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The Joy of Thinking: The Beauty and Power of Classical Mathematical Ideas

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Overview

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Discover mathematics as an artistic and creative realm that contains some of the greatest ideas of human history in these 24 lectures that explore infinity, the fourth dimension, probability, chaos, fractals, and other fantastic themes. Here are a series of lectures about fun, aesthetics, and mystery - about great mathematical ideas that arise from puzzles, observations of everyday life, and habits of curiosity and effective thinking. They are as much about learning to think abstractly as they are about what we traditionally think of as mathematics. You'll explore the fourth dimension, coincidences, fractals, the allure of number, and geometry, and bring these weighty notions back down to earth to see how they apply to your own life. Rather than focusing on adding figures or creating equations (in fact, there are fewer numbers than you might expect), the lectures enable you to uncover and grasp insightful strategies for approaching, enjoying, and understanding the world around you. This is probably not like the mathematics you had at school. Some people might not even want to call it math. But these aren't any ordinary math lectures. They're a fascinating, enjoyable way to experience the kind of thinking that opens doors, opens minds, and leaves you smiling while pondering some of the greatest concepts ever conceived.

Syllabus

  • Great Ideas that Bring Our World into Focus
  • How Many? Counting Surprises
  • Fermat’s Last Theorem and the Allure of Number
  • Pining for Nature’s Numbers
  • Sizing up the Fibonacci Numbers
  • The Sexiest Rectangle
  • The Hidden Beauty of the Golden Rectangle
  • The Pythagorean Theorem and Geometry of Ellipses
  • Not-so-Platonic Relationships in the Platonic Solids
  • Hunting for a Sixth Platonic Solid
  • Is There a Fourth Dimension? Can We See It?
  • The Invisible Art of the Fourth Dimension
  • A Twisted Idea—The Möbius Band
  • A One-Sided, Sealed Surface—The Klein Bottle
  • Ordinary Origami—Creating Beautiful Patterns
  • Unfolding Paper to Reveal a Fiery Fractal
  • Fractals—Infinitely Complex Creations
  • Fractal Frauds of Nature
  • Chance Surprises—Measuring Uncertainty
  • Door Number Two or Door Number Three?
  • Great Expectations—Weighing the Uncertain Future
  • Random Thoughts—Randomness in Our World
  • How Surprising are Surprising Coincidences?
  • Life Lessons Learned from Mathematical Thinking

Taught by

Michael Starbird and Edward B. Burger

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