Chaos

Course No. 1333
Professor Steven Strogatz, Ph.D.
Cornell University
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Course No. 1333
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Course Overview

It has been called the third great revolution of 20th-century physics, after relativity and quantum theory. But how can something called chaos theory help you understand an orderly world? What practical things might it be good for? What, in fact, is chaos theory? "Chaos theory," according to Dr. Steven Strogatz, Director of the Center for Applied Mathematics at Cornell University, "is the science of how things change." It describes the behavior of any system whose state evolves over time and whose behavior is sensitive to small changes in its initial conditions.

The 24 lectures of Chaos take you to the heart of chaos theory as it is understood today. Taught by Professor Strogatz, an award-winning Ivy League professor and a scientist described by Nature magazine as "one of the most creative biomathematicians of the past few decades," Chaos introduces you to a fascinating discipline that has more to do with your everyday life than you may realize.

A Revolutionary Way of Thinking

Surprisingly, you have already encountered chaos theory before, although you might not have recognized it at the time. From the flapping of a butterfly's wings to the dripping of a leaky faucet, chaos theory draws a wealth of unordinary insight from the most ordinary of occurrences.

Chaos theory affects nearly every field of human knowledge and endeavor, from astronomy and zoology to the arts, the humanities, and business. It can:

  • help analysts understand price fluctuations in the stock market,
  • ensure a smooth flow of data traffic on the Internet, and
  • show insurance companies how to manage the risks of natural catastrophes.

This course shows you the importance of this revolutionary field and how it has helped us come closer than ever to solving some of life's mysteries. Today, the underlying mathematics of science's major unsolved problems—including the nature of consciousness, the origin of life, and cancer—are essentially nonlinear; express any of these problems as a mathematical system and you learn that the whole may be either more or less than the sum of its parts.

In its ability to tackle bewilderingly complex problems, chaos theory has revolutionized the way we perceive the world around us. It allows scientists to reach beyond a dependency on the analytical limitations of the deterministic, "clockwork" universe that was the legacy of thinkers like Galileo, Kepler, and especially Newton.

Throughout the lectures, Professor Strogatz makes the case for why chaos theory marks such a radical departure from traditional science:

  • It asks unusual questions at the everyday scale of human life.
  • It shifts the focus off the laws of nature and onto their consequences.
  • It uses the computer not as a calculating tool but as a means of amplifying intuition.
  • It does not reduce complex problems into their separate parts but puts the parts back together to help understand the whole.
  • It is radically interdisciplinary in an era of increasingly specialized disciplines.
  • It paints a topsy-turvy picture of the world in which simple systems can show complex behavior.
  • It is a scientific field in which change came about suddenly.

Follow the Exciting Story of Chaos

As you delve into this ever-evolving field, you learn the surprising tale of how chaos theory was discovered—a story that Professor Strogatz likens to a detective novel filled with twists and turns.

First glimpsed by the French mathematician Henri Poincaré, the notion of chaos theory was lost for nearly a century before being rediscovered—almost accidentally. It was revived by a mathematically oriented meteorologist named Edward Lorenz, whose development of the butterfly effect (the extreme sensitivity of a chaotic system to tiny changes in its initial conditions) had little impact until the 1970s and 1980s, when the wave of chaos theory finally crashed onto the shores of the scientific community.

As you follow the story of chaos theory's development, you approach the core ideas of chaos in the same way the world's greatest thinkers, grounded in their historical contexts, once did. This story not only helps you understand the fundamentals of this field, but it also helps you appreciate the extraordinary intellectual feat that chaos theory represents.

Learn Chaos Theory Visually

This course offers you a unique opportunity to get an expert's instruction on the field of chaos theory and is one of the only places outside the halls of academia where you can follow along with detailed computer graphics—specifically developed for this course—as visual aids.

"For understanding these core concepts [of chaos theory], pictures turn out to be much more powerful than formulas," notes Professor Strogatz. Forgoing a heavy reliance on advanced math, he uses clear and powerful computer graphics to clarify chaos theory's core concepts.

A large portion of the course explores the intimate relationship between chaos theory and fractals: shapes or processes whose structures repeat ad infinitum such that the tiniest parts resemble the original whole. You see how fractals are unique from more commonly known shapes like circles and cubes and how they can be used to describe a variety of processes and phenomena like the jagged coastline of Norway or the drip paintings of Jackson Pollock.

Find the Unordinary in the Ordinary

Professor Strogatz's expert guidance lays bare the complexities of chaos theory in a way that any interested layperson can understand. With the insights he provides in Chaos, news stories about key scientific discoveries and new directions in research take on a fresh importance.

Professor Strogatz is a teacher repeatedly honored by institutions and students alike. During his tenure at the Massachusetts Institute of Technology, he received the E. M. Baker Memorial Award for Excellence in Undergraduate Teaching, the university's only institute-wide teaching prize selected and awarded solely by students. In 2007, he received a lifetime achievement award for the communication of mathematics to the general public from the Joint Policy Board for Mathematics, which represents the four major American mathematical societies.

