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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.
Joy of Thinking: The Beauty and Power of Classical Mathematical Ideas is rated 4.1 out of 5 by 51.
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Rated 1 out of 5 by from Not much math here The profs go over the same things again and again. They should spend less time telling us how wonderful math is, and show a lot more examples.
Date published: 2021-12-01
Rated 3 out of 5 by from What, no streaming? While Great Courses says digital is available with the purchase of a DVD apparently not for this course, worse yet I could find no disclosure that digital content was not available. This is the first disappointment I’ve had after over 70 Great Courses.
Date published: 2021-05-11
Rated 2 out of 5 by from Disappointed Not what I expected from the reviews. Hardly any math, and too much paper cutting. The lectures on fractals was the highlight for me.
Date published: 2020-02-12
Rated 1 out of 5 by from An Old Course This course is disjointed, poorly put together, doesn't live up to its title. Presenters look at notes (no teleprompter) and have a hard time keeping the flow going. Later courses by the same presenters are well worth while. Skip this one for sure!
Date published: 2019-07-04
Rated 5 out of 5 by from An interesting set of topics, all well presented Some of the topics in this course I already had some knowledge of. But even in those areas I learned at least one new thing. I enjoyed the demonstrations and examples applied to each topic and I appreciated the patience that accompanied the explanations. I can see where a student with little or no knowledge of the topics covered can be rewarded with expanded understanding after taking the course.
Date published: 2017-12-16
Rated 5 out of 5 by from Entertaining as well as informative. The course has two instructors which gives the course pazzaz. The content is very interesting and informative.
Date published: 2017-09-23
Rated 5 out of 5 by from Math fun advice for life Eye opening math topics with clear examples. I enjoyed the math surprises. The applications to critical thinking would be useful tools for anyone.
Date published: 2017-06-26
Rated 4 out of 5 by from Fun & well presented Review of course #1423 made in 2003 The Joy of Thinking 4 star , but highly recommended. Each presenter is fun to watch, good clear diction, clearly knows the subject, very enthusiastic. My background in math, statistics, computers, etc. made most of their concepts easy, fundamental , and well presented. Very good graphics to illustrate the concepts. Last lesson # 24 very good – 10 points: 1. Just do it 2. Make mistakes & fail, but never give up. 3. Keep an open mind. 4. Explore the consequences of new ideas. 5. Seek the essential. 6. Understand the issue. 7. Understand simple things deeply. 8. Break a difficult problem into easier ones. 9. Examine issues from several pints of view. 10. Look for patterns.
Date published: 2016-11-08
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Overview

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.

About

Michael Starbird

The geometrical insights that I most like are those where different ideas come together unexpectedly to reveal some sort of a relationship that was not obvious at first

INSTITUTION

The University of Texas at Austin

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.

By This Professor

Change and Motion: Calculus Made Clear, 2nd Edition
854
Meaning from Data: Statistics Made Clear
854
What Are the Chances? Probability Made Clear
854
Edward B. Burger

For the truly wise individual, learning never ends.

INSTITUTION

Southwestern University

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.

By This Professor

Great Ideas that Bring Our World into Focus

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
How Many? Counting Surprises

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
Fermat’s Last Theorem and the Allure of Number

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
Pining for Nature’s Numbers

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
Sizing up the Fibonacci Numbers

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
The Sexiest Rectangle

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
The Hidden Beauty of the Golden Rectangle

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
The Pythagorean Theorem and Geometry of Ellipses

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
Not-so-Platonic Relationships in the Platonic Solids

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
Hunting for a Sixth Platonic Solid

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
Is There a Fourth Dimension? Can We See It?

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
The Invisible Art of the Fourth Dimension

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
A Twisted Idea—The Möbius Band

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
A One-Sided, Sealed Surface—The Klein Bottle

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
Ordinary Origami—Creating Beautiful Patterns

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
Unfolding Paper to Reveal a Fiery Fractal

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
Fractals—Infinitely Complex Creations

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
Fractal Frauds of Nature

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
Chance Surprises—Measuring Uncertainty

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
Door Number Two or Door Number Three?

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
Great Expectations—Weighing the Uncertain Future

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
Random Thoughts—Randomness in Our World

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
How Surprising are Surprising Coincidences?

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
Life Lessons Learned from Mathematical Thinking

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

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