comparing Simple and Compound Interest
2.2.6
Finding the Principal, or Present Value
2.2.7
The Present Value Spreadsheet Formula
2.2.8
Continuously Compounded Interest
2.2.9
Finding the Amount of Interest Earned and the Percentage
2.2.10
Effective Rate
2.2.11
Exercises
2.3
Savings Plans
2.3.1
Savings Plan Formulas
2.3.2
Finding Payment Amounts Usings Spreadsheets and Formulas
2.3.3
Comparing Lump Sum and Regular Savings Payments
2.3.4
Deriving the Savings Plan Formula (Optional)
2.3.5
Exercises
2.4
Loan Payments
2.4.1
Installment Loans
2.4.2
Loan Formulas
2.4.3
Remaining Loan Balance
2.4.4
Credit Cards
2.4.5
Summary of Spreadsheet Formulas
2.4.6
When to use each spreadsheet formula: What is the question asking?
2.4.7
Summary of Mathematical Formulas
2.4.8
When to use each mathematical formula: What is the question asking?
2.4.9
Exercises
2.5
Income Taxes
2.5.1
A Very Brief History of Taxes
2.5.2
Types of Income Tax
2.5.3
Federal Income Tax
2.5.4
State Income Tax
2.5.5
Municipal Income Tax
2.5.6
Calculating Federal Income Tax
2.5.7
Gross Income
2.5.8
Adjusted Gross Income
2.5.9
Taxable Income
2.5.10
Filing Status
2.5.11
Tax Tables
2.5.12
Tax Credits
2.5.13
Calculating a Refund or Payment Due
2.5.14
Exercises
2.6
Chapter 2 Review
3
Statistics
3.1
Overview of the Statistical Process
3.1.1
Statistical Process
3.1.2
Population
3.1.3
Parameter
3.1.4
Sample
3.1.5
Statistic
3.1.6
Sampling
3.1.7
Sampling Methods
3.1.8
Simple random sample (SRS)
3.1.9
Stratified sampling
3.1.10
Systematic sampling
3.1.11
Convenience sampling
3.1.12
Statistical Bias
3.1.13
Types of bias
3.1.14
Observational Studies
3.1.15
Experiments
3.1.16
Confounding
3.1.17
Control group
3.1.18
Placebo effect
3.1.19
Placebo and Placebo-controlled experiments
3.1.20
Blind studies
3.1.21
Margin of Error and Confidence Intervals
3.1.22
Exercises
3.2
Describing Data
3.2.1
Types of Data
3.2.2
Presenting Categorical Data
3.2.3
Frequency Tables
3.2.4
Relative Frequency Tables
3.2.5
Bar graphs
3.2.6
Pie Charts
3.2.7
Using a Spreadsheet to Make Bar Charts and Pie Charts
3.2.8
Misleading Graphs
3.2.9
Perceptual Distortion
3.2.10
Misleading Scale
3.2.11
Stacked Bar Graphs
3.2.12
Presenting Quantitative Data
3.2.13
Histograms
3.2.14
Class Intervals
3.2.15
Histograms Using Technology
3.2.16
The Shape of a Distribution
3.2.17
Modality
3.2.18
Symmetry
3.2.19
Skewness
3.2.20
Skewed to the Left
3.2.21
Skewed to the Right
3.2.22
The Normal Distribution
3.2.23
Outlier
3.2.24
Exercises
3.3
Summary Statistics: Measures of Center
3.3.1
Calculating Summary Statistics
3.3.2
Measures of Center
3.3.3
Mode
3.3.4
Mean
3.3.5
Median
3.3.6
The Relationship Between the Mean and the Median
3.3.7
Exercises
3.4
Summary Statistics: Measures of Variation
3.4.1
Measures of Variation
3.4.2
Standard Deviation
3.4.3
Range
3.4.4
Quartiles and the Interquartile Range
3.4.5
The Five-Number Summary and Boxplots
3.4.6
Modified Boxplot (Optional)
3.4.7
Percentiles
3.4.8
Comparing Distributions
3.4.9
