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Book DetailsAMS/MAA TextbooksVolume: 33; 2016; 308 pp
Now available in Second Edition: TEXT/63
Common Sense Mathematics is a text for a one semester college-level course in quantitative literacy. The text emphasizes common sense and common knowledge in approaching real problems through popular news items and finding useful mathematical tools and frames with which to address those questions.
We asked ourselves what we hoped our students would remember about this course in ten years' time. From that ten year perspective, thoughts about syllabus—"what topics should we cover?"—seemed much too narrow. What matters more is our wish to change the way our students' minds work the way they approach a problem, or, more generally, the way they approach the world. Most people skip the numbers in newspapers, magazines, on the web, and, more importantly, even in financial information. We hope that in ten years our students will follow the news, confident in their ability to make sense of the numbers they find there and in their daily lives.
Most quantitative reasoning texts are arranged by mathematical topics to be mastered. Since the mathematics is only a part of what we hope students learn, we've chosen another strategy. We look at real life stories that can be best understood with careful reading and a little mathematics.
Ancillaries:
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Table of Contents
-
Cover
-
Half title
-
Copyright
-
Title
-
Series
-
Contents
-
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 at Wing 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
-
About the Authors
-
-
Additional Material
-
Reviews
-
Bolker and Mast has excellent scope, covering all the essential topics that I would want my students to know.
Keith Erickson, Georgia Gwinnett College -
This book contains many diverse topics and guides the students through examples in a logical way. While every problem is unique, the goal is for the student to think critically and develop a multitude of problem-solving skills so that they are prepared for 21st-century current events. I certainly see this book being used in a special topics course, in a mathematics competition, or as a supplemental text for applications. I will certainly use this text myself for my mathematics finance and sustainability courses. Thank you Bolker and Mast for writing such an insightful text.
Peter Olszewski, Pennsylvania State University -
The authors present a remarkable collection of problem situations gleaned from public media and supplemented by topics of personal finance. The problem situations are not only central to students' everyday lives but also provide a venue for continuing learning beyond a course and beyond school. Based on years of teaching quantitative reasoning, the book offers a clear model for such a course for the inexperienced teacher as well as opportunities for localizing and extending the material for the more experienced teacher.
Bernard L. Madison, University of Arkansas, Fayetteville
-
- Book Details
- Table of Contents
- Additional Material
- Reviews
Now available in Second Edition: TEXT/63
Common Sense Mathematics is a text for a one semester college-level course in quantitative literacy. The text emphasizes common sense and common knowledge in approaching real problems through popular news items and finding useful mathematical tools and frames with which to address those questions.
We asked ourselves what we hoped our students would remember about this course in ten years' time. From that ten year perspective, thoughts about syllabus—"what topics should we cover?"—seemed much too narrow. What matters more is our wish to change the way our students' minds work the way they approach a problem, or, more generally, the way they approach the world. Most people skip the numbers in newspapers, magazines, on the web, and, more importantly, even in financial information. We hope that in ten years our students will follow the news, confident in their ability to make sense of the numbers they find there and in their daily lives.
Most quantitative reasoning texts are arranged by mathematical topics to be mastered. Since the mathematics is only a part of what we hope students learn, we've chosen another strategy. We look at real life stories that can be best understood with careful reading and a little mathematics.
Ancillaries:
-
Cover
-
Half title
-
Copyright
-
Title
-
Series
-
Contents
-
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 at Wing 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
-
About the Authors
-
Bolker and Mast has excellent scope, covering all the essential topics that I would want my students to know.
Keith Erickson, Georgia Gwinnett College -
This book contains many diverse topics and guides the students through examples in a logical way. While every problem is unique, the goal is for the student to think critically and develop a multitude of problem-solving skills so that they are prepared for 21st-century current events. I certainly see this book being used in a special topics course, in a mathematics competition, or as a supplemental text for applications. I will certainly use this text myself for my mathematics finance and sustainability courses. Thank you Bolker and Mast for writing such an insightful text.
Peter Olszewski, Pennsylvania State University -
The authors present a remarkable collection of problem situations gleaned from public media and supplemented by topics of personal finance. The problem situations are not only central to students' everyday lives but also provide a venue for continuing learning beyond a course and beyond school. Based on years of teaching quantitative reasoning, the book offers a clear model for such a course for the inexperienced teacher as well as opportunities for localizing and extending the material for the more experienced teacher.
Bernard L. Madison, University of Arkansas, Fayetteville
