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Thinking Mathematically, 8th edition

Published by Pearson (January 31, 2022) © 2023

  • Robert F. Blitzer Miami Dade College

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For courses in Liberal Arts Mathematics.

Helps students see the world as mathematical and meaningful

Thinking Mathematically captivates students with Blitzer's distinctive, relatable voice and compelling applications, which range from the value of online classes to modeling coronavirus cases to highest paid celebrities. Understanding that most students in this course are not math majors, Blitzer shows students how truly relevant and fun math can be using current data compiled from hundreds of books, magazines and online sources. The 8th Edition updates its acclaimed exercises and examples with new topics and data and offers more interactive resources for students.

Hallmark features of this title

  • Compelling applications with real-world data engage readers with Blitzer's distinctive, relatable voice, evident through the chapter and section openers, exercise sets, and Blitzer Bonus enrichment feature.
  • Well-rounded exercise sets include Concept and Vocabulary Checks, more challenging Practice Plus problems, Application exercises, Explaining the Concepts, Critical Thinking exercises, Technology exercises, and Group exercises.
  • Worked-out, annotated examples provide step-by-step solutions to help students work through "sticking points". Check Points, a similar matched problem, follow every example and give students a chance to test their understanding of the example.
  • Brief Reviews summarize prerequisite math skills that some students may need a refresh on and appear whenever a skill is first needed.
  • Voice balloons translate mathematical language into plain English, clarify problem-solving procedures, present alternative ways of understanding, and connect complex problems to basic concepts.

New and updated features of this title

  • New, relevant applications pulled from a variety of fields pique students' interest and help them see the mathematical nature of the world around them. New applications range from the COVID-19 pandemic to student college loans to smartphone use.
  • More Brief Reviews have been added to the text's sections, with some practice exercises added to key Brief Reviews for student reinforcement.
  • Content updates in the 8th edition include the inclusion of the use of spreadsheets in Ch. 8 (Personal Finance), discussion on logical fallacies in Ch. 3 (Logic), and the use of free online technology to help solve problems.
  • Margin icons at point of use now indicate if a MyLab® animation or StatCrunch® activity is available and would be helpful to enhance a student's understanding of a topic.
  • In the Annotated Instructor's Edition, a MyLab Resource List for each section indicates to instructors what resources may be useful to students, while Learning Catalytics keywords in the instructor's text help instructors easily make use of new Learning Catalytics questions that can be accessed through the MyLab course.

Features of Pearson eText for the 8th Edition

  • A new corequisite eText is available at the end of the main Thinking Mathematically eText, giving students comprehensive coverage of the prerequisite developmental topics they need to be successful in this course.
  • Videos embedded within the eText give students additional support or an alternate mode to learn, right where they need it.

Features of MyLab Math for the 8th Edition

  • Expanded corequisite coverage can work for any corequisite model.
    • Includes new Corequisite Support eText; videos and assignable exercises for each corequisite objective; Worksheets with instruction and exercises; Mindset Videos and assignable exercises; a new Corequisite Implementation Guide.
    • Premade Integrated Review assignments, including a Skills Check Quiz and a personalized homework assignment, are available for each chapter.
  • New and revised Animations powered by GeoGebra help students visualize concepts, and StatCrunch® activities help them understand certain statistical topics. These are now marked at point-of-use in the book. Margin icons indicate if a resource is available to help students understand that topic.
  • The Learning Catalytics student response system includes new text-specific questions. Keywords in the text's instructor's edition guide instructors to use this tool.
  • New, editable Enhanced Assignments for each section strategically turn off learning aids for some exercises to ensure that students can work the exercises independently. They also contain prerequisite skill exercises for gaps identified in the chapter-level Skills Check Quiz. New section-level Video Assignments are especially helpful for online or flipped classes.

(NOTE: Each chapter concludes with a Chapter Summary, Review, and Test.)

