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The Heart of Mathematics: An Invitation to Effective Thinking, 3rd Edition
John Wiley and Sons Ltd, Dec 2009, Pages: 976
Make mathematics fun and satisfying for everyone
Math can be a living source of powerful ideas that transcend mathematics; a window into mind-opening philosophical concepts such as infinity, fourth dimensions, chaos, and fractals; and a practical training ground for developing skills in analysis, reasoning, and thought, if you have the right approach and the right guide.
The Heart of Mathematics: An Invitation to Effective Thinking, now in its third edition, transforms mathematics into an engaging, relevant experience even for the most math-phobic student. Infusing this book with humor and enthusiasm, Edward B. Burger and Michael Starbird, both recipients of the Mathematical Association of America’s foremost national teaching award and countless state, regional, and campus-wide teaching honors introduce students to the most important and interesting ideas in mathematics while inspiring them to actively engage in mathematical thinking.
Richer and more rewarding than ever, this new edition features:
- An emphasis on mathematical methods of investigation
- Visualization techniques that make key concepts easier to understand
- Accessible, 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
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.
- 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.
- 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.
- 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.
- 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.
- A new section in Chapter 7 discusses several real-life issues involving probability:
-- the meaning of the surprisingly poorly understood phrase, “There is a 30% chance of rain tomorrow.”
-- some game theory including an application to decision-making on the football field, and
-- how a doctor can use probabilistic reasoning when new test results alter the diagnosis of a disease.
-- Probabilistic reasoning can help us all understand our world in a more nuanced manner. The new features of Chapter 7 explore that perspective.
- 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.
- Chapter 8 emphasizes the challenge of taking a set of data and finding strategies for extracting meaning from those data.
- The themes of organizing, describing, and summarizing a collection of data lead naturally to the concepts of descriptive statistics.
- 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.
- Commonsense is a fundamental tenet of sound statistical reasoning, and commonsense is front and center in our presentation.
- 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.
- Throughout the book, new expanded hints illustrate for the student how to apply sound methods of reasoning to selected Mindscapes.
- The expanded hints and many additional Mindscapes allow students to translate ideas into action and effective learning.
- 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.
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