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"Jeffrey Bennett served as the first director
of the program in Quantitative Reasoning and Mathematical Skills at the
University of Colorado, where he developed the groundbreaking curriculum
that became the basis of his best-selling college textbook in
mathematics. He holds a PhD in astrophysics and is also the lead author
of top-selling college textbooks in statistical reasoning, astronomy,
and astrobiology. Math for Life is his third book for the general
public, following the critically acclaimed
On the Cosmic Horizon
[out of print]
and
Beyond UFOs. He is also the author of award-winning children's books about science, including
Max Goes to the Moon,
Max
Goes to Mars,
Max Goes to Jupiter, and
The Wizard Who
Saved the World. "
Check out Jeff Bennett's home page.
MATH FOR LIFE: Crucial Ideas You Didn't Learn in School
216 pages, hc. November 2011. Roberts
and Company Publishers.
Book
Description:
How can we solve the national debt crisis? Should you or
your child take on a student loan? Is it safe to talk on a cell phone
while driving? Are there viable energy alternatives to fossil fuels?
Could simple policy changes reduce political polarization? These
questions may all seem very different, but they share two things in
common. First, they are all questions with important implications for
either personal success or our success as a nation. Second, they all
concern topics that we can fully understand only with the aid of clear
quantitative or mathematical thinking. In other words, they are topics
for which we need math for life--a kind of math that looks quite
different from most of the math that we learn in school, but that is
just as (and often more) important. In Math for Life, award-winning
author Jeffrey Bennett simply and clearly explains the key ideas of
quantitative reasoning and applies them to all the above questions and
many more. He also uses these questions to analyze our current education
system, identifying both shortfalls in the teaching of mathematics and
solutions for our educational future. No matter what your own level of
mathematical ability, and no matter whether you approach the book as an
educator, student, or interested adult, you are sure to find something
new and thought-provoking in Math for Life.
Reviews:
Full marks to Jeffrey Bennett for delivering exactly what
his title promises. This is not the math your teacher (probably) said
you would need in adult life but never did; it's the math you know you
need but likely don t have. It's not a traditional textbook; it's a
how-to manual for clear thinking about the quantitative aspects of
everyday life, bursting with intriguing, practical, real-life examples.
I recommend it. --Keith Devlin, Ph.D., Stanford University, author of
The Man of Numbers: Fibonacci's Arithmetic Revolution and The
Math Gene, and the Math Guy on National Public Radio.
Sprinkled with illuminating examples, Math for Life
presents issues critical to personal and national security even survival
in clear and forthright terms. Underlying this important message is the
obvious failure of U.S. mathematics education to meet the enormous
quantitative reasoning demands of U.S. society. Jeffrey Bennett makes
plain how current political and economic crises stem from this failure.
--Bernard L. Madison, Professor of Mathematics, University of Arkansas
Should be required reading for every American. There's no
more powerful way to equip yourself for our increasingly complex and
quantitative world than to read Math for Life. Every concept is
presented in a clear and engaging way. --K. Shane Goodwin, Professor of
Mathematics, Brigham Young University Idaho
Table of Contents:
Preface vii
1 (Don't Be) "Bad at Math" 1
2 Thinking with Numbers 11
3 Statistical Thinking 33
4 Managing Your Money 65
5 Understanding Taxes 89
6 The U.S. Deficit and Debt 105
7 Energy Math 119
8 The Math of Political Polarization 147
9 The Mathematics of Growth 163
Epilogue: Getting "Good at Math" 183
To Learn More 197
Acknowledgments 199
Also by Jeffrey Bennett 201
Index 203
Index of Examples 209
Preface
"The housing bubble. Lotteries. Cell phones and driving.
Personal budgeting. The federal debt. Social Security. Tax reform.
Energy policy. Global warming. Political redistricting. Population
growth. Radiation from nuclear power plants.
What do all the above have in common? Each is a topic
with important implications for all of us, but also a topic that we can
fully understand only if we approach it with clear quantitative or
mathematical thinking. In other words, these are all topics for
which we need "math for life" — a kind of math that looks quite
different from most of the math that we learn in school, but that is
just as (and sometimes more) important.
