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

Course No. 1423
Taught By Multiple Professors
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Course No. 1423
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Course Overview

Discover mathematics as an artistic and creative realm that contains some of the greatest ideas of human history. This course explores infinity, the fourth dimension, probability, chaos, fractals, and other fantastic themes.

Is it worth Bill Gates's time to pick up a $100 bill if he sees it on the sidewalk? Amidst the frenzied screaming from the audience on television's Let's Make a Deal, is there sound advice to give the contestant trying to decide whether to swi

The world of mathematics contains some of the greatest ideas of humankind—ideas comparable to the works of Shakespeare, Plato, and Michelangelo. These mathematical ideas can add texture, beauty, and wonder to your life. Most importantly, you don't have to be a mathematician to have access to this world.

A Mathematical Journey

The Joy of Thinking is a course about fun, aesthetics, and mystery—about great mathematical ideas that arise from puzzles, observations of everyday life, and habits of curiosity and effective thinking. It is as much about learning to think abstractly as it is about what we traditionally think of as mathematics.

You 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), this course enables you to uncover and grasp insightful strategies for approaching, enjoying, and understanding the world around you.

"Wonderful ... the Best"

Taught by Professors Edward B. Burger of Williams College and Michael Starbird of the University of Texas at Austin, this course is based on their innovative textbook, The Heart of Mathematics: An invitation to effective thinking, which a reviewer for The American Mathematical Monthly called "wonderful ... possibly the best 'mathematics for the non-mathematician' book that I have seen."

Paradoxical Phenomena

Consider these examples:

  • The game show Let's Make a Deal® entertained viewers with Monty Hall urging contestants to pick a door. The choice involves a question of chance that has been the source of many heated arguments. You explore the mathematics that prepares you for future game-show stardom and explains a paradoxical example of probability.
  • Coincidences are striking because any particular one is extremely improbable. However, what is even more improbable is that no coincidence will occur. You see that finding two people having the same birthday in a room of 45 is extremely likely, by chance alone, even though the probability that any particular two people will have the same birthday is extremely low.
  • One of the most famous illustrations of randomness is the scenario of monkeys randomly typing Hamlet. Another, called "Buffon's needle," shows how random behavior can be used to estimate numbers such as pi. Physicists discovered that a similar needle-dropping model accurately predicts certain atomic phenomena.

The Fourth Dimension

Mathematical thinking leads not only to insights about our everyday lives and everyday world but also points us to worlds far beyond our own. Take the fourth dimension. The very phrase conjures up notions of science fiction or the supernatural.

Because the fourth dimension lies beyond our daily experience, visualizing, exploring, and understanding it requires us to develop an intuition about a world that we cannot see. Nevertheless, that understanding is within our reach.

You learn how to construct a four-dimensional cube and why a four-dimensional surgeon could remove your appendix without making an incision in your skin.

Fractals

Or take a world that we can see: the two-dimensional realm. It can be just as rich with surprises. You learn how the simple exercise of repeatedly folding a sheet of paper introduces the concept of fractals—a geometric pattern that is infinitely complex—repeated at ever smaller scales to produce irregular shapes and surfaces that cannot be represented by classical geometry.

You discover that the paper-folding sequence offers an example of the classical computational theory of "automata," developed by Alan Turing—the father of modern computing. Fractal construction processes may also relate to the behavior of the stock market and even to your heart rate.

Life Lessons

As Professors Burger and Starbird lead you through these and other examples, you pick up some valuable life lessons:

