The Heart of Mathematics
An Invitation to Effective Thinking -- Available October 2009!
Transform your mathematics course into an engaging and mind-opening experience for even your most math-phobic students. The Heart of Mathematics: An invitation to effective thinking --now in its third edition--succeeds at reaching non-math, non-science-oriented majors and encouraging them to discover the mathematics inherent in the world around them. Infused throughout with the authors' humor and enthusiasm, The Heart of Mathematics introduces students to the most important and interesting ideas in mathematics while inspiring them to actively engage in mathematical thinking.
- Accessible, student-friendly writing style that encourages critical thinking
- "Life Lessons"-effective methods of thinking that students will retain and apply beyond the classroom
- End of section Mindscape activities for the development of application, problem-solving, and argumentation skills
- Activities that encourage collaborative learning and group work -hands-on manipulative kit that directs students to model their thinking and actively explore the world around them
New to This Edition:
- A new section (5.3) called Circuit Training: From the Königsberg Bridge Conundrum to graphs demonstrates how a specific question can lead to a whole new branch of mathematics. Important concepts arise from isolating essential features from specific conundrum.
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The new Section 5.3 Circuit Training combines well with the next Section 5.4 Feeling Edgy?: Exploring relationships among vertices, edges, and faces to give a nice introduction to graph theory.
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The second edition’s Chapter 6, Chaos and Fractals, has been re-organized to create the new Chapter 6, Fractals and Chaos. The re-organization allows the reader to more clearly appreciate the various features of fractals separately from the conundrums of chaos.
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The second edition’s Chapter 7, Taming Uncertainty, which dealt with probability and statistics has been greatly expanded and split into two new chapters: Chapter 7, Taming Uncertainty, focuses on probability while Chapter 8, Meaning from Data, treats statistical reasoning.
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In Chapter 7, Taming Uncertainty, readers will find intriguing illustrations of what to expect from randomness. Visual examples and results from coin flips illustrate the wisdom that from randomness, we should learn to expect the unexpected.
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A new section in Chapter 7 discusses several real-life issues involving probability:
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the meaning of the surprisingly poorly understood phrase, “There is a 30% chance of rain tomorrow.”
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some game theory including an application to decision-making on the football field, and
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how a doctor can use probabilistic reasoning when new test results alter the diagnosis of a disease.
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Probabilistic reasoning can help us all understand our world in a more nuanced manner. The new features of Chapter 7 explore that perspective.
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The new Chapter 8, Meaning from Data, begins by presenting statistical ideas through statistical pitfalls. These examples of dubious reasoning expose the themes that sound statistical reasoning develops.
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Chapter 8 emphasizes the challenge of taking a set of data and finding strategies for extracting meaning from those data.
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The themes of organizing, describing, and summarizing a collection of data lead naturally to the concepts of descriptive statistics.
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The goal of understanding what we can infer about an entire data set when all we actually see is a sample from that data set leads us to concepts of inferential statistics.
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Commonsense is a fundamental tenet of sound statistical reasoning, and commonsense is front and center in our presentation.
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An entirely new section presents statistical challenges in real life from estimating the numbers of Nazi tanks in World War II to understanding how great baseball players of the past might have been.
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Throughout the book, new expanded hints illustrate for the student how to apply sound methods of reasoning to selected Mindscapes.
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The expanded hints and many additional Mindscapes allow students to translate ideas into action and effective learning.
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New Mindscapes that bolster mathematical techniques allow instructors who wish to do so to include more quantitative skill development in the course along with conceptual richness.
WileyPLUS
With WileyPLUS, students achieve concept mastery in a rich structured environment that’s available 24/7. WileyPLUS includes the entire digital textbook plus interactive learning resources, immediate feedback on assignments, a gradebook to track progress, and more.
Manipulative Kit
Includes dice, platonic solids kit, Pythagorean proof puzzle, topological puzzle, Fibonacci square-to-rectangle puzzle.
WileyPLUS
With WileyPLUS, instructors personalize and manage their course more effectively with assessment, assignments, grade tracking and more. WileyPLUS’ unique service offerings provide all the help, resources, and personal support you and your students need.
Instructor's Edition
Includes an annotated TOC and supplementary frontmatter material for instructors.
Manipulative Kit
Includes dice, platonic solids kit, Pythagorean proof puzzle, topological puzzle, Fibonacci square-to-rectangle puzzle