Z-Scores
3.4.10
Exercises
3.5
Chapter 3 Review
3.6
The Normal Distribution
3.6.1
Introduction to The Normal Distribution
3.6.2
Properties of the Normal Distribution
3.6.3
The Empirical Rule
3.6.4
Using the Empirical Rule to Calculate Approximate Probabilities
3.6.5
Using Technology to Calculate Exact Probabilities
3.6.6
The Standard Normal Distribution and Z-Scores
3.6.7
Confidence Intervals and Margin of Error
3.6.8
Exercises
4
Probability
4.1
Contingency Tables
4.1.1
Contingency Tables
4.1.2
Contingency Tables and Venn Diagrams
4.1.3
“And” Statements
4.1.4
“Or” Statements
4.1.5
Conditional Statements
4.1.6
Contingency Tables with More Than Two Categories
4.1.7
Empirical Probability
4.1.8
Finding Empirical Probabilities with a Contingency Table
4.1.9
Conditional Probabilities
4.1.10
Exercises
4.2
Theoretical Probability
4.2.1
Basic Probability Concepts
4.2.2
Experiment
4.2.3
Events and Outcomes
4.2.4
Sample Space
4.2.5
Equally Likely Outcomes
4.2.6
Certain and Impossible Events
4.2.7
Complementary Events
4.2.8
Experimental vs. Theoretical Probability
4.2.9
The Law of Large Numbers
4.2.10
Probability of Compound Events
4.2.11
“And” Probabilities
4.2.12
Independent and Dependent Events
4.2.13
“Or” Probabilities
4.2.14
Overlapping or Disjoint Sets
4.2.15
Exercises
4.3
Expected Value
4.3.1
Expected Value
4.3.2
Exercises
4.4
Chapter 4 Review
5
Democracy
5.1
Apportionment
5.1.1
Historical Context for This Chapter
5.1.2
Formation of the United States
5.1.3
What is Apportionment?
5.1.4
Hamilton’s Method
5.1.5
Problems with Hamilton’s Method
5.1.6
Jefferson’s Method
5.1.7
Webster’s Method
5.1.8
Land Rights, Citizenship and Voting Rights
5.1.9
Huntington-Hill Method
5.1.10
What is the Geometric Mean?
5.1.11
Exercises
5.2
Voting Methods
5.2.1
Voting Rights
5.2.2
Ranked Choice Ballots
5.2.3
Preference Schedule
5.2.4
Plurality Method
5.2.5
How Many Votes are Needed to Win?
5.2.6
Insincere Voting
5.2.7
Instant Runoff Method
5.2.8
Borda Count (Point System)
5.2.9
Pairwise Comparison: Copeland’s Method
5.2.10
Which Method is the Most Fair?
5.2.11
Primaries and Sequential Voting
5.2.12
Exercises
5.3
The Popular Vote, Electoral College and Electoral Power
5.3.1
Choosing the U.S. President
5.3.2
How Electoral Votes are Determined
5.3.3
Electoral Power
5.3.4
Exercises
5.4
Gerrymandering and How to Measure It
5.4.1
Forming State Legislative Districts
5.4.2
Proportionality and Fairness
5.4.3
How to Gerrymander
5.4.4
The Efficiency Gap
5.4.5
Exercises
5.5
Chapter 5 Review
5.6
Federal Budget, Deficit and National Debt
5.6.1
Federal Income and Spending
5.6.2
The Federal Budget Process
5.6.3
The Federal Surplus or Deficit
5.6.4
Debt to GDP Ratio
5.6.5
National Debt
5.6.6
National Debt Clocks
5.6.7
Pie Charts and Percentages
5.6.8
Exercises
Back Matter
References
A
Odd Answers
Dedication
Dedication
We dedicate this book to our students. May you have greater ease in paying for college and grow your proficiency and confidence in math.