  • Just do it. If you're faced with a problem and you don't know how to solve it, begin by taking some action.
  • Make mistakes and fail but never give up. Mathematicians are supremely gifted at making mistakes. The key is to use the insight from your mistakes to identify the features of a correct solution to your problem.
  • Keep an open mind. If we are never willing to consider new ideas, then we can never hope to increase our understanding of the world around us.
  • Explore the consequences of new ideas. This strategy pushes us to see where an idea leads and in this way to discover new ideas and insights.
  • Seek the essential. One of the biggest obstacles in solving real-world problems is the noise and clutter of irrelevant issues that surround them.
  • Understand the issue. Identifying and clarifying the problem to be solved in a situation is often a significant step in reaching a solution.
  • Understand simple things deeply. We can never understand unknown situations without an intense focus on those aspects of the unknown that are familiar. The familiar, in other words, serves as the best guide to the unfamiliar.
  • Break a difficult problem into easier ones. This strategy is fundamental to mathematics and, indeed, applicable in everyday life.
  • Examine issues from several points of view. We can, for example, gain new insights by looking at the construction of an object, rather than the object itself.
  • Look for patterns. Similarities among situations and objects that are different on the surface should be viewed as flashing lights urging us to look for explanations. Patterns help us to structure our understanding of the world, and similarities are what we use to bring order and meaning to chaos.

The Un-Math Math

This is probably not like the mathematics you had at school. Some people might not even want to call it math, but you experience a way of thinking that opens doors, opens minds, and leaves you smiling while pondering some of the greatest concepts ever conceived.

One of the great features about mathematics is that it has an endless frontier. The farther you travel, the more you see over the emerging horizon. The more you discover, the more you understand what you've already seen, and the more you see ahead. Deep ideas truly are within the reach of us all. How many more ideas are there for you to explore and enjoy? Well, how long is your life?

tch his choice to Door Number 2? How can we see the fourth dimension in a Salvador Dali painting?

These certainly aren't the kinds of questions you would normally ask in typical lectures about mathematics. But then again, this isn't an ordinary math course.

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24 lectures
 |  Average 30 minutes each
  • 1
    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. x
  • 2
    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. x
  • 3
    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. x
  • 4
    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. x
  • 5
    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. x
  • 6
    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. x
  • 7
    The Hidden Beauty of the Golden Rectangle
    Why, exactly, is the Golden Rectangle so visually appealing? A surprising property may hold the answer. x
  • 8
    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. x
  • 9
    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. x
  • 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. x
  • 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. x
  • 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. x
  • 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. x
  • 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. x
  • 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." x
  • 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. x
  • 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. x
  • 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. x
  • 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. x
  • 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. x
  • 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. x
  • 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. x
  • 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. x
  • 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. x

Lecture Titles

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Video DVD
DVD Includes:
  • 24 lectures on 4 DVDs
  • 144-page printed course guidebook

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Course Guidebook Details:
  • 144-page printed course guidebook
  • Equations & tables
  • Suggested readings
  • Questions to consider

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Your professors

Michael Starbird Edward B. Burger

Professor 1 of 2

Michael Starbird, Ph.D.
The University of Texas at Austin

Professor 2 of 2

Edward B. Burger, Ph.D.
Southwestern University
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,...
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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 B.A. with distinction in Mathematics. He earned his Ph.D. in Mathematics from The University of Texas at Austin. Professor Burger is the recipient of many teaching...
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Reviews

