- 1. Thinking Critically
- Activity: Bursting Bubble
- 1A. Living in the Media Age
- In Your World: Fact Checking on the Web
- 1B. Propositions and Truth Values
- 1C. Sets and Venn Diagrams
- Brief Review: Sets of Numbers
- 1D. Analyzing Arguments
- Mathematical Insight: Deductive Proof of the Pythagorean Theorem
- 1E. Critical Thinking in Everyday Life
- In Your World: Beware of “Up to” Deals
- 2. Approaches to Problem Solving
- Activity: Global Melting
- 2A. Understand, Solve, and Explain
- Brief Review: Common Fractions
- Brief Review: Decimal Fractions
- Using Technology: Currency Exchange Rates
- In Your World: Changing Money in Foreign Countries
- 2B. Extending Unit Analysis
- In Your World: Gems and Gold Jewelry
- Brief Review: Powers of 10
- Using Technology: Metric Conversions
- In Your World: Save Money and Save the Earth
- 2C. Problem-Solving Hints
- Mathematical Insight: Zeno’s Paradox
- 3. Numbers in the Real World
- Activity: Big Numbers
- 3A. Uses and Abuses of Percentages
- Brief Review: Percentages
- Brief Review: What Is a Ratio?
- 3B. Putting Numbers in Perspective
- Brief Review: Working with Scientific Notation
- Using Technology: Scientific Notation
- 3C. Dealing with Uncertainty
- Brief Review: Rounding
- Using Technology: Rounding in Excel
- 3D. Index Numbers: The CPI and Beyond
- Using Technology: The Inflation Calculator
- In Your World: The Chained CPI and the Federal Budget
- 3E. How Numbers Can Deceive: Polygraphs, Mammograms, and More
- 4. Managing Money
- Activity: Student Loans
- 4A. Taking Control of Your Finances
- 4B. The Power of Compounding
- Brief Review: Powers and Roots
- Using Technology: Powers
- Using Technology: The Compound Interest Formula
- Using Technology: The Compound Interest Formula for Interest Paid More Than Once a Year
- Using Technology: APY in Excel
- Using Technology: Powers of e
- Brief Review: Four Basic Rules of Algebra
- In Your World: Effects of Low Interest Rates
- 4C. Savings Plans and Investments
- Mathematical Insight: Derivation of the Savings Plan Formula
- Using Technology: The Savings Plan Formula
- Using Technology: Fractional Powers (Roots)
- In Your World: Building a Portfolio
- 4D. Loan Payments, Credit Cards, and Mortgages
- Using Technology: The Loan Payment Formula (Installment Loans)
- Mathematical Insight: Derivation of the Loan Payment Formula
- Using Technology: Principal and Interest Portions of Loan Payments
- In Your World: Avoiding Credit Card Trouble
- In Your World: Choosing or Refinancing a Loan
- 4E. Income Taxes
- 4F. Understanding the Federal Budget
- 5. Statistical Reasoning
- Activity: Cell Phones and Driving
- 5A. Fundamentals of Statistics
- Using Technology: Random Numbers
- 5B. Should You Believe a Statistical Study?
- In Your World: The Gun Debate: Defensive Gun Use
- 5C. Statistical Tables and Graphs
- Using Technology: Frequency Tables in Excel
- Using Technology: Bar Graphs and Pie Charts in Excel
- Using Technology: Line Charts in Excel
- 5D. Graphics in the Media
- Using Technology: Graphs with Multiple Data Sets
- 5E. Correlation and Causality
- Using Technology: Scatterplots in Excel
- 6. Putting Statistics to Work
- Activity: Are We Smarter Than Our Parents?
- 6A. Characterizing Data
- Using Technology: Mean, Median, and Mode in Excel
- 6B. Measures of Variation
- Using Technology: Standard Deviation in Excel
- 6C. The Normal Distribution
- Using Technology: Standard Scores and Percentiles in Excel
- 6D. Statistical Inference
- In Your World: Is Polling Reliable?
- 7. Probability: Living With The Odds
- Activity: Lotteries
- 7A. Fundamentals of Probability
- Brief Review: The Multiplication Principle
- 7B. Combining Probabilities
- 7C. The Law of Large Numbers
- 7D. Assessing Risk
- In Your World: Terrorism, Risk, and Human Psychology
- 7E. Counting and Probability
- Using Technology: Factorials
- Brief Review: Factorials
- Using Technology: Permutations
- Using Technology: Combinations
- 8. Exponential Astonishment
- Activity: Towers of Hanoi
- 8A. Growth: Linear vs. Exponential
- 8B. Doubling Time and Half-Life
- Using Technology: Logarithms
- Brief Review: Logarithms
- 8C. Real Population Growth
- In Your World: Choosing Our Fate
- 8D. Logarithmic Scales: Earthquakes, Sounds, and Acids
- In Your World: Ocean Acidification
- 9. Modeling Our World
- Activity: Climate Modeling
- 9A. Functions: The Building Blocks of Mathematical Models
- Brief Review: The Coordinate Plane
- 9B. Linear Modeling
- Using Technology: Graphing Functions
- In Your World: Algebra’s Baghdad Connection
- 9C. Exponential Modeling
- Brief Review: Algebra with Logarithms
- Mathematical Insight: Doubling Time and Half-Life Formulas
- In Your World: Changing Rates of Change
- 10. Modeling With Geometry
- Activity: Eyes in the Sky
- 10A. Fundamentals of Geometry
- Mathematical Insight: Archimedes and Pi
- In Your World: Plato, Geometry, and Atlantis
- 10B. Problem Solving with Geometry
- 10C. Fractal Geometry
- 11. Mathematics and The Arts
- Activity: Digital Music Files
- 11A. Mathematics and Music
- In Your World: Music Just for You
- 11B. Perspective and Symmetry
- 11C. Proportion and the Golden Ratio
- 12. Mathematics and Politics
- Activity: Partisan Redistricting
- 12A. Voting: Does the Majority Always Rule?
