The Heart of Mathematics: An Invitation to Effective Thinking, 4th Edition

Book Cover

The Heart of Mathematics: An Invitation to Effective Thinking, 4th Edition

By Edward B. Burger, Michael Starbird

Now in its Fourth Edition, The Heart of Mathematics: An Invitation to Effective Thinking succeeds at reaching non-math, non-science-oriented majors, encouraging them to discover the mathematics inherent in the world around them. Infused with the authors’ humor and enthusiasm throughout, this book introduces students to the most important and interesting ideas in mathematics while inspiring them to actively engage in mathematical thinking.

WileyPLUS is a research-based, online environment for effective teaching and learning. WileyPLUS is packed with interactive study tools and resources—including the complete e-textbook—to give students more value for their money.

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Instructors can insert relevant questions at the point of learning

In the Collaborative eTextbook, you can create and assign multiple questions at various points in each chapter to engage your students.

3D images bring concepts to life

Integrated throughout the Collaborative eTextbook, vivid 3D images help to promote a more visual learning experience.

Adaptive practice helps students learn at their own pace

The new ORION Algebra Refresher module allows student lacking the needed prerequisite Algebra and Pre-Algebra skills to have a personalized, adaptive experience. Students can work on the prerequisite concepts they need to be successful in a Liberal Arts Mathematics course.

    What’s New

  • Accessible, student-friendly writing style: Engages students to read and understand the concepts and encourages critical thinking.
  • “Life Lessons” offer effective methods of thinking that students will retain and apply beyond the classroom.
  • End-of-Section Mindscape Activities promote the development of application, problem solving, and argumentation skills.
  • Activities that encourage collaborative learning and group work like the hands-on manipulative kit direct students to model their thinking and actively explore the world around them.
  • “A Look Back” provides a review of concepts taught in that section.
  • Technology Icons located throughout the book indicate an interactive activity available online (e-manipulatives).
  • Visual techniques inspire students to model their thinking and actively explore the world around them.
  • WileyPLUS for The Heart of Mathematics: An Invitation to Effective Thinking, 4th Edition provides a research-based, online environment for effective teaching and learning. WileyPLUS builds students’ confidence because it takes the guesswork out of studying by providing students with a clear roadmap: what to do, how to do it, if they did it right.


Edward B. Burger is professor of mathematics in the Department of Mathematics and Statistics at Williams College. He graduated from Connecticut College in 1985, where he earned a B.A. Summa Cum Laude with Distinction in Mathematics, and received his Ph.D. in mathematics from the University of Texas at Austin. He did his postdoctoral work at the University of Waterloo in Canada. Dr. Burger has received numerous awards, including: the Award of Excellence for “educational mathematics videos that break new ground from the Technology & Learning magazine and the Distinguished Achievement Award for Educational Video Technology from The Association of Educational Publishers. He was honored as one of the “100 Best of America,” listed in Reader’s Digest’s Annual Special Issue as Best Math Teacher. He also received the Residence Life Academic Teaching Award, University of Colorado at Boulder and the Robert W. Hamilton Book Award for The Heart of Mathematics.


Michael Starbird is a University Distinguished Teaching Professor of Mathematics at The University of Texas at Austin. He has also received numerous teaching awards, including the Mathematical Association of America’s national 2007 Deborah and Franklin Tepper Haimo Award for Distinguished College or University Teaching; the Minnie Stevens Piper Professorship, which is awarded to ten professors from any discipline or college in Texas; a 2009 inaugural UT Regents Outstanding Teaching Award; and several awards given to one professor at UT annually, including the Jean Holloway Award for Teaching Excellence, the Chad Oliver Award, and the Friar Society Centennial Teaching Fellowship. Some of these awards were significantly based on his course using The Heart of Mathematics.

Chapter 1. Fun and Games: An Introduction to Rigorous Thought
Chapter 2. Number Contemplation
Chapter 3. Infinity
Chapter 4. Geometric Gems
Chapter 5. Contortions of Space
Chapter 6. Modeling Our World Through Graphs
Chapter 7. Fractals and Chaos
Chapter 8. Taming Uncertainty
Chapter 9. Meaning from Data
Chapter 10. Deciding Wisely

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