Joy of Thinking: The Beauty and Power of Classical Mathematical Ideas is rated 4.3 out of 5 by 48.
Rated 3 out of 5 by from Many Gems, Much Dross, Very Basic Were the worthwhile passages of this course excerpted and presented alone, they would take up half the time and warrant a 5-star rave in every category. This is true for both professors. The gems are wonderful, from the fine introductions to Fermat's last theorem and the Fibonacci numbers, through the outstanding presentations of the Golden Rectangle, Platonic solids, and the Möbius strip and Klein bottle (Prof. Starbird makes a heroic effort to give Möbius his proper German pronunciation) , to the somewhat less stellar but still well done lessons on fractals. (The last section, on probability, was the only one whose mathematics I found poorly presented and uninteresting. And I was astonished that the overlong discussion there of what to expect from typing monkeys did not include a reference to Borge's brilliant story, "The Library of Babel.") The level of instruction is very, very basic, on purpose. This course is aimed at non-mathematicians, in fact at people who think they, um, don't care for math. (This is mostly, I think, due to the mistaken notion that all of math is like that stuff you had to learn in grade school.) If you are one of these, strongly consider the course - you may be very pleasantly surprised, and may come to a better understanding of why so many (including me) find math fascinating and wonderful. You may even decide you like math yourself. While I was already familiar with almost all of the topics presented, I still appreciated, enjoyed, and learned from them. I was disappointed that the discussion of Buffon's needle (using tosses of a needle onto a lined surface to estimate pi) in lecture 22 did not explicate the math. But the physical demonstration, in lecture 8, of why an ellipse really is a conic section, which I had never seen before, was stunning. However - that leaves half of the course as entirely forgettable. This is also true of the presentations of both professors, and comprises much unamusing silliness, many lame jokes, a condescending attitude, and a great deal of tedious repetition of very simple points. Regarding the latter, the double redundancy in lecture 8, "you pick a round sphere, a ball," is just the most concise example of what occurs throughout. Almost all of the lectures sound as if they are being given to middle schoolers. (Speaking of middle school, the repeated reference to a map of Great Britain and Ireland in lecture 17 as "England" was not very helpful.) Finally, the "life lessons" which our professors apparently think are a source of wisdom and a hook to hold our interest were, for me, just off-putting. These are found in every lecture, and include such sage advice as "just do it," "keep an open mind," "seek the essential," and "understand simple things deeply." Now, there's nothing wrong with these particular counsels, but most of them should be pretty obvious to anyone who has managed to survive to adulthood, and I found this approach to a math course to provide no added value. So - a half-wonderful, half-forgettable course. Still, I recommend it as a very worthwhile introduction to some of the truly fascinating ideas of mathematics for those with no experience in these areas.
Date published: 2015-04-16
Rated 4 out of 5 by from Introductory level I like the presentations of these two fine instructors, but the course needs to be defined for the intended audience. I would only recommend this to a person who has a limited math background [essentially high school level]. It poses many interesting features to someone who has no previous knowledge of Fibonacci, probability, fractals, topology, etc. It could whet the appetite of such a person to take a more rigorous exploration of these ideas. There is practically no math prerequisite needed here, so it should not intimidate anyone with an interest in expanding their knowledge base of some general concepts.
Date published: 2015-03-16
Rated 2 out of 5 by from The Tedium of Thinking Some of the Great Courses are specifically labeled as "high school". Perhaps if "The Joy of Thinking" had been so labeled, I would have given it another star, but to do so would almost be to insult the intelligence of the average high-schooler. These lectures are extremely simple, and describe several curious aspects of our world, Platonic solids, the Mobius band, fractals and so forth, but only at the most elementary, descriptive level. For someone who has never heard of any of these, and has never taken any kind of math or science course, these lectures provide a suitable introduction. Even so, both professors Starbird and Burger speak as if their audience consisted of children. For instance, to illustrate fractals Dr. Starbird starts with a head of broccoli, pointing out that its structure appears the same whether you look at the entire thing, or a small part of it, and says you could use this fact to convince your mother that you ate a lot of broccoli when in fact you ate only a little. The worst lectures were numbers fifteen and sixteen in which Dr. Burger spends an hour telling you what happens when you fold a piece of paper in half several times. He repeats himself endlessly. The entire subject could have been covered in ten minutes. (It's also a little annoying that Dr. Burger uses the word "actually" in almost every sentence.) I had high hopes of this course from other reviews, but found it extremely disappointing.
