Using and Understanding Mathematics: A Quantitative Reasoning Approach by Jeffrey O. Bennett
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Using and Understanding Mathematics
Summary
With all of the topics needed to fulfill a general education requirement, this text, one of the few for the emerging Quantitative Literacy/Quantitative Reasoning Course, helps to reduce mathematical anxiety and focuses on the practicality of mathematics in college, career, and life.
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Using and Understanding Mathematics Summary
About Jeffrey O. Bennett
Jeffrey O. Bennett?s academic home is the University of Colorado at Boulder, where he has been teaching on and off since 1983 and from which he received his Ph.D. in Astrophysics in 1987. During this time, he?s taught more than 50 college courses in subjects including mathematics, astronomy, physics, environmental science, and science education. He began work on Using and Understanding Mathematics because he is particularly interested in helping students overcome difficulties with mathematics. For similar reasons, he has recently completed a textbook for introductory astronomy (The Cosmic Perspective, with M. Donahue, N. Schneider, and G.M. Voit, Addison Wesley Longman, 1999).
He is also working on several books about mathematics and science for the general public. In addition, he is now working on science books for children. Jeff is perhaps best known for his role in creating the Voyage Scale Model Solar System on the National Mall in Washington, DC (opening October 2001); he proposed the project and worked on the team that developed it as a collaborative effort between the Challenger Center for Space Science Education, the Smithsonian Institution, and NASA.
When not working, he enjoys participating in masters swimming and 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 17 years. He teaches throughout the undergraduate and graduate curriculum with a special interest in teaching mathematical modeling as it applies to problems in biology and medicine. He developed the quantitative reasoning course for liberal arts students at CU-Denver supported by the textbook Using and Understanding Mathematics, which he co-authored with Jeff Bennett. He has written two other tutorial monographs, The Multigrid Tutorial and The DFT: An Owner's Manual for the Discrete Fourier Transform.
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, his daughter, Katie, and two dogs, Midnight and Seamus, in Boulder, Colorado. He loves to bake bread, as well as run trails and rock climb in the mountains near his home.
Table of Contents
I. LOGIC AND PROBLEM SOLVING.
1. Thinking Critically.Recognizing Fallacies.Propositions and Truth Values.Sets and Venn Diagrams.A Brief Review: Sets of Numbers. Analyzing Arguments.Critical Thinking in Everyday Life.2. Approaches to Problem Solving.
The Problem-Solving Power of Units.A Brief Review: Working with Fractions. Standardized Units: More Problem-Solving Power.A Brief Review: Powers of 10. Problem-Solving Guidelines and Hints.
II. QUANTITATIVE INFORMATION IN EVERYDAY LIFE.
3. Numbers in the Real World.Uses and Abuses of Percentages.A Brief Review: Percentages. A Brief Review: What is ratio?. Putting Numbers in Perspective.A Brief Review: Working with Scientific Notation. Dealing with Uncertainty.A Brief Review: Rounding. Index Numbers: The CPI and Beyond.How Numbers Deceive: Polygraphs, Mammograms, and More.4. Financial Management.
The Power of Compounding.A Brief Review: Three Basic Rules of Algebra. Savings Plans and Investments.A Brief Review: Algebra with Powers and Roots. Loan Payments, Credit Cards, and Mortgages.Income Taxes.Understanding the Federal Budget.
III. PROBABILITY AND STATISTICS.
5. Statistical Reasoning.Fundamentals of Statistics.Should You Believe a Statistical Study?Statistical Tables and Graphs.Graphs in the Media.Correlation and Causality.6. Putting Statistics to Work.
Characterizing a Data Distribution.Measures of Variation.The Normal Distribution.Statistical Inference.7. Probability: Living with the Odds.
Fundamentals of Probability.A Brief Review: The Multiplication Principle. Combining Probabilities.The Law of Large Numbers.Assessing Risk.Counting and Probability.A Brief Review: Factorials.
IV. MODELING.
8. Exponential Astonishment.Growth: Linear Versus Exponential.Doubling Time and Half-Life.A Brief Review: Logarithms. Real Population Growth.Logarithmic Scales: Earthquakes, Sounds, and Acids.9. Modeling Our World.
Functions: The Building Blocks of Mathematical Models.A Brief Review: The Coordinate Plane. Linear Modeling.Exponential Modeling.A Brief Review: Algebra with Logarithms. 10. Modeling with Geometry.
Fundamentals of Geometry.Problem Solving with Geometry.Fractal Geometry.
V. FURTHER APPLICATIONS.
11. Mathematics and the Arts.Mathematics and Music.Perspective and Symmetry.Proportion and the Golden Ration.12. Mathematics and Politics.
Voting: Does the Majority Always Rule?Theory of Voting.Apportionment: The House of Representatives and Beyond.13. Mathematics and Business.
Network Analysis.The Traveling Salesman Problem.Scheduling Problems.Credits.
Answers.
Index.
Additional information
CIN0321227735G
9780321227737
0321227735
Using and Understanding Mathematics: A Quantitative Reasoning Approach by Jeffrey O. Bennett
Used - Good
Hardback
Pearson Education (US)
20040407
800
N/A
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