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Mathematical Ideas, 14th edition

Published by Pearson (January 1, 2019) © 2020

  • Charles D. Miller American River College
  • Vern E. Heeren American River College
  • John Hornsby University of New Orleans
  • Christopher Heeren American River College

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For courses in Liberal Arts Mathematics.

Engages non-STEM students with a practical presentation

Mathematical Ideas is a versatile text that has evolved to meet changing needs, but maintains its primary objectives: comprehensive coverage, appropriate organization, clear exposition, many examples, and well-planned exercise sets with numerous applications. With a fresh focus on math in the workplace, this program shows students in liberal arts and survey courses how math plays an important role in their current and future lives, while helping them to develop a solid understanding of mathematical concepts. The 14th Edition updates hallmark features and expands teaching and learning resources.

Hallmark features of this title

  • Numerous, carefully written examples illustrate concepts and skills, giving students step-by-step directions for solving similar problems. Annotations clarify these examples and prepare students for the exercises that follow.
  • Problem-Solving Strategies found in specific sections relate the discussion of problem-solving strategies to techniques that have been presented earlier.
  • For Further Thought entries encourage students to share their reasoning processes among themselves to gain a deeper understanding of key mathematical concepts.

New and updated features of this title

  • An even stronger emphasis on career applications includes additional "When Will I Ever Use This?" feature boxes, along with many new or modified exercises tied to career applications. Updated exercise sets include over 1000 new or modified exercises; many emphasize career applications.
  • Real data in the form of graphs, charts, and tables offers updated information from online resources, magazines and newspapers to create real applications that are relevant and meaningful.
  • Actual screen captures from the TI-84 Plus C model calculator are included.
  • StatCrunch® applets and activities are available as indicated by the icon in the margin. Data sets will also be available for ease of use in the StatCrunch program.
  • Revised and additional Chapter Openers address a situation related to a particular career; some include a problem that the reader is asked to solve.
  • Concept Check questions now begin each exercise set to confirm students' understanding of concepts before they dive right into homework.