Date published: 2015-02-14
Rated 5 out of 5 by from Basic Concepts of Higher Mathematics This course will teach you about the basic concepts of higher mathematics: Fermat's last theorem, the golden rectangle, Platonic solids, Fibonacci numbers, the Moebius band, fractals....all sorts of wonderful things. There are two professors, Edward B. Burger, Ph.D., and Michael Starbird, Ph.D., from whom I have taken another Great Course and on whom I have developed a crush. Each lecture covers a single topic in considerable depth and explains how it applies to life. For example, make mistakes and fail but never give up (Fibonacci numbers; Sierpinski carpet), keep an open mind (fourth dimension; probability), understand simple things deeply (Klein bottle), and break a difficult problem into easier ones (fractal dragon curve; Euler characteristic). The final lecture has the two professors alternating to summarize the course. This is so valuable I copied its summary from the Guidebook. There is a timeline of mathematical development and a valuable glossary (sample entries: algorithm = procedure for solving a problem in a finite number of steps; fair game = game in which the expected value is zero; torus = a surface having the shape of the boundary of a doughnut). There also are short biographies of important mathematicians, such as Leonardo da Vinci (yes, that Leonard da Vinci), Euclid, Benoit Mandelbrot, and Srinivasa Ramanujan. Recommended as a supplement is Burger and Starbird's The Heart of Mathematics: An Invitation to Effective Thinking, which I loved so much I am not giving away along with the disks, as I usually would. If you want to know something about higher mathematics without being overwhelmed by technical stuff you can't understand, this is definitely the course you should take.
Date published: 2014-12-14
Rated 5 out of 5 by from Excellent presenters and visual aids The two lecturers were very articulate, thoughtful and fun to listen to. I was particularly impressed with their connection of mathematical thinking to the more mundane problems of life.
Date published: 2014-12-13
Rated 4 out of 5 by from A Fun and Interesting Exploration This 24 lecture course presented by Professors Starbird and Burger explores many of the somewhat eccentric and quirky mathematical ideas of history. It held my interest throughout as it explored aspects of number theory, geometry, and probability. The mathematics is not complex. However, the ideas and the basic principles behind them open up some new ways of thinking. The professors focus attention on the principles of mathematical thinking as a guiding theme throughout the course. Professors Starbird and Burger are both excellent teachers and clearly enjoy presenting this material. If you are an aficionado of Teaching Company mathematics courses you will find some of the material covered in this course a bit repetitious. Professor Benjamin’s "Joy of Mathematics", Professor Burger’s "Zero to Infinity: A History of Numbers", and Professor Starbird’s "What are the Chances? Probability Made Clear" are courses where similar material has appeared. Forays into the 4th dimension and probability issues that defy our intuition and expectations were favorite sections of the course for me. I recommend this course for those with an interest in things mathematical and for those with little previous mathematics experience. It has something to offer to everyone.
Date published: 2014-06-18
Rated 5 out of 5 by from Informative and Entertaining Mathematics can be entertaining? Professors Burger and Starbird introduce complex concepts by looking at simple things deeply. By looking at simple things deeply, cultivating an open mind, approaching an unknown from multiple perspectives, some amazing and unexpected insights can be gained. The course is divided into three sections, numbers and counting, shapes and forms, and uncertainty and the unknown. They explore the conceptual elegance, the aesthetics of mathematics and show and draw lessons applicable to any endeavor. This course is perfect for the non-math person to approach, understand and appreciate mathematics as more than a tool relegated to calculators when absolutely necessary. It requires no advanced math knowledge, just curiosity and a willingness to explore. I recommend their 2005 book, "Coincidences, Chaos, and All That Math Jazz" if you want to explore the themes of this course while viewing or to reenforce your learning. The answer to my question at the beginning of this review, is an unqualified 'Yes,' mathematics can be entertaining and learning at the same time.
Date published: 2013-06-26