Whether charting the exciting history of the field, focusing on fractals as "the footprints of chaos," or journeying to the frontiers of chaos research, this course shows you new ways to think about and view the world around you.

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24 lectures
 |  Average 30 minutes each
  • 1
    The Chaos Revolution
    Chaos was once ignored by traditional science but is now both a pop sensation and a tremendously important field. But what is the science of chaos and why is it revolutionary and important? x
  • 2
    The Clockwork Universe
    The scientific revolution launched by Galileo, Kepler, and Newton left a great legacy: the idea of an orderly universe ruled by mathematical laws. But is there something disquieting in the idea of a vast, impersonal, clockwork universe of determinism with no room for chance? x
  • 3
    From Clockwork to Chaos
    By the late 19th century, three cracks appeared in determinism's foundations: relativity, quantum mechanics—and chaos. The "three-body problem" was considered the mathematical challenge of the era, and its solution, involving a still-unimagined chaos, eluded some of mathematics' greatest minds. x
  • 4
    Chaos Found and Lost Again
    Henri Poincaré's groundbreaking work on the three-body problem implied that a system governed by deterministic laws could still be unpredictable; chaos had crept into the clockwork. Although Poincaré invented a new, visual way of thinking about the mathematics involved, his brilliant discovery was quickly forgotten. x
  • 5
    The Return of Chaos
    For 70 years, chaos remained a scientific backwater. The calm ended with a thunderclap from a man fascinated by storms and weather. You see how Edward Lorenz discovered chaos in a model of weather patterns that allowed him to happen upon the "butterfly effect." x
  • 6
    Chaos as Disorder—The Butterfly Effect
    The butterfly effect—the extreme sensitivity of a chaotic system to tiny changes in its initial conditions—has become part of popular culture but is frequently misunderstood. You begin to understand not only its importance and power but also its limitations. x
  • 7
    Picturing Chaos as Order—Strange Attractors
    Your introduction to chaos has highlighted its unpredictable, random side, as exemplified by the butterfly effect. But there is also an amazing order inherent in chaos, and you learn how this can be visualized through the infinitely complex image known as a "strange attractor." x
  • 8
    Animating Chaos as Order—Iterated Maps
    If a strange attractor is analogous to an image created through time-lapse photography, Lorenz's "iterated map" might be the product of a series of strobe-light photographs. But despite its profound implications, Lorenz's discovery failed to attract the scientific community's notice. x
  • 9
    How Systems Turn Chaotic
    By the 1970s, there was an unprecedented convergence of disciplines. Researchers in mathematics, ecology, and fluid mechanics found themselves asking the same question: How does an orderly system suddenly turn chaotic? You see how a famous iterated map known as the logistic map reveals the most basic route. x
  • 10
    Displaying How Systems Turn Chaotic
    You deepen your understanding of the logistic map with the icon of chaos known as the orbit diagram. Its breathtaking imagery amounts to a Rosetta Stone for making sense of certain forms of chaos in the natural world. x
  • 11
    Universal Features of the Route to Chaos
    In 1978, physicist Mitchell Feigenbaum made a stunning breakthrough, showing that the logistic map displayed universal features so generic that they must also occur in nature, even though no laws of nature are built into it. You begin to understand how such universality arises. x
  • 12
    Experimental Tests of the New Theory
    In the early 1980s, painstaking experiments on such disparate systems as swirling fluids, electronic circuits, and oscillating chemical reactions confirmed the predictions of chaos theory. Overreaching by some advocates, however, has provoked a backlash of skepticism to this day. x
  • 13
    Fractals—The Geometry of Chaos
    The pioneers of chaos were bewildered by the fantastic shapes they encountered while trying to visualize chaos. In the first of several lectures devoted to these intricate shapes—now called fractals—you learn why they are so inextricably connected to chaos. x
  • 14
    The Properties of Fractals
    You are introduced to the two most distinctive properties of fractals—inexhaustible structural richness and "self-similarity," or the resemblance of the parts to the whole—before learning how the science of fractals came into being and its situation in the broader scientific landscape. x
  • 15
    A New Concept of Dimension
    Using some idealized geometric examples, you learn how to define the dimension of a fractal—discovering that the usual categories of one-, two-, or three-dimensional usually do not apply, and that fractals are so convoluted they fall somewhere in between, such as 1.26-dimensional! x
  • 16
    Fractals Around Us
    Fractals are not merely static geometric shapes but also can represent erratic processes in time, such as fluctuating stock prices, Internet data bursts, or earthquakes. You learn that their gyrations are wilder and more frequent than conventional statistical methods would predict and make their management more complex. x
  • 17
    Fractals Inside Us
    From lungs to nervous systems to the nutrient supply systems of plants, all living things are built from fractal networks. You examine this geometry of life, including a recent theory that invokes fractal architecture to explain one of the most comprehensive laws in biological science. x
  • 18
    Fractal Art
    This lecture shows you some of the manifestations of fractals in art, including the controversial drip paintings of Jackson Pollock. Some have suggested that they contain fractal characteristics that changed over the course of his career in a very systematic way. x
  • 19
    Embracing Chaos—From Tao to Space Travel
    Does chaos have practical applications? Because tiny nudges to a chaotic system can have potent effects, these systems are exceptionally responsive. You see the advantages of harnessing chaos in the dramatic story of how a NASA mathematician "surfed" the gravitational field to salvage a Japanese lunar mission gone wrong. x
  • 20
    Cloaking Messages with Chaos
    Although the feasibility of encrypting electronic messages by cloaking them in chaotic "noise" has been verified in real-world tests, questions remain. Could an eavesdropper crack the chaos? This lecture shows you what such an application could mean in a world of growing concerns about cyberterrorism, national security, and cell phone and Internet privacy. x
  • 21
    Chaos in Health and Disease
    Building on decades of biological research, chaos theorists have been asking questions about the dynamics of bodily rhythms. Can the mathematics of chaos help predict an epileptic seizure? Quell or prevent cardiac arrhythmias? Perhaps most controversially, can chaos in the body ever be a sign of health rather than of sickness? x
  • 22
    Quantum Chaos
    Can chaos theory coexist with quantum theory? Can it survive the descent to the strange world of the atom, where Newtonian trajectories dissolve into a haze of quantum probability waves? You see how scientists reconcile two radically different views of reality. x
  • 23
    Synchronization
    Large, complex systems having many interacting parts often display a remarkable capacity for organizing themselves, with their individual parts becoming synchronized. This lecture shows you systems as diverse as pendulum clocks, fireflies, heart cells, and menstrual cycles and takes you inside the opening-day swaying of London's Millennium Bridge. x
  • 24
    The Future of Science
    You review what you've learned and examine the future role of chaos theory. In a world where most of the major unsolved issues facing science—including cancer, consciousness, the origin of life, and AIDS—involve fundamentally nonlinear systems, chaos theory can be a crucial first step toward their solution x

