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# Thinking Mathematically (7th Edition)

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## Book Preface

Thinking Mathematically, Seventh Edition provides a general survey of mathematical topics that are useful in our contemporary world. My primary purpose in writing the book was to show students how mathematics can be applied to their lives in interesting, enjoyable, and meaningful ways. The book’s variety of topics and flexibility of sequence make it appropriate for a one- or two-term course in liberal arts mathematics, quantitative reasoning, finite mathematics, as well as for courses specifically designed to meet state-mandated requirements in mathematics.

I wrote the book to help diverse students, with different backgrounds and career plans, to succeed. Thinking Mathematically, Seventh Edition, has four major goals:
1. To help students acquire knowledge of fundamental mathematics.
2. To show students how mathematics can solve authentic problems that apply to their lives.
3. To enable students to understand and reason with quantitative issues and mathematical ideas they are likely to encounter in college, career, and life.
4. To enable students to develop problem-solving skills, while fostering critical thinking, within an interesting setting.

One major obstacle in the way of achieving these goals is the fact that very few students actually read their textbook. This has been a regular source of frustration for me and my colleagues in the classroom. Anecdotal evidence gathered over years highlights two basic reasons why students do not take advantage of their textbook:
“I’ll never use this information.”
I’ve written every page of the Seventh Edition with the intent of eliminating these two objections. The ideas and tools I’ve used to do so are described for the student in
“A Brief Guide to Getting the Most from This Book,” which appears inside the front cover.

What’s New in the Seventh Edition?
• New and Updated Applications and Real-World Data. I’m on a constant search for real-world data that can be used to illustrate unique mathematical applications.

I researched hundreds of books, magazines, newspapers, almanacs, and online sites to prepare the Seventh Edition. This edition contains 110 worked-out examples and exercises based on new data sets and 104 examples and exercises based on updated data. New applications include student-loan debt (Exercise Set 1.2), movie rental options (Exercise Set 1.3), impediments to academic performance (Section 2.1), measuring racial prejudice, by age (Exercise Set 2.1), generational support for legalized adult marijuana use (Exercise Set 2.3), different cultural values among nations (Exercise Set 2.5), episodes from the television series The Twilight Zone (Section 3.6) and the film Midnight Express (Exercise Set 3.7), excuses by college students for not meeting assignment deadlines (Exercise Set 5.3), fraction of jobs requiring various levels of education by 2020 (Exercise Set 5.3), average earnings by college major (Exercise Set 6.5), the pay gap (Exercise Set 7.2), inmates in federal prisons for drug offenses and all other crimes (Exercise Set 7.3), time breakdown for an average 90-minute NFL broadcast (Section 11.6), Scrabble tiles (Exercise Set 11.5), and are inventors born or made? (Section 12.2).
• New Blitzer Bonuses. The Seventh Edition contains a variety of new but optional enrichment essays. There are more new Blitzer Bonuses in this edition than in any previous revision of Thinking Mathematically. These include “Surprising Friends with Induction” (Section 1.1),
“Predicting Your Own Life Expectancy” (Section 1.2),
“Is College Worthwhile?” (Section 1.2), “Yogi-isms”(Section 3.4), “Quantum Computers” (Section 4.3),
“Slope and Applauding Together” (Section 7.2),
“A Brief History of U.S. Income Tax” (Section 8.2)
“Three Decades of Mortgages” (Section 8.7), “Up to Our Ears in Debt” (Section 8.8), “The Best Financial Advice for College Graduates” (Section 8.8), “Three Weird Units of Measure” (Section 9.1), “Screen Math” (Section 10.2), “Senate Voting Power” (Section 13.3),
“Hamilton Mania” (Section 13.3), “Dirty Presidential Elections” (Section 13.3), “Campaign Posters as Art” (Section 13.4), and “The 2016 Presidential Election” (Section 13.4).
• New Graphing Calculator Screens. All screens have been updated using the TI-84 Plus C.
• Updated Tax Tables. Section 8.2 (Income Tax) contains the most current federal marginal tax tables and FICA tax rates available for the Seventh Edition.
• New MyLabTM Math. In addition to the new functionalities within an updated MyLab Math, the new items specific to Thinking Mathematically, Seventh Edition MyLab Math include
~ All new objective-level videos with assessment
~ Interactive concept videos with assessment
~ Animations with assessment
~ StatCrunch integration.