- In Your World: Counting Votes - Not as Easy as It Sounds
- 12B. Theory of Voting
- In Your World: The Electoral College and the Presidency
- 12C. Apportionment: The House of Representatives and Beyond
- 12D. Dividing the Political Pie
In the 7th Edition of Using & Understanding Mathematics, the Bennett/Briggs author team provides content and resources that help students see the relevance of math in everyday life, preparing them with math skills for college, career and life. The authors' unique pedagogy and modular approach offer an engaging and flexible combination of technology and text. In addition, this revision provides a wide range of exercises and support for students to test their knowledge of text concepts.
About the Book
- Chapter Overviews have an infographic feel including a multiple-choice question designed to illustrate an important way in which the chapter content connects with the book themes of college, career, and life.
- REVISED! Chapter 4, Managing Money has been extensively revised to include the most current financial information regarding loans, taxes and budgets.
- Now Try exercise references appear at the end of every example and direct students to a specific exercise, immediately testing their comprehension of the material.
- NEW! Caution! These short notes are found throughout the text, highlighting common errors.
- Think About It features build on the main narrative and are designed to encourage a deeper level of mathematical understanding. Examples include the proof of the Pythagorean Theorem and Zeno's paradox.
- Brief Reviews summarize key mathematical skills that students have learned previously but may require a refresher to support success in the section. These appear wherever a particular skill is first needed, and exercises based on the review boxes can be found at the end of the unit as well as in MyLab Math. These can be skipped if students already have a firm grasp of the requisite skill.
- Using Technology boxes appear throughout to highlight technologies such as Excel, graphing calculators, Apps and websites that can be used for the corresponding concept further emphasizing how the math is useful for careers and life outside the classroom.
- NEW and UPDATED! In Your World boxes focus on topics that students are likely to encounter in the world around them, whether in the news, in consumer decisions, or in political discussions. This is further enhanced with a section of In Your World exercises in the exercise sets and videos in MyLab Math.
- Quick Quizzes appear before the exercise sets, offering ten questions for students to briefly check their understanding of the unit’s concepts before attempting the homework.
- Exercises within each chapter include the following types:
- Review Questions are non-computationalrequiring students to explain and provide examples reinforcing understanding of concepts.
- Does It Make Sense? are qualitative exercises that test conceptual understanding by asking whether given statements are sensible, and then asking students to explain why or why not.
- Basic Skills & Concepts cover skills review
- Further Applications put the skills in context continuing to emphasize the relevancy of the math for college, career and life.
- In Your World exercises are similar to the In Your World feature in the text in that they have student look to the world around them to answer questions. These questions do not directly assess content in the book feature.
- Technology Exercises provide students an opportunity to practice skills with technology such as a graphing calculator, Excel®, or StatCrunch, apps or websites.
- Review Questions are non-computationalrequiring students to explain and provide examples reinforcing understanding of concepts.
New Printed Student Supplement
A printed Activity Manual is available, for those who wish to do more activities in the course. The Activity Manual is correlated to the textbook and activities can be completed by students individually or in a group. Instructor notes with background information and discussion points are provided in the Instructor’s Resources section of the MyLab Math course. The Activity Manual is available to package with the text and also appears in the MyLab Math course.
Also available with MyLab Math
MyLab™ Math is the teaching and learning platform that empowers you to reach every student. By combining trusted author content with digital tools and a flexible platform, MyLab Math personalizes the learning experience and improves results for each student. Learn more about MyLab Math.
Features of the MyLab
- Robust video program including
- NEW! A new series of example-based videos is fresh and modern, accompanied by assessment questions that give the instructor the ability to not just assign the videos but gauge student understanding.
- NEW! Dynamic Concept videos focus on some of the most interesting and challenging concepts to help students gain a deeper understanding. An engaging visuallightboard functionality is used to explain these concepts — such as comparisons of quantities, student loans, and percentages — in a visual way.
- NEW! When Will I Ever Use This? videos demonstrate how various math concepts are utilized in various jobs and careers.
