Enjoy discovering the bold and insightful habits of thinking that arise in the world of mathematics as you grasp strategies for approaching, enjoying, and understanding the world.
The Joy of Thinking: The Beauty and Power of Classical Mathematical Ideas
Enjoy discovering the bold and insightful habits of thinking that arise in the world of mathematics as you grasp strategies for approaching, enjoying, and understanding the world.
Overview
About
Dr. Michael Starbird is Professor of Mathematics and University Distinguished Teaching Professor at The University of Texas at Austin, where he has been teaching since 1974. He received his B.A. from Pomona College in 1970 and his Ph.D. in Mathematics from the University of Wisconsin-Madison in 1974. Professor Starbird's textbook, The Heart of Mathematics: An Invitation to Effective Thinking, coauthored with Edward B. Burger, won a 2001 Robert W. Hamilton Book Award. Professors Starbird and Burger also collaborated on Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas, published in 2005. Professor Starbird has won many teaching awards, including the Mathematical Association of America's 2007 Deborah and Franklin Tepper Haimo National Award for Distinguished College or University Teaching of Mathematics, which is the association's most prestigious teaching award. It is awarded nationally to 3 people from its membership of 27,000. Professor Starbird is interested in bringing authentic understanding of significant ideas in mathematics to people who are not necessarily mathematically oriented. He has developed and taught an acclaimed class that presents higher-level mathematics to liberal arts students.
Dr. Edward B. Burger is President of Southwestern University in Georgetown, Texas. Previously, he was Francis Christopher Oakley Third Century Professor of Mathematics at Williams College. He graduated summa cum laude from Connecticut College, where he earned a BA with distinction in Mathematics. He earned his PhD in Mathematics from The University of Texas at Austin. Professor Burger is the recipient of many teaching awards and accolades. He was named by Baylor University as the 2010 recipient of the Robert Foster Cherry Award for Great Teaching for his proven record as an extraordinary teacher and distinguished scholar. Baylor University lauded Dr. Burger as truly one of our nation's most outstanding, passionate, and creative mathematics professors. His other teaching awards include the Nelson Bushnell Prize for Scholarship and Teaching from Williams College, the Distinguished Achievement Award for Educational Video Technology from the Association of Educational Publishers, and the Deborah and Franklin Tepper Haimo Award for Distinguished College or University Teaching of Mathematics from the Mathematical Association of America. In 2006 Reader's Digest honored him in its annual 100 Best of America special issue as Best Math Teacher. Professor Burger is the author of more than 40 scholarly papers and books, including Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas, which has been translated into seven languages. He was honored with the Robert W. Hamilton Book Award for his coauthored work with Michael Starbird, The Heart of Mathematics: An invitation to effective thinking. He served for three years as mathematics advisor for the educational series NUMB3RS, produced by CBS, Paramount Studios, and Texas Instruments.
01: Great Ideas that Bring Our World into Focus
A way to refine our worldview is to become more precise in describing what we see. Each of the classical theories of numbers, geometry, topology, fractals, and probability offer tools.
35 min
02: How Many? Counting Surprises
Numbers accompany us throughout our lives and play a fundamental role in the realm of mathematics. By counting and quantifying, we understand our world with more refinement.
33 min
03: Fermat’s Last Theorem and the Allure of Number
To a mathematician, numbers have their own personalities. This lecture explores the ways they have been used and understood - and have captivated humankind through the ages.
30 min
04: Pining for Nature’s Numbers
We see how a hidden order of numbers actually underlies much of nature's beauty, and explore the remarkable insights available in the pattern known as Fibonacci numbers.
30 min
05: Sizing up the Fibonacci Numbers
A potent method for discovering new insights is to isolate and examine patterns - a process that leads us to the most pleasing proportion in art and architecture: the Golden Mean.