Rated 5 out of 5 by from An aptly named course I enjoyed this course in no small part due to the presentation styles of Professors Starbird and Burger. It would be really, really hard to find two professors who express more “joy” and enthusiasm for their course material. The professors appear together in the first and last lectures and split the remainder between them. If I had to pick a favorite, it would be Burger, especially in his coverage of the Fibonacci numbers. However, they are both excellent lecturers offering detailed explanations which employ excellent graphics and models. The professors make a strong effort to drive a point home. If you have a good math background you may find some lectures to be a bit repetitious. However, if your math is more limited, you’ll likely find that sometimes repetitious teaching technique to be a positive. Their technique is as it should be in order to have broad appeal. This course is dependent on mathematics up through basic algebra. Math is utilized to provide insight into the world we live in…in sometimes surprising ways. Examples here would include lectures on the Fibonacci numbers, fractals and probability. In a few of the courses, mathematical and geometric concepts are explored for the sheer “Joy of Thinking” as per the course title. Lectures on the Mobius Band and the Klein bottle would fit into this category. The final lecture is philosophical in providing an approach to life based on mathematical thinking. I have a background in mathematics. It was the title of the course that intrigued me….I was interested in discovering what justified it. I didn’t expect to learn any math. However, I truly enjoyed the way these professors explored the world through math and showed math as a thing of beauty in its own right. The purchase was worth it for those reasons alone. Yes, I could quibble about the content of a few of the lectures…the two platonic solids lectures seemed to degrade into an endless discussion of vertices, edges, faces, and lines until my eyes glazed over. The lecture on the Klein bottle pushed the limits of my geometric interest. However, I felt most lectures were outstanding in both subject and content. There’s something in here for everyone. At least some interest and ability in basic math is a prerequisite to taking this course. Without it, there would be less “joy of thinking”. However, if you have any mathematical interest at all, this course will likely go a long way towards expanding upon it. I highly recommend it to those having that interest. It definitely does make you think and the course is aptly named.
Date published: 2013-04-05
Rated 5 out of 5 by from Superb course for the neophyte mathematician This course has touched my life as the two professors hoped the course would do to its participants. It has opened the doors of mathematics for me in a surprisingly accessible way.. Both profeeors are superb instructors. I appreciated the pace of delivery, the clarity and the careful presentation of material, The review lecture at the end -- the recapitulation of the course and a reminder of its application to life-- is absolutely top notch. Both professors are also very charming and delightful persons Thank you both.
Date published: 2012-08-26
Rated 4 out of 5 by from The joy of learning about Math... This is a fascinating course that, like at least two other Teaching Company courses, tries to get you interested in Mathematics. It succeeds. Great ideas are presented, and we don't have to be math teachers to understand and enjoy them. The course is easily understandable for anyone with some high school math. Professors Starbird and Burger do the impossible, by making math enjoyable. You won't learn advanced Calculus here, but you might be motivated to learn more math, after watching the course. I especially enjoyed the later lectures on uncertainty, chance, randomness, and coincidence. The last lecture on Life Lessons we can learn from thinking about math was wonderful. A delightful way to spend your time.
Date published: 2012-05-08
Rated 5 out of 5 by from Outstanding tour through math concepts This course is fascinating, and something I've been searching for for awhile! I wanted a nice overview of what mathematics tells us about the real world, and how mathematicians came to figure out how to apply equations and math concepts to real world scenarios. This is exactly what I wanted! I feel like I'm getting a great overview of how math extends thinking, how it's applied to real world objects, and how math can lead beyond our usual way of thinking. I have Professor Burger in a few of my other math courses. He's a great teacher, very entertaining, and at times just silly. But it's wonderful to see how enthusiastic both of these teachers are, and it's infectious. Now I can see some math areas I'm interested in learning more about, in addition to the algebra and geometry I've been learning. I hated math growing up, and now at almost 50 years old I'm fascinated by it!
Date published: 2012-03-20
Rated 4 out of 5 by from Should be "math for the non-mathematician" This is another course from the teaching Company that fills the need for prerequisite courses or jumping off spots for more rigorous material. It really should be retitled "mathematics for the non-mathematician". The two professors pair off and alternately present different aspects of our everyday experience and deftly make the connection with understandable, yet sophisticated mathematical concepts. If you are not mathematically inclined but yearn to better understand things "mathematical", then this is a course you will appreciate.