- NEW! Interactive Concept Videos discuss a concept in depth and then the video pauses asking students to try a problem on their own. Incorrect answers are followed by further explanation, taking into consideration what may have led to the student selecting that particular wrong answer. Incorrect answer ‘A’ goes down one path while incorrect answer ‘B’ provides a different explanation based on why the student may have selected that option.
- In Your World videos based on the In Your World feature in the book are a fun, visual way intended to introduce topics, engage students and show the relevancy of the math in their daily lives.
- NEW! A new series of example-based videos is fresh and modern, accompanied by assessment questions that give the instructor the ability to not just assign the videos but gauge student understanding.
- NEW! Animations let students interact with the math in a visual, tangible way. These animations allow students to explore and manipulate the mathematical concepts, leading to more durable understanding. Corresponding exercises in MyLab Math make these truly assignable.
- NEW! StatCrunch® Integration — a powerful web-based statistical software that allows users to collect data, perform analyses, and generate compelling results. For this edition, StatCrunch questions have been added to relevant Technology Exercises and access to the software has been integrated into the MyLab Math course.
- Skillbuilder support integrated into the courseoffers adaptive practice designed to increase a student’s ability to complete assignments. By monitoring student performance on homework, Skill Builder adapts to each student’s needs and provides just-in-time, in-assignment practice to help them improve their proficiency of key learning objectives.
- In addition to the exercises in MyLab Math, there are also questions to assess student understanding of the following resources:
- Chapter openers
- Unit openers
- Quick Quiz
- Brief Review
- Example videos
- Dynamic concept videos
- Interactive concept videos
- Animations
- Chapter openers
- Also available, an Integrated Review version of the MyLab Math course offers a complete course for your textbook plus embedded and personalized review of prerequisite topics.
Reach every student with MyLab Math
- Deliver trusted content: You deserve teaching materials that meet your own high standards for your course. That’s why we partner with highly respected authors to develop interactive content and course-specific resources that you can trust—and that keep your students engaged.
- Empower each learner: Each student learns at a different pace. Personalized learning pinpoints the precise areas where each student needs practice, giving all students the support they need—when and where they need it—to be successful.
- Teach your course your way: Your course is unique. So whether you’d like to build your own assignments, teach multiple sections, or set prerequisites, MyLab gives you the flexibility to easily create your course to fit your needs.
- Improve student results: When you teach with MyLab, student performance improves. That’s why instructors have chosen MyLab for over 15 years, touching the lives of over 50 million students.
In the Book
- Chapter 2 Approaches to Problem Solving introduces a new 3-step strategy: Understand - Solve - Explain, moving away from the Polya based 4-step method to simplify problem solving encouraging students to more easily put it into practice.
- The financial chapter (Chapter 4, Managing Money) has been extensively revised to include the most current financial information regarding loans, taxes and budgets.
- Where particularly helpful, solutions for certain examples are broken down by step to help students follow along more easily.
- Updated data throughout the text reflects the most current information and events. Examples include health insurance, demographic data, and the federal budget.
- New In Your World boxes have been added continuing the focus on topics that students are likely to encounter in the world around them, whether in the news, consumer decisions, or political discussions.
- Caution! These short notes are found throughout the text where students tend to struggle preventing common errors and pitfalls.
- A printed Activity Manual is available for those who wish to do more activities in the course. The Activity Manual is correlated to the textbook and activities can be completed by students individually or in a group. Instructor notes with background information and discussion points are provided in the Instructor’s Resources section of the MyLab Math course. The Activity Manual is available to package with the text and also appears in the MyLab Math course.
Also available with MyLab Math
- A new lecture video series of example-based videos is fresh and modern, accompanied by assessment questions that give the instructor the ability to not just assign the videos but gauge student understanding
- Dynamic Concept videos focus on some of the most interesting and challenging concepts to help so students gain a deeper understanding. can better grasp them. An engaging visual lightboard functionality is used to explain these concepts in the world around us — such as comparisons of quantities, student loans, and percentages — in a visual way.
- Interactive Concept Videos discuss a concept in depth and then the video pauses asking students to try a problem on their own. Incorrect answers are followed by further explanation, taking into consideration what may have led to the student selecting that particular wrong answer. Incorrect answer ‘A’ goes down one path while incorrect answer ‘B’ provides a different explanation based on why the student may have selected that option.
- StatCrunch® Integration – a powerful web-based statistical software that allows users to collect data, perform analyses, and generate compelling results. For this edition, StatCrunch questions have been added to relevant Technology Exercises and access to the software has been integrated into the MyLab Math course.
- When Will I Ever Use This? videos demonstrate how various math concepts are utilized in various jobs and careers.
- Animations let students interact with the math in a visual, tangible way. These animations allow students to explore and manipulate the mathematical concepts, leading to more durable understanding. Corresponding exercises in MyLab Math make these truly assignable.
- New assessment questions corresponding to the example videos, dynamic concept videos, interactive concept videos, and animations can now be assigned in the course.
- Skillbuilder support integrated into the cour
Produktdetaljer
Om bidragsyterne
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 & 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.