31 min
06: The Sexiest Rectangle
We investigate our newly honed sense of mathematical aesthetics to see how it illuminates the structure behind aesthetically pleasing art and architecture to arrive at a new appreciation for what is known as the Golden Rectangle.
30 min
07: The Hidden Beauty of the Golden Rectangle
Why, exactly, is the Golden Rectangle so visually appealing? A surprising property may hold the answer.
30 min
08: The Pythagorean Theorem and Geometry of Ellipses
The Pythagorean Theorem perhaps best represents all of mathematics, and we examine some of its most elegant proofs, along with the alluring relationship between the conic section and the ellipse.
32 min
09: Not-so-Platonic Relationships in the Platonic Solids
Symmetry and regularity lie at the heart of classical beauty. The five regular, or Platonic, solids embody not only elegant symmetry but also an elegant duality in their nature.
32 min
10: Hunting for a Sixth Platonic Solid
For millennia, the five Platonic solids inspired thinkers with a mystical allure. Kepler mistakenly thought they explained the orbits of the then-known planets. But planets aren't involved, as we see when we discover why there are only five Platonic solids.
33 min
11: Is There a Fourth Dimension? Can We See It?
Though the fourth dimension lies beyond our daily experience, understanding is within our reach, and we can visualize and explore it by using our knowledge of familiar realms and arguing by analogy.
30 min
12: The Invisible Art of the Fourth Dimension
We consider the geometry of the fourth dimension, beginning with artistic works inspired by dimension, then building and visualizing our own four-dimensional cube.
31 min
13: A Twisted Idea—The Möbius Band
Must every surface have two sides? Surprisingly, the answer is no. We explore a remarkable surface known as a Möbius band.
32 min
14: A One-Sided, Sealed Surface—The Klein Bottle
Though a single-sided surface with no edge at all cannot be constructed entirely in three-dimensional space, it can be effectively described and modeled, as illustrated by the elegant surface of the Klein bottle.
30 min
15: Ordinary Origami—Creating Beautiful Patterns
Even the act of folding a piece of paper can be the gateway to a rich trove of nuance, introducing us to the idea of fractals and showing how patterns and structure can emerge from seemingly unpredictable randomness.
31 min
16: Unfolding Paper to Reveal a Fiery Fractal
Our simple paper-folding sequence leads us not only to the secrets of the dragon curve fractal, but to an example of the classic computational theory of automata developed by Alan Turing, the father of modern computing.
31 min
17: Fractals—Infinitely Complex Creations
What does it mean to speak of an infinitely detailed image? We look at what is possible by repeating a simple process infinitely and then reasoning about the result, producing images that illustrate the ideas of self-similarity and symmetry.
31 min
18: Fractal Frauds of Nature
We examine how chance, with some simple rules, leads us to an infinitely intricate world of fractals, which quite possibly overlaps with our own physical world.
30 min
19: Chance Surprises—Measuring Uncertainty
The uncertain and unknown are not forbidding territories into which we dare not tread. Instead, they can be organized and understood as we construct a means to measure the possibilities for an undetermined future.
33 min
20: Door Number Two or Door Number Three?
The game show "Let's Make a Deal®" involved a question of chance that surprises people to this day, and leads us to an exploration of probability and the ways we measure it.
31 min
21: Great Expectations—Weighing the Uncertain Future
This lecture shows us how to put a number to the possibilities of the unknowable future as it examines the quantitative measure known as expected value and how it can be used.
30 min
22: Random Thoughts—Randomness in Our World
Coincidences and random behavior do occur, often with predictable frequency. This lecture takes a look at randomness and how the principles of probability help us to understand it better.
31 min
23: How Surprising are Surprising Coincidences?
Coincidences are so striking because any particular one is extremely improbable. But what is even more improbable is that no coincidences will occur. We examine why.
31 min
24: Life Lessons Learned from Mathematical Thinking
This final lecture looks at 10 "lessons for life" that can be drawn from a range of mathematical themes and concepts.
31 min