Date published: 2011-10-05
Rated 4 out of 5 by from Good, but redundant I watched this course about 5 years ago before TTC had us review the courses. So I have bgeen looking at my list to see what courses I had a strong memory of. This was one of them. What I remembered about this course was that it had good content but was way too redundant. Once the point was made it was repeated a couple of times more just to be sure we got it. Maybe I know too much math to have taken this course, but it seems as if the professor felt we wouldn't get it right away so had to keep repeating his point with more examples. It was like I could have watched the first 15 minutes of each lecture and skipped to the next one.
Date published: 2011-01-14
Rated 5 out of 5 by from Best math lecture series I have found I am a lifelong math lover, and part time adjunct math instructor. I received this DVD series in conjunction with teaching this course at a local community college. I have listened to this series of lectures three times. I am always pleasantly surprised with the enjoyment I receive in watching these lectures. There is a lot of interesting content to share with my students. I would recommend this to any student wanting to discover the fun and beauty of mathematics.
Date published: 2010-08-28
Rated 5 out of 5 by from About thinking, not just math My mother asked me why it is important to study math, to which I replied that it teaches people to think. I don't think I convinced her, but I can remember how I felt that studying math (besides being hugely fun) really made a large difference in my ability to figure things out. Being able to figure things out is wonderful. It makes one more capable in the world, but even more, it just makes life more enjoyable. The teachers make a point of how the ideas they are presenting are examples of general strategies for thinking. This is totally true, though it is also true that it is practice that changes idea from being theoretical to being habits. Still, it's totally great that they bring out the ways that math can help people think more clearly. The teachers are excellent also -- they are truly passionate about helping people learn. Beth
Date published: 2010-07-07
Rated 3 out of 5 by from A little disjointed and need to be faster Although this course has some interesting insights and examples, I only give it a three star rating. Here are some insights and examples from the course that I found interesting: 1. Fibonacci patterns in nature: Pineapples, cone flower and daisy. 2. The existence of 5 platonic solids (and no more than 5). 3. The representation of fourth dimension in the third dimension. 4. Probability trivia: Door number 2 or 3 --> contemplating extreme value & how our intuition may not be accurate. 5. Non-transitive dice. 6. St Peterburg's paradox - how an infinite expected value may not mean that it's a good idea to bet any large $ amount. 7. Experiment with 2 decks of cards - withdrawing each card simultaneously and figuring out the probability we find the exact same card in the same sequence, and 8. The birthday probability trivia. But why the three star rating? Several reasons: a. Too slow & not enough insights per lecture: I define whether a course is good or not from how many new, insightful ideas I can learn from each lecture. This one here doesn't provide as many new, insightful ideas as it could have. In comparison, the course "The Art and Craft of Mathematical Problem Solving" by Prof Paul Zeits (which I have also reviewed) have many new insightful ('AHA') ideas packed (too heavily in fact! - I had to 'pause' a lot) into each lecture. I recommend faster delivery for most of the lectures in this course. b. The lectures are somewhat disjointed / too random: e.g., talking about Mobius Band and Klein Bottle --> so what? how does it link to the rest of the lectures? or how does it link to the 'geometry' section? what's the implication to the real world? c. Some typo (typing error): For e.g., in the DVD in lecture 20, the probability of winning the car by switching the first guess (in a 1 billion door example) is written on the DVD as 1 / 999,999,999 --> this is wrong! (the lecturer said it correctly - but it was written wrongly). d. I feel Prof Ed Burger is better than Prof Michael Starbird in explaining the lectures' examples, although both are enthusiastic. e. Awkward camera perspectives/angles - for instance, when Prof Michael Starbird was explaining the cones and ellipses, the camera moved from the schematics to the closed-up real example (i.e., cone held by Prof Starbird) too much that it confused me. I figured out the insight myself through my own experimentation but this could have been explained clearer by just having the camera sticking to the schematics only. f. Not enough mathematics. For instance, in lecture 22 (on randomness), Prof Ed Burger noted that the probability