Common Sense Mathematics

Preface
1. Calculating on the Back of an Envelope
1.1 Billions of phone calls?
1.2 How many seconds?
1.3 Heartbeats
1.4 Calculators
1.5 Millions of trees?
1.6 Carbon footprints
1.7 Kilo, Mega, Giga
1.8 Exercises
2 Units and Unit Conversions
2.1 Rate times time equals distance
2.2 The MPG illusion
2.3 Converting currency
2.4 Unit pricing and crime rates
2.5 The metric system
2.6 Working on the railroad
2.7 Scientific notation milli and micro
2.8 Carpeting and paint
2.9 Exercises
3 Percentages, Sales Tax and Discounts
3.1 Don't drive and text
3.2 Red Sox ticket prices
3.3 Patterns in percentage calculations
3.4 The one-plus trick
3.5 Two raises in a row
3.6 Sales tax
3.7 20 percent off
3.8 Successive discounts
3.9 Percentage points
3.10 Exercises
4 Inflation
4.1 Red Sox ticket prices
4.2 Inflation is a rate
4.3 More than 100%
4.4 The Consumer Price Index
4.5 How much is your raise worth?
4.6 The minimum wage
4.7 Exercises
5 Average Values
5.1 Average test score
5.2 Grade point average
5.3 Improving averages
5.4 The consumer price index
5.5 New car prices fall
5.6 An averaging paradox
5.7 Exercises
6 Income Distribution―Excel, Charts and Statistics
6.1 Salaries atWing Aero
6.2 What if?
6.3 Using software
6.4 Median
6.5 Bar charts
6.6 Pie charts
6.7 Histograms
6.8 Mean, median, mode
6.9 Computing averages from histograms
6.10 Percentiles
6.11 The bell curve
6.12 Margin of error
6.13 Bimodal data
6.14 Exercises
7 Electricity Bills and Income Taxes―Linear Functions
7.1 Rates
7.2 Reading your electricity bill
7.3 Linear functions
7.4 Linear functions in Excel
7.5 Which truck to rent?
7.6 Energy and power
7.7 Taxes: sales, Social Security, income
7.8 Exercises
8 Climate Change―Linear Models
8.1 Climate change
8.2 The greenhouse effect
8.3 How good is the linear model?
8.4 Regression nonsense
8.5 Exercises
9 Compound Interest―Exponential Growth
9.1 Money earns money
9.2 Using Excel to explore exponential growth
9.3 Depreciation
9.4 Doubling times and half lives
9.5 Exponential models
9.6 Exercises
10 Borrowing and Saving
10.1 Credit card interest
10.2 Can you afford a mortgage?
10.3 Saving for college or retirement
10.4 Annual and effective percentage rates
10.5 Instantaneous compounding
10.6 Exercises
11 Probability―Counting, Betting, Insurance
11.1 Equally likely
11.2 Odds
11.3 Raffles
11.4 State lotteries
11.5 The house advantage
11.6 One-time events
11.7 Insurance
11.8 Sometimes the numbers don't help at all
11.9 Exercises
12 Break the Bank―Independent Events
12.1 A coin and a die
12.2 Repeated coin flips
12.3 Double your bet?
12.4 Cancer clusters
12.5 The hundred year storm
12.6 Improbable things happen all the time
12.7 Exercises
13 How Good Is That Test?
13.1 UMass Boston enrollment
13.2 False positives and false negatives
13.3 Screening for a rare disease
13.4 Trisomy 18
13.5 The prosecutor's fallacy
13.6 The boy who cried “Wolf”
13.7 Exercises
Hints
References
Index