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Using and Understanding Mathematics: A Quantitative Reasoning Approach: United States Edition de Jeffrey O. Bennett

Using and Understanding Mathematics: A Quantitative Reasoning Approach: United States Edition

Autor Jeffrey O. Bennett, William L. Briggs
en Limba Engleză Hardback – 21 ian 2007
Most students taking this course do so to fulfill a requirement, but the true benefit of the course is learning how to use and understand mathematics in daily life. This quantitative reasoning text is written expressly for those students, providing them with the mathematical reasoning and quantitative literacy skills they'll need to make good decisions throughout their lives. Common-sense applications of mathematics engage students while underscoring the practical, essential uses of math.
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Specificații

ISBN-13: 9780321458209
ISBN-10: 0321458206
Pagini: 848
Dimensiuni: 216 x 254 x 32 mm
Greutate: 1.79 kg
Ediția:Nouă
Editura: Pearson Education
Colecția Pearson Education
Locul publicării:Upper Saddle River, United States

Cuprins

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
 
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 Your 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 a Data Distribution
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
 
Chapter 13   Mathematics and Business 13A     Network Analysis
13B     The Traveling Salesman Problem
13C     Scheduling Problems
 
Credits Answers
Index
 
 

Notă biografică

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 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 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.

Caracteristici

  • Practical Matters. Focusing on matters of high practical importance, this feature highlights common-sense applications of math such as avoiding credit card trouble and spotting a bad cell phone deal.
  • A Brief Review. This feature reviews key mathematical skills students should have learned previously, but which many students still need review and practice. They appear in the book wherever a particular skill is first needed, and exercises based on the review boxes can be found at the end of the unit.
  • Thinking About. Building upon the main narrative, this feature reaches beyond to a deeper level of mathematical understanding. Examples include boxes on the proof of the Pythagorean theorem and on Zeno's paradox.
  • Time Out to Think. Appearing throughout the book, the Time Out to Think features pose short conceptual questions designed to help students reflect on important new ideas. They also serve as excellent starting points for classroom discussions.
  • Margin Features. A wide margin leaves room for students to make notes while studying. The margin also contains material that spurs student interest in three basic forms:            
  •     By the Way features contain interesting notes and asides relevant to the topic at hand           
  •     Historical Note remarks give historical context to the ideas presented in the chapter            
  •     Technical Notes contain details that are important mathematically for students looking for more depth
  • Now Try Exercises. At the end of every in-text example students are directed to Now Try a specific exercise, immediately testing their comprehension of the material.
  • Does It Make Sense? These qualitative exercise questions test conceptual understanding by asking whether given statements are sensible and asking students to explain why or why not.  
  • Basic Skills and Concepts. Covering concepts from the unit, these exercises can be used for homework assignments or for self-study. Answers to most odd-numbered exercises appear in the back of the book.
  • Web Projects. The Web Projects require students to search for data or other information online. They can be used for extended projects, discussions, group activities, or essays.
  • In the News. In these exercises, students are challenged to find examples of unit concepts in the news or in their daily lives. These questions may be assigned as homework or used for class discussions.

Caracteristici noi

  • Two new units increase students’ understanding of how math applies to daily life. New Unit 4A: Taking Control of Your Finances provides an introduction to the personal budgeting issues presented in Chapter 4. In addition, a new unit on redistricting and what it means has been added as Unit 12D: Dividing the Political Pie, to show students how math affects their day-to-day life with a topic that is especially important in the upcoming elections.
  • Each set of exercises now begins with a Quick Quiz to test students’ conceptual understanding. These multiple choice questions are designed to be answered with an explanation on why a particular answer was selected, and will help students prepare for the rest of the exercise set.
  • All of the Applications Exercises are updated or revised with more current data or more relevant information for students.
  • New Art Annotations have been included to make the art a more useful learning tool.
  • Over 500 new exercises have been added, wtih more exercises focusing on basic skills. Over 50% of the exercises are new or have been revised and improved for better student understanding.