Now, in
case the word "math" has you worried for any reason, rest assured that
this is not a math book in any traditional sense. You won't find any
complex equations in this book, nor will you see anything that looks
much like what you might have studied in high school or college
mathematics classes. Instead, the focus of this book will be on what is
sometimes called quantitative reasoning, which means using numbers and
other mathematically based ideas to reason our way through the kinds of
problems that confront us in everyday life. As the list in the first
paragraph should show, these problems range from the personal to the
global, and over everything in between.
So what
exactly will you learn about "math for life" in this
short book? Perhaps the best way for me to explain it is to list my
three major goals in writing this book:
1. On a personal level, I hope this book will prove
practical in helping you make decisions that will improve your health,
your happiness, and your financial future. To this end, I'll discuss
some general principles of quantitative reasoning that you may not have
learned previously, while also covering specific examples that will
include how to evaluate claims of health benefits that you may hear in
the news (or in advertisements) and how to make financial decisions that
will keep you in control of your own life.
2. On a societal level, I hope to draw attention to what I believe are
oft-neglected mathematical truths that underlie many of the most
important problems of our time. For example, I believe that far too few
of us and far too few politicians) understand the true magnitude of our
current national budget predicament, the true challenge of meeting our
future energy needs, or what it means to live in a world whose
population may increase by another 3 billion people during the next few
decades. I hope to show you how a little bit of quantitative reasoning
can illuminate these and other issues, thereby making it more likely
that we'll find ways to bridge the political differences that have up
until now stood in the way of real solutions.
3. On the level of educational policy, I hope that this book will have
an impact on the way we think about mathematics education. As I'll argue
throughout the book, I believe that we can and must do a much better job
both in teaching our children traditional mathematics — meaning the kind
of mathematics that is necessary for modern, high-tech careers —
and in teaching the mathematics of quantitative reasoning that we all
need as citizens in today's society. I'll discuss both the problems that
exist in our current educational system and the ways in which I believe
we can solve them.
With
those three major goals in mind, I'll give you a brief overview of how
I've structured the book. The first chapter focuses on the general
impact of societal attitudes toward math. In particular, I'll explain
why I think the fact that so many people will
without embarrassment say that they are "bad at math" was a major
contributing factor to the housing bubble and the recent recession; I'll
also discuss the roots of poor attitudes toward math and how we can
change those attitudes in the future. The second and third chapters
provide general guidance for understanding the kinds of mathematical and
statistical thinking that lie at the heart of many modern issues and
that are in essence the core concepts of "math for life." The remaining
chapters are topic-based, covering all the issues I listed above, and
more; note that, while I'd like to think you'll read the book cover to
cover, I've tried to make the individual chapters self-contained enough
so that you could read them in any order. Finally, in the epilogue, I'll
offer my personal suggestions for changing the way we approach and teach
mathematics.
As an
author, I always realize that readers are what make my work possible,
and I thank you for taking the time to at least have a look at this
book. If I've convinced you to read it through, I hope you find it
both enjoyable and useful."
Excerpts:
More excerpts on
Jeff Bennets "Math for Life" web page
"Focus on quantitative reasoning. If you accept my rationale for no
longer allowing algebra to fulfill the college math requirement, then
the question becomes what to replace it with. To me, the answer is
clear: quantitative reasoning. As you've seen throughout this book, most
of the mathematical skills needed for quantitative reasoning are fairly
basic, but the level of conceptual thinking can be quite advanced. This
means that quantitative reasoning can be taught at a clearly collegiate
level, and there is plenty to cover in a semester or even a yearlong
course; this entire book contains only about 5% to 10% as much material
as a quantitative reasoning course typically covers. Moreover, because
quantitative reasoning is so important to modern life, it is a great
disservice to make the requirement anything else. For example, some
colleges have recently introduced course requirements in financial
literacy while others offer courses in statistical literacy; both types
of courses are clearly useful, but neither covers the breadth of topics
that we've covered in this book, which means they are not by themselves
enough. (Note, however, that such courses can be great options for one
semester of a two-semester quantitative reasoning requirement.)
