Using and Understanding Mathematics: A Quantitative Reasoning Approach / Edition 2

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Overview

The premier book for alleviating math anxiety, Using and Understanding Mathematics helps readers develop the ability to reason with quantitative information, so they can be successful in using math in the rapidly changing work environment. It covers principles of reasoning, statistical reason, numbers in the real world, probability, and discrete mathematics. These topics are all presented in the context of real world situations from the social sciences, environmental issues, politics, economics, personal finance, art, and music.
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Editorial Reviews

Booknews
This textbook's practical focus and arsenal of interesting problems should put an end to the piteous question, "but, whyyyyy do we have to learn this stuff?," once and for all. Topics include statistical reasoning, exponential growth and decay, financial management, probability, mathematics in business, problem solving techniques, numbers in the real world, and the principles of reasoning. Background in algebra is assumed. Annotation c. by Book News, Inc., Portland, Or.
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Product Details

  • ISBN-13: 9780201717112
  • Publisher: Addison Wesley
  • Publication date: 7/2/2001
  • Edition description: Older Edition
  • Edition number: 2
  • Pages: 744
  • Product dimensions: 8.50 (w) x 10.00 (h) x 1.20 (d)

Meet the Author

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.

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Table of Contents

Prologue: Literacy for the Modern World.

I. LOGIC AND PROBLEM SOLVING.

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.

2. Approaches to Problem Solving.
2A The Problem-Solving Power of Units.
2B Standardized Units: More Problem-Solving Power.
2C Problem Solving: General Guidelines and Hints.

II. QUANTITATIVE INFORMATION IN EVERYDAY LIFE.

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.

4. Financial Management.
4A The Power of Compounding.
4B Savings Plans and Investements.
4C Loan Payments, Credit Cards, and Mortgages.
4D Income Taxes.
4E Understanding the Federal Budget.

III. PROBABILITY AND STATISTICS.

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 andCausality.

6. Putting Statistics to Work.
6A Characterizing Data.
6B Measures of Variation.
6C The Normal Distribution.
6D Statistical Inference.

7. Probability: Living with the Odds.
7A Fundamentals of Probability.
7B Combining Probabilities.
7C The Law of Averages.
7D Assessing Risk.
7E Counting and Probability.

IV. MODELING.

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.

9. Modeling Our World.
9A Functions: The Building Blocks of Mathematical Models.
9B Linear Modeling.
9C Exponential Modeling.

V. FURTHER APPLICATIONS.

10. Mathematics and the Arts.
10A Fundamentals of Geometry.
10B Mathematics and Music.
10C Perspective and Symmetry.
10D Proportion and the Golden Ratio.
10E Fractal Geometry.

11. Mathematics and Politics.
11A Voting: Does the Majority Always Rule?.
11B Theory of Voting.
11C Apportionment: The House of Representatives and Beyond.

12. Mathematics in Business.
12A Network Analysis.
12B The Traveling Salesman Problem.
12C Project Design.

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