that the needle in Buffon's needle will cross a line is exactly equal to 2 / pi. But how was this answer arrived at?? Prof Paul Zeits, in contrast, will go through this in detail. Another example is: In lecture 23, there's a very interesting probability problem where Prof Ed Burger talked about two decks of cards and withdrawing the cards simultaneously. He said that the probability of flipping over two of the exact same cards at the same time = two thirds (66.7%). But how did he arrive at this conclusion? Out of curiosity, I googled it and couldn't find it. So I calculated this myself and found that the answer is actually 63.9% (but I could be wrong). I wish Prof Burger explained this more! g. Need answers to the questions at the back. h. Advice/life lessons too vague and basic, and most can be grouped together.
Date published: 2010-04-25
Rated 4 out of 5 by from Extremely Interesting and Fun This course was very interesting and even entertaining. The concepts explored were fun and intriguing. I especially liked the Fibonacci lecture and the fourth dimension lectures. The visuals were extremely helpful, and the professors clearly loved their subject.
Date published: 2010-02-28
Rated 5 out of 5 by from A joy to watch! I love math but left school early to pursue a musical career and never studied it again. I begged my husband to buy me this series for my birthday, 30 years on. It was not only I who loved it - my mother, who's in her 80s and says "I never understood math", was fascinated by it, and my son at age 7 was riveted by the Fibonacci and golden rectangle lectures and watched them several times. Recently I dug the CDs out again, 3 years on, and again both my mother and son were drawn in to watch. These lectures are absolutely fascinating and the professors' childlike enthusiasm for the subject adds to the fun of watching them. Bravo!
Date published: 2010-01-07
Rated 5 out of 5 by from Outstanding! My 13 year old son has a keen interest in math and his teacher gave him this as a gift. What a gift! He LOVED these lectures. He'd already read "Heart of Mathematics," by the same professors, and was familiar with many of the concepts (moebius strip, infinity, probability, etc), but he still found the DVD lectures riveting. I highly recommend this series of lectures for math lovers of all ages. (A friend who is a science professor told me that she heard these lectures some time ago, and also loved them.) What surprised me is that I enjoyed the lectures as well, and I have very little background in math. In fact, I'm widely considered a math turtle. But the lectures appealed to my imagination, and I hope to work some of the content into a novel that I'm writing. By the way, both Prof. Starbird and Prof. Burger are entertaining lecturers. Lots of humour!
Date published: 2009-08-12
Rated 5 out of 5 by from You don't have to be math-oriented I am not mathematically inclined, my husband is but I so enjoyed these lectures too. I learned things I have never been exposed to before: Fibonacci Numbers was the best lecture as was the one on 4th dimenisions, the one on fractals, etc. Okay, so I enjoyed every one of them. Dr's Starbird and Burger tag teamed the lectures and played to each others strengths - the lectures were spontaneous, natural and FUN! My husband tand I horoughly enjoyed this course. We love all the Teaching Company lectures by these two wonderful teachers. We highly recommend this course.
Date published: 2009-07-02
Rated 5 out of 5 by from Mathematical delight! In a nutshell, this course is a delight to experience. I have enjoyed it several times, sometimes showing single lectures to unsuspecting friends (especially the segments on Fibonacci numbers, fractals, and the Mobius band). It never fails to please or even amaze. You don't need a mathematics background to enjoy this course, just a curious mind. I especially recommend it for bright youngsters!
Date published: 2009-04-25
Rated 4 out of 5 by from A good worthwhile course overall Joy of Thinking: The Beauty and Power of Classical Mathematical Ideas Taught by Michael Starbird and Edward B. Burger 24 lectures on DVD In 24 lectures Dr. Starbird and Dr. Burger present a number of interesting mathematical topics .The lectures are given with much enthusiasm and effort toward making presentations entertaining and approachable. Topics are presented one per lecture with consideration to differing backgrounds that the audience may have.The topics chosen are interesting and important mathematical concepts. Examples are chosen from geometry, number theory, fractals and statistics among others.for example several lectures discuss topics in the fourth dimension. The teaching aids are well chosen to assist the viewer's comprehension. It must be difficult to provide a mathematics series which is approachable to viewers of drastically different backgrounds. With the exception of the topic on Fermat’s Last Theorem, most of the lectures could benefit from being at a bit higher level but at the same time would risk losing interest to some. A good worthwhile course overall.
Date published: 2009-03-10