Still other colleges offer courses giving students a brief introduction
to some of the esoteric branches of mathematics that mathematicians
study. These courses can be immensely interesting but I don't think they
are covering the material that students need for their everyday lives;
for that reason, I'd make such courses electives, to come after a
quantitative reasoning course requirement is fulfilled." P.
194-195
Statistical Reasoning for Everyday Life
By
Jeffrey Bennett, Bill Briggs and Mario Triola.
512 pages, pb. 3rd edition 2008. 2nd
edition 2003.
Addison Wesley.
Based on STATISTICAL REASONING FOR EVER by Jeffrey O. Bennett (2002).
Table of Contents:
Preface
Supplements
To the
Student: How to Succeed in Your Statistics Course
Applications Index
1.
Speaking of Statistics
1.1 What
Is/Are Statistics?
1.2
Sampling
1.3
Types of Statistical Studies
1.4
Should You Believe a Statistical Study?
Focus on
Sociology: Does Daycare Breed Bullies?
Focus on
Public Health: Is Your Lifestyle Healthy?
2.
Measurement in Statistics
2.1 Data
Types and Levels of Measurement
2.2
Dealing with Errors
2.3 Uses
of Percentages in Statistics
2.4
Index Numbers
Focus on
Politics: Who Benefits from a Tax Cut?
Focus on
Economics: Is our Standard of Living Improving?
3.
Visual Displays of Data
3.1
Frequency Tables
3.2
Picturing Distributions of Data
3.3
Graphics in the Media
3.4 A
Few Cautions About Graphics
Using
Technology
Focus on
History: Can War Be Described with a Graph?
Focus on
Environment: How Can We Visualize Global Warming?
4.
Describing Data
4.1 What
Is Average?
4.2
Shapes of Distributions
4.3
Measures of Variation
4.4
Statistical Paradoxes
Using
Technology
Focus on
The Stock Market: What’s Average About the Dow?
Focus on
Economics: Are the Rich Getting Richer?
5. A
Normal World
5.1 What
Is Normal?
5.2
Properties of the Normal Distribution
5.3 The
Central Limit Theorem
Using
Technology
Focus on
Education: What Can We Learn from SAT Trends?
Focus on
Psychology: Are We Smarter than Our Parents?
6.
Probability in Statistics
6.1 The
Role of Probability in Statistics: Statistical Significance 226
6.2
Basics of Probability
6.3
Probabilities with Large Numbers
6.4
Ideas of Risk and Life Expectancy
6.5
Combining Probabilities (Supplementary Section)
Focus on
Social Science: Are Lotteries Fair?
Focus on
Law: Is DNA Fingerprinting Reliable?
7.
Correlation and Causality
7.1
Seeking Correlation
7.2
Interpreting Correlations
7.3
Best-Fit Lines and Prediction
7.4 The
Search for Causality
Using
Technology
Focus on
Education: What Helps Children Learn to Read?
Focus on
Environment: What Causes Global Warming?
8.
From Samples to Populations
8.1
Sampling Distributions
8.2
Estimating Population Means
8.3
Estimating Population Proportions
Using
Technology
Focus on
History: Where Did Statistics Begin?
Focus on
Literature: How Many Words Did Shakespeare Know?
9.
Hypothesis Testing
9.1
Fundamentals of Hypothesis Testing
9.2
Hypothesis Tests for Population Means
9.3
Hypothesis Testing: Population Proportions
Using
Technology
Focus on
Health & Education: Will Your Education Help You Live Longer?
Focus on
Agriculture: Are Genetically Modified Foods Safe?
10. t
Tests, Two-Way Tables, and ANOVA
10.1
Distribution for Inferences about a Mean
10.2 t
Hypothesis Testing with Two-Way Tables
10.3
Analysis of Variance (One-Way ANOVA)
Using
Technology
Focus on
Criminology: Can You Tell a Fraud When You See One?
Focus on
Education: What Can a Fourth-Grader Do with Statistics?
Epilogue: A Perspective on Statistics
Appendix
A: z-Score Tables
Appendix
B: Table of Random Numbers
Suggested Readings
Credits
Glossary
Answers
Index
Book
Description:
Themes of the "Times": Quantitative Literacy
By Jeffrey Bennett.