Features of MyLab Math for the 14th Edition

  • Integrated Review content uses newly developed worksheets including key terms, summaries, notes, guided problems and practice problems.
  • Corequisite course content expands on the Integrated Review course to provide additional instructional materials and exercises for use in a support course. This allows students to enroll in a corequisite course without having to purchase another text.
  • Author-developed group review modules in Learning Catalytics complement each chapter review test. Using this student engagement, assessment, and classroom intelligence system gives instructors real-time feedback on student learning before the test.
  • The Animations Library helps students explore concepts more deeply, encouraging them to visualize and interact with concepts such as Venn diagrams, probability, logic, debt, graph theory, geometry, statistics and more. An icon in the text indicates where the animations can aid in understanding.
  • Section lecture videos cover the section objectives with a modern, clear and engaging approach. The videos incorporate the use of animations, applets and StatCrunch to demonstrate concepts, making use of resources available to students in the MyLab Math course.
  • Mindset materials that help students develop a growth mindset are now included.
  1. The Art of Problem Solving
    • 1.1 Solving Problems by Inductive Reasoning
    • 1.2 An Application of Inductive Reasoning: Number Patterns
    • 1.3 Strategies for Problem Solving
    • 1.4 Numeracy in Today’s World
    • CHAPTER 1 SUMMARY
    • CHAPTER 1 TEST
  2. The Basic Concepts of Set Theory
    • 2.1 Symbols and Terminology
    • 2.2 Venn Diagrams and Subsets
    • 2.3 Set Operations
    • 2.4 Surveys and Cardinal Numbers
    • CHAPTER 2 SUMMARY
    • CHAPTER 2 TEST
  3. Introduction to Logic
    • 3.1 Statements and Quantifiers
    • 3.2 Truth Tables and Equivalent Statements
    • 3.3 The Conditional and Circuits
    • 3.4 The Conditional and Related Statements
    • 3.5 Analyzing Arguments with Euler Diagrams
    • 3.6 Analyzing Arguments with Truth Tables
    • CHAPTER 3 SUMMARY
    • CHAPTER 3 TEST
  4. Numeration Systems
    • 4.1 Historical Numeration Systems
    • 4.2 More Historical Numeration Systems
    • 4.3 Arithmetic in the Hindu-Arabic System
    • 4.4 Conversion Between Number Bases
    • CHAPTER 4 SUMMARY
    • CHAPTER 4 TEST
  5. Number Theory
    • 5.1 Prime and Composite Numbers
    • 5.2 Large Prime Numbers
    • 5.3 Selected Topics from Number Theory
    • 5.4 Greatest Common Factor and Least Common Multiple
    • 5.5 The Fibonacci Sequence and the Golden Ratio
    • 5.6 Magic Squares (online)*
    • CHAPTER 5 SUMMARY
    • CHAPTER 5 TEST
  6. The Real Numbers and Their Representations
    • 6.1 Real Numbers, Order, and Absolute Value
    • 6.2 Operations, Properties, and Applications of Real Numbers
    • 6.3 Rational Numbers and Decimal Representation
    • 6.4 Irrational Numbers and Decimal Representation
    • 6.5 Applications of Decimals and Percents
    • CHAPTER 6 SUMMARY
    • CHAPTER 6 TEST
  7. The Basic Concepts of Algebra
    • 7.1 Linear Equations
    • 7.2 Applications of Linear Equations
    • 7.3 Ratio, Proportion, and Variation
    • 7.4 Linear Inequalities
    • 7.5 Properties of Exponents and Scientific Notation
    • 7.6 Polynomials and Factoring
    • 7.7 Quadratic Equations and Applications
    • CHAPTER 7 SUMMARY
    • CHAPTER 7 TEST
  8. Graphs, Functions, and Systems of Equations and Inequalities
    • 8.1 The Rectangular Coordinate Systems and Circles
    • 8.2 Lines, Slope, and Average Rate of Change
    • 8.3 Equations of Lines
    • 8.4 Linear Functions, Graphs, and Models
    • 8.5 Quadratic Functions, Graphs, and Models
    • 8.6 Exponential and Logarithmic Functions, Graphs, and Models
    • 8.7 Systems of Linear Equations
    • 8.8 Applications of Linear Systems
    • 8.9 Linear Inequalities, Systems, and Linear Programming
    • CHAPTER 8 SUMMARY
    • CHAPTER 8 TEST
  9. Geometry
    • 9.1 Points, Lines, Planes, and Angles
    • 9.2 Curves, Polygons, Circles, and Geometric Constructions
    • 9.3 The Geometry of Triangles: Congruence, Similarity, and the Pythagorean Theorem
    • 9.4 Perimeter, Area, and Circumference
    • 9.5 Volume and Surface Area
    • 9.6 Transformational Geometry
    • 9.7 Non-Euclidian Geometry and Topology
    • 9.8 Chaos and Fractal Geometry
    • CHAPTER 9 SUMMARY
    • CHAPTER 9 TEST
  10. Counting Methods
    • 10.1 Counting by Systematic Listing
    • 10.2 Using the Fundamental Counting Principle
    • 10.3 Using Permutations and Combinations
    • 10.4 Using Pascal’s Triangle
    • 10.5 Counting Problems Involving “Not” and “Or”
    • CHAPTER 10 SUMMARY
    • CHAPTER 10 TEST
  11. Probability
    • 11.1 Basic Concepts
    • 11.2 Events Involving “Not” and “Or”
    • 11.3 Conditional Probability and Events Involving “And”
    • 11.4 Binomial Probability
    • 11.5 Expected Value and Simulation
    • CHAPTER 11 SUMMARY
    • CHAPTER 11 TEST
  12. Statistics
    • 12.1 Visual Displays of Data
    • 12.2 Measures of Central Tendency
    • 12.3 Measures of Dispersion
    • 12.4 Measures of Position
    • 12.5 The Normal Distribution
    • CHAPTER 12 SUMMARY
    • CHAPTER 12 TEST
  13. Personal Financial Management
    • 13.1 The Time Value of Money
    • 13.2 Consumer Credit
    • 13.3 Truth in Lending
    • 13.4 The Costs and Advantages of Home Ownership
    • 13.5 Financial Investments
    • CHAPTER 13 SUMMARY
  14. Graph Theory
    • 14.1 Basic Concepts
    • 14.2 Euler Circuits and Route Planning
    • 14.3 Hamilton Circuits and Algorithms
    • 14.4 Trees and Minimum Spanning Trees
    • CHAPTER 14 SUMMARY
    • CHAPTER 14 TEST
  15. Voting and Apportionment
    • 15.1 The Possibilities of Voting
    • 15.2 The Impossibilities of Voting
    • 15.3 The Possibilities of Apportionment
    • 15.4 The Impossibilities of Apportionment
    • CHAPTER 15 SUMMARY
    • CHAPTER 15 TEST

Answers to Selected Exercises (Annotated Instructor’s Edition only)

Answers to Selected Exercises (Student Edition Only)

Credits

Index of Applications

Index

About our authors

Vern Heeren grew up in the Sacramento Valley of California. After earning a Bachelor of Arts degree in mathematics with a minor in physics at Occidental College, and completing his Master of Arts degree in mathematics at the University of California - Davis, he began a 38-year teaching career at American River College teaching math and a little physics. He coauthored Mathematical Ideas in 1968 with office mate Charles Miller, and he has enjoyed researching and revising it over the years. It has been a joy for him to complete the 14th Edition along with long-time coauthor John Hornsby and with son Christopher. These days, besides pursuing his mathematical interests, Vern enjoys spending time with his wife Carole and their family, exploring the wonders of nature at and near their home in central Oregon.

John Hornsby joined the author team of Margaret Lial, Charles Miller and Vern Heeren in 1988. In 1990, the 6th Edition of Mathematical Ideas became the first of nearly 150 titles he has coauthored for Scott Foresman, HarperCollins, Addison-Wesley and Pearson in the years that have followed. His books cover the areas of developmental and college algebra, precalculus, trigonometry, and mathematics for the liberal arts. He is a native and resident of New Roads, Louisiana.

Christopher Heeren is a native of Sacramento, California. While studying engineering in college, he had an opportunity to teach a math class at a local high school, and this sparked both a passion for teaching and a change of major. He received a Bachelor of Arts degree and a Master of Arts degree, both in mathematics, from California State University, Sacramento. Chris has taught mathematics at the middle school, high school and college levels, and he currently teaches at American River College in Sacramento. He has a continuing interest in using technology to bring mathematics to life. When not writing, teaching or preparing to teach, Chris enjoys spending time with his lovely wife Heather and their 3 children.

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