In the words of the author, "I have written Mathematics All Around based on the belief that there are three things a student must focus on in order to learn and remember mathematics--understanding, understanding, understanding. Instead of simply presenting the students with an equation or method and asking them to repeat the procedure, I explain the thinking behind the subject so they have a better grasp of the material and an easier time with the work. With this approach, one can discuss topics usually considered "too difficult" for liberal arts students. As a result, students end up with an understanding of and positive attitude toward many different and often challenging mathematical topics."
Features

• Motivation with Emphasis on Applications: Applications throughout the text motivate the discussion of the mathematics and increase the student's interest in the material. In addition, each chapter opener emphasizes realistic problem situations and gives a broad overview of the chapter material. Toward the end of this brief section, the author frequently presents problems to motivate the mathematics that will be discussed. After developing the necessary mathematical tools, the author returns to solve the problem, reinforcing the value of the concepts studied in the chapter.
• Problem Solving: Problem solving is one of the main themes of this text. Section 1.1 discusses strategies and principles that help the student understand and attack problems more effectively. For example, Three-Way Principle is introduced, which encourages students to approach mathematical ideas graphically, verbally, and by constructing examples. Students are returned to these discussions frequently, via the "Problem Solving" boxes, thereby making problem solving an integrated component of each chapter. Remarks titled "Some Good Advice" point out common mistakes, provide further advice on problem solving, and make connections between different areas of mathematics.
• Quiz Yourself: Each section contains numerous short quizzes called "Quiz Yourself," which students can use to check their understanding of the material immediately preceding the quiz. These quizzes can be used as a break in the flow of the lecture material and to encourage student participation.
• Highlights: Each chapter contains "Highlight" boxes that discuss the history and applications of the topics being presented. These highlights help students understand the material that they are learning in a broader context. "Historical Highlights" discuss the mathematical contributions of individuals such as Aristotle, George Polya, and Georg Cantor.
• Using Technology: Also in the "Highlight" boxes, students are encouraged to take advantage of available technology. The author explains how tools such as spreadsheets, graphing calculators, and computer algebra systems can be used effectively to solve problems.
• Exercises: The exercises begin with straightforward problems that closely follow the examples and "Quiz Yourself" questions. In addition to these problems, other exercises require the student to think critically about extensions of ideas. These also include questions that require the student to write a response. These questions may be open-ended and noncomputational in nature, or they may ask students to explain and justify their work after a short computation. The exercises in these categories are placed in a section labeled "Further Exercises." New to this edition are "Communicating Mathematics" exercises, which ask the student to write about the mathematics he/she is studying. Exercises that can be used as group exercises are circled in red.
• Summary and Chapter Test: Each chapter has a summary followed by a chapter test. Chapter test questions are cross-referenced to the sections that cover the points being tested. This enables a student who is not comfortable with a particular concept to return to the section covering that material.
• Of Further Interest: Brief sections called "Of Further Interest" introduce subjects that go beyond the main chapter material but are of interest for students. The section "The Annual Percentage Rate" in the consumer mathematics chapter illustrates this intent. Because the "Of Further Interest" section appears at the end of the chapter, it can be treated as a bonus topic or easily omitted at the instructor's discretion.