  1. Problem Solving and Critical Thinking
    • 1.1 Inductive and Deductive Reasoning
    • 1.2 Estimation, Graphs, and Mathematical Models
    • 1.3 Problem Solving
  2. Set Theory
    • 2.1 Basic Set Concepts
    • 2.2 Subsets
    • 2.3 Venn Diagrams and Set Operations
    • 2.4 Set Operations and Venn Diagrams with Three Sets
    • 2.5 Survey Problems
  3. Logic
    • 3.1 Statements, Negations, and Quantified Statements
    • 3.2 Compound Statements and Connectives
    • 3.3 Truth Tables for Negation, Conjunction, and Disjunction
    • 3.4 Truth Tables for the Conditional and the Biconditional
    • 3.5 Equivalent Statements and Variations of Conditional Statements
    • 3.6 Negations of Conditional Statements and De Morgan's Laws
    • 3.7 Arguments and Truth Tables
    • 3.8 Arguments and Euler Diagrams
  4. Number Representation and Calculation
    • 4.1 Our Hindu-Arabic System and Early Positional Systems
    • 4.2 Number Bases in Positional Systems
    • 4.3 Computation in Positional Systems
    • 4.4 Looking Back at Early Numeration Systems
  5. Number Theory and the Real Number System
    • 5.1 Number Theory: Prime and Composite Numbers
    • 5.2 The Integers; Order of Operations
    • 5.3 The Rational Numbers
    • 5.4 The Irrational Numbers
    • 5.5 Real Numbers and Their Properties; Clock Addition
    • 5.6 Exponents and Scientific Notation
    • 5.7 Arithmetic and Geometric Sequences
  6. Algebra: Equations and Inequalities
    • 6.1 Algebraic Expressions and Formulas
    • 6.2 Linear Equations in One Variable and Proportions
    • 6.3 Applications of Linear Equations
    • 6.4 Linear Inequalities in One Variable
    • 6.5 Quadratic Equations
  7. Algebra: Graphs, Functions, and Linear Systems
    • 7.1 Graphing and Functions
    • 7.2 Linear Functions and Their Graphs
    • 7.3 Systems of Linear Equations in Two Variables
    • 7.4 Linear Inequalities in Two Variables
    • 7.5 Linear Programming
    • 7.6 Modeling Data: Exponential, Logarithmic, and Quadratic Functions
  8. Personal Finance
    • 8.1 Percent, Sales Tax, and Discounts
    • 8.2 Income Tax
    • 8.3 Simple Interest
    • 8.4 Compound Interest
    • 8.5 Annuities, Methods of Saving, and Investments
    • 8.6 Cars
    • 8.7 The Cost of Home Ownership
    • 8.8 Credit Cards
  9. Measurement
    • 9.1 Measuring Length; The Metric System
    • 9.2 Measuring Area and Volume
    • 9.3 Measuring Weight and Temperature
  10. Geometry
    • 10.1 Points, Lines, Planes, and Angles
    • 10.2 Triangles
    • 10.3 Polygons, Perimeter, and Tessellations
    • 10.4 Area and Circumference
    • 10.5 Volume and Surface Area
    • 10.6 Right Triangle Trigonometry
    • 10.7 Beyond Euclidean Geometry
  11. Counting Methods and Probability Theory
    • 11.1 The Fundamental Counting Principle
    • 11.2 Permutations
    • 11.3 Combinations
    • 11.4 Fundamentals of Probability
    • 11.5 Probability with the Fundamental Counting Principle, Permutations, and Combinations
    • 11.6 Events Involving Not and Or; Odds
    • 11.7 Events Involving And; Conditional Probability
    • 11.8 Expected Value
  12. Statistics
    • 12.1 Sampling, Frequency Distributions, and Graphs
    • 12.2 Measures of Central Tendency
    • 12.3 Measures of Dispersion
    • 12.4 The Normal Distribution
    • 12.5 Problem Solving with the Normal Distribution
    • 12.6 Scatter Plots, Correlation, and Regression Lines
  13. Voting and Apportionment
    • 13.1 Voting Methods
    • 13.2 Flaws of Voting Methods
    • 13.3 Apportionment Methods
    • 13.4 Flaws of Apportionment Method 
  14. Graph Theory
    • 14.1 Graphs, Paths, and Circuits
    • 14.2 Euler Paths and Euler Circuits
    • 14.3 Hamilton Paths and Hamilton Circuits
    • 14.4 Trees

Answers to Selected Exercises

Credits

Subject Index

About our author

Bob Blitzer is a native of Manhattan and received a Bachelor of Arts degree with dual majors in mathematics and psychology (minor: English literature) from the City College of New York. His unusual combination of academic interests led him toward a Master of Arts in mathematics from the University of Miami and a doctorate in behavioral sciences from Nova University.

Bob's love for teaching mathematics was nourished for nearly 30 years at Miami Dade College, where he received numerous teaching awards, including Innovator of the Year from the League for Innovations in the Community College and an endowed chair based on excellence in the classroom. In addition to Thinking Mathematically, Bob has written textbooks covering introductory algebra, intermediate algebra, college algebra, algebra and trigonometry, precalculus, and trigonometry. When not secluded in his Northern California writer's cabin, Bob can be found hiking the beaches and trails of Point Reyes National Seashore and tending to the chores required by his beloved entourage of horses, chickens, and irritable roosters.

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