4 edition
2007.
This
collection of engaging articles from The New York Times explores
a wide range of quantitative topics appearing in recent news items and
stories. Articles are correlated to chapters in Using and Understanding
Mathematics: A Quantitative Reasoning Approach, and chapter-specific
references make it easy for you to relate each article to the textbook.
A series of follow-up questions are also included for homework or class
discussion.
TOC:
Page 1
Page 2
Using and Understanding Mathematics: A Quantitative Reasoning Approach
Jeffrey
Bennett and William Briggs 5th edition 2010
Pearson (Addison-Wesley)
Using
and Understanding Mathematics: A Quantitative Reasoning Approach
increases students‘ mathematical literacy so that they better understand
the mathematics used in their daily lives.
Ideal for
courses that emphasize quantitative reasoning, Bennett and Briggs
prepare students to use math effectively to make better decisions
throughout their lives. Contents are organized with that in mind, with
engaging coverage in sections like Taking Control of Your Finances,
Dividing the Political Pie, and a full chapter about Mathematics and the
Arts.
This Fifth
Edition offers new hands-on Activities for use with students in class,
new ways for students to check their understanding through Quick
Quizzes, and a new question type in MyMathLab that applies math to
recent events in the news. In addition, the authors increase their
coverage of consumer math, and provide a stronger emphasis on technology
through new Using Technology features and exercises. The new Insider's
Guide provides instructors with tips and ideas for effective use of the
text in teaching the course.
Table of Contents
Preface, Prologue, Literacy for the Modern World.
Part 1 Logic and Problem Solving
Chapter 1 Thinking Critically 1A Recognizing Fallacies
1B Propositions and Truth Values 1C Sets and Venn Diagrams 1D Analyzing
Arguments 1E Critical Thinking in Everyday Life
Part 2 Quantitative Information in Everyday Life.
Chapter 2 Approaches to Problem Solving 2A The
Problem-Solving Power of Units 2B Standardized Units: More
Problem-Solving Power 2C Problem-Solving Guidelines and Hints
Chapter 3 Numbers in the Real World 3A Uses and Abuses
of Percentages 3B Putting Numbers in Perspective 3C Dealing with
Uncertainty 3D Index Numbers: The CPI and Beyond 3E How Numbers Deceive:
Polygraphs, Mammograms, and More
Chapter 4 Managing Money 4A Taking Control of Your
Finances 4B The Power of Compounding 4C Savings Plans and Investments 4D
Loan Payments, Credit Cards, and Mortgages 4E Income Taxes 4F
Understanding the Federal Budget
Part 3 Probability and Statistics
Chapter 5 Statistical Reasoning 5A Fundamentals of
Statistics 5B Should You Believe a Statistical Study? 5C Statistical
Tables and Graphs 5D Graphics in the Media 5E Correlation and Causality
Chapter 6 Putting Statistics to Work 6A Characterizing
Data 6B Measures of Variation 6C The Normal Distribution 6D Statistical
Inference
Chapter 7 Probability: Living with the Odds 7A
Fundamentals of Probability 7B Combining Probabilities 7C The Law of
Large Numbers 7D Assessing Risk 7E Counting and Probability
Part 4 Modeling
Chapter 8 Exponential Astonishment 8A Growth: Linear
versus Exponential 8B Doubling Time and Half-Life 8C Real Population
Growth 8D Logarithmic Scales: Earthquakes, Sounds, and Acids
Chapter 9 Modeling Our World 9A Functions: The
Building Blocks of Mathematical Models 9B Linear Modeling 9C Exponential
Modeling
Chapter 10 Modeling with Geometry 10A Fundamentals of
Geometry 10B Problem Solving with Geometry 10C Fractal Geometry
Part 5 Further Applications
Chapter 11 Mathematics and the Arts 11A Mathematics
and Music 11B Perspective and Symmetry 11C Proportion and the Golden
Ratio
Chapter 12 Mathematics and Politics 12A Voting: Does
the Majority Always Rule? 12B Theory of Voting 12C Apportionment: The
House of Representatives and Beyond 12D Dividing the Political Pie
Credits Answers Index |
