Using and Understanding Mathematics A Quantitative Reasoning Approachby Bennett, Jeffrey O.; Briggs, Bill
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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.
The real-world focus turns studentsí attention to the math they will need for their daily lives, and keeps them engaged during the course. A wide range of exercises and problem types end each unit, making it easy for instructors to create assignments to fit their course goals.
Jeffrey Bennett specializes in mathematics and science education. He has taught at every level from pre-school through graduate school, including more than 50 college courses in mathematics, physics, astronomy, and education. His work on Using and Understanding Mathematics began in 1987, when he helped create a new mathematics course for the University of Colorado’s core curriculum. Variations on this course, with its quantitative reasoning approach, are now taught at hundreds of colleges nationwide. In addition to his work in mathematics, Dr. Bennett (whose PhD is in astrophysics) has written leading college-level textbooks in astronomy, statistics, and the new science of astrobiology, as well as books for the general public. He also proposed and developed both the Colorado Scale Model Solar System on the University of Colorado at Boulder campus and the Voyage Scale Model Solar System, a permanent, outdoor exhibit on the National Mall in Washington, DC. He has recently begun writing science books for children, including the award-winning Max Goes to the Moon and Max Goes to Mars. When not working, he enjoys swimming as well as hiking the trails of Boulder, Colorado with his family.
William L. Briggs has been on the mathematics faculty at the University of Colorado at Denver for 22 years. He teaches numerous courses within the undergraduate and graduate curriculum, and has special interest in teaching calculus, differential equations, and mathematical modeling. He developed the quantitative reasoning course for liberal arts students at University of Colorado at Denver supported by his textbook Using and Understanding Mathematics. He has written two other tutorial monographs, The Multigrid Tutorial and The DFT: An Owner's Manual for the Discrete Fourier Transform, as well as Ants, Bikes, Clocks, a mathematical problem solving text for undergraduates. He is a University of Colorado President's Teaching Scholar, an Outstanding Teacher awardee of the Rocky Mountain Section of the MAA, and the recipient of a Fulbright Fellowship to Ireland. Bill lives with his wife, Julie, and their Gordon setter, Seamus, in Boulder, Colorado. He loves to bake bread, run trails, and rock climb in the mountains near his home.
Table of Contents
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
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
Part 2 Quantitative Information in Everyday Life
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