What Familiar Features Have Been Retained in the Seventh Edition?

• Chapter-Opening and Section-Opening Scenarios. Every chapter and every section open with a scenario presenting a unique application of mathematics in students’ lives outside the classroom. These scenarios are revisited in the course of the chapter or section in an example, discussion, or exercise. The often humorous tone of these openers is intended to help fearful and reluctant students overcome their negative perceptions about math. A feature called “Here’s Where You’ll Find These Applications” is included with each chapter opener.
• Section Objectives (What Am I Supposed to Learn?). Learning objectives are clearly stated at the beginning of each section. These objectives help students recognize and focus on the section’s most important ideas. The objectives are restated in the margin at their point of use.
• Detailed Worked-Out Examples. Each example is titled, making the purpose of the example clear. Examples are clearly written and provide students with detailed step-by-step solutions. No steps are omitted and each step is thoroughly explained to the right of the mathematics.
• Explanatory Voice Balloons. Voice balloons are used in a variety of ways to demystify mathematics. They translate mathematical language into everyday English, help clarify problem-solving procedures, present alternative ways of understanding concepts, and connect problem solving to concepts students have already learned.
• Check Point Examples. Each example is followed by a similar matched problem, called a Check Point, offering students the opportunity to test for conceptual understanding by working a similar exercise. The answers to the Check Points are provided in the answer section in the back of the book. Worked-out video solutions for many Check Points are in the MyLab Math course.
• Great Question! This feature presents study tips in the context of students’ questions. Answers to the questions offer suggestions for problem solving, point out common errors to avoid, and provide informal hints and suggestions. As a secondary benefit, this feature should help students not to feel anxious or threatened when asking questions in class.
• Brief Reviews. The book’s Brief Review boxes summarize mathematical skills that students should have learned previously, but which many students still need to review. This feature appears whenever a particular skill is first needed and eliminates the need to reteach that skill.
• Concept and Vocabulary Checks. The Seventh Edition contains 653 short-answer exercises, mainly fill-inthe blank and true/false items, that assess students’ understanding of the definitions and concepts presented in each section. The Concept and Vocabulary Checks appear as separate features preceding the Exercise Sets. These are assignable in the MyLab Math course.
• Extensive and Varied Exercise Sets. An abundant collection of exercises is included in an Exercise Set at the end of each section. Exercises are organized within seven category types: Practice Exercises, Practice Plus Exercises, Application Exercises, Explaining the Concepts, Critical Thinking Exercises, Technology Exercises, and Group Exercises.
• Practice Plus Problems. This category of exercises contains practice problems that often require students to combine several skills or concepts, providing instructors the option of creating assignments that take Practice Exercises to a more challenging level.
• Chapter Summaries. Each chapter contains a review chart that summarizes the definitions and concepts in every section of the chapter. Examples that illustrate these key concepts are also referenced in the chart.
• End-of-Chapter Materials. A comprehensive collection of review exercises for each of the chapter’s sections follows the Summary. This is followed by a Chapter Test that enables students to test their understanding of the material covered in the chapter. Worked-out video solutions are available for every Chapter Test Prep problem in the MyLab Math course or on YouTube.
• Learning Guide. This study aid is organized by objective and provides support for note-taking, practice, and video review. The Learning Guide is available as PDFs in MyLab Math. It can also be packaged with the textbook and MyLab Math access code.

I hope that my love for learning, as well as my respect for the diversity of students I have taught and learned from over the years, is apparent throughout this new edition. By connecting mathematics to the whole spectrum of learning, it is my intent to show students that their world is profoundly mathematical, and indeed, p is in the sky.
Robert Blitzer