Rated 5 out of 5 by from Pure Pleasure As a scientist, I'm sure I had been introduced to all of the subjects in this course before. But, I am quite certain that this was the most enjoyable review. Not only are the subjects very important for an educated person to know about, they are presented clearly and brought to life with a little of the flavor of an insiders point of view (mathematicians really do have different way of looking at the world). This course was a real pleasure to watch and to think about.
Date published: 2009-02-28
Rated 4 out of 5 by from This was a fun course As a life long maths phobe I bought this course in the hope that it would be fun and relatively easy to follow, and go very easy on the 'hard maths'. And that's exactly what it did. Yes the two professors don't actually teach together but pick a number of topics each, the introcutory lecture and the final one on the theme of' 'Now what have we learned from all this, children?' were unnecessary, and Prof Starbird is not always the most fluent speaker. But this was fun, interesting, totally unthreatening and if there are some subjects that are easier than others - well there is no need to work through and fully understand each and every lecture. On the other hand, some you will want to watch again and again. There is quite a big geek-charm factor here, all sorts of props are employed (I am sure someone raided a child's toy box) and it is all presented with great enthusiasm. To my surprise, I went on to buy more advanced lectures by both professors, which is the strongest recommendation I can think of.
Date published: 2009-02-14
Rated 3 out of 5 by from MATH IS STILL MATH These two professors do everything except stand on their heads to show you how much fun math is!!! And I still shudder when I even hear the word. These are wonderful teachers, but the subject is nothing my brain can embrace. I have to face it--math is not my cup of tea. But if it WERE my cup of tea, I'm sure there are no better math teachers than these two gentlemen. Hopefully, you will find the joy in math that is hiding from me!
Date published: 2009-01-25
Rated 5 out of 5 by from Nice intro to math beyond the textbook I realize these courses are designed for adults, but this one has broader age range appeal than most. Our whole family has enjoyed at least some lectures, and some have been great for younger kids, such as Burger's presentation of Fibonacci numbers. I recommend people skim lecture 1 or skip it altogether, and the lecture on Fermat's Last Theorem is beyond most people I know who are using the course to gain a new perspective on what mathematics is. I liked the varying lecture styles of the two presenters, and had no problem at all with the fact they didn't present together.
Date published: 2009-01-22
Rated 4 out of 5 by from Mixed reaction Overall this was a OK course, but I also have some criticisms: Although this is a "joint course" by 2 professors, they lecture separately, so there is little interplay between them . I think this could have been a more provocative course if it were really "team teaching" with each prof playing off the other. In spite of the professors trying to make it appealing, even entertaining, it never really held my interest, which is why I might not recommend it. Somehow, it seemed dry. It does seem the professors would be good for math majors, but as a "lay person" I couldn't get "into" it eve tho I wanted to. It was like an intro to "topics in mathematics" for scientists, engineers, etc. but not really approachable to me. Sorry.
Date published: 2009-01-13
Rated 5 out of 5 by from Good for math lovers and math haters My child loves math. I hated it. Or, maybe I don't. I thought I did, but I have to admit I was shocked to find, I really enjoyed this course and so did my math loving child. The professors are engaging and fun to watch. The topics like fractals are much more interesting that what most of us non math majors encountered when we were in school. This is a good buy.
Date published: 2009-01-08
Rated 3 out of 5 by from Content good but Presentation Halting This should have been better and one feels that with a bit more rehearrsal it could easily have been. Starbird and Burger have made quite a name for themsleves as popularisers of mathematics but their presentations were often halting and so not as compelling as the good material deserved - much of which is supported by good in-class and graphical representations. The problem seems arise from the classical mistake of believing that the casual approach that can work in a live lecture will necessarily work on screen. They have prepared all this wonderful material and seem to imagine that they can just 'talk to it' without realising that there is no audience interaction to make that approach work. Starbird, no doubt a wonderful mathematics professor in the flesh - is by far the worse offender of the two, often seeming to lose his way and resorting to tedious repetition (and some truly awful jokes) to fill the 30 minutes.
Date published: 2009-01-06
Rated 5 out of 5 by from As a college teacher myself, I can say that the course is fantastic.
Date published: 2008-10-17
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