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  • 152-page printed course guidebook
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  • 152-page printed course guidebook
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Your professor

Steven Strogatz

About Your Professor

Steven Strogatz, Ph.D.
Cornell University
Professor Steven Strogatz is the Jacob Gould Schurman Professor of Applied Mathematics and Professor of Theoretical and Applied Mechanics at Cornell University. He graduated summa cum laude from Princeton University with a B.A. in Mathematics and received his Ph.D. from Harvard University. Before joining Cornell University in 1994, Professor Strogatz was a faculty member at MIT. Professor Strogatz's books include Nonlinear...
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Reviews

Chaos is rated 4.6 out of 5 by 107.
Rated 4 out of 5 by from Very good presentation and explanation of Chaos Professor Strogatz is engaging and clearly explains what chaos IS as well as what it is not. It's a theory that seems poorly understood by the general public, and if they were to take this course, they'd end up with a solid understanding of the topic. I didn't find the course to be very challenging, but even so, it was quite informative. I see some folks complained that there was too much theory and not enough about how chaos involves 'real life' - well, I feel the opposite! I think there was more than needed about the application of chaos, and I'd have preferred to have gone more into depth about the theory. Strogatz spends more time than needed on fractals and less than needed on the rest of chaos theory, in my opinion. However, it's a light course, easy to watch and understand, and WELL worth the time spent watching it.
Date published: 2009-12-29
Rated 2 out of 5 by from Very Slow I am of a very small minority here, but I did not learn much from this course. Clearly, Professor Strogatz knows his stuff, but unfortunately it did not transfer from his mind to mine. (Of course, that is not entirely HIS fault, for I am not very adept in math or science--but then that is precisely why I sought the help of this course.) I listened very intently to the first ten or eleven lectures and then quit, frustrated by how slowly things were proceeding and by my perception that the professor was never going to get to "the POINT," which always seemed to be promised for the NEXT lecture. I think the course might have been improved by cuttng its length by half, and getting sooner to the point. This review might be helpful only to a few who, like me, are not very good with math and science; but it is my honest opinion. (And remember TTC's liberal return policy. If you think YOU might like this course, give it a try.)
Date published: 2009-12-17
Rated 5 out of 5 by from One of the best in TTC Loved listening to the course, VERY VERY VERY interesting. Haven't been that excited for ages!
Date published: 2009-10-13
Rated 5 out of 5 by from Chaos Made Fun I'm not a mathematician but I was curious about chaos so I bought this course. Out of all of the courses I've watched or listened to by the Teaching Company, this was one of the most enjoyable. I'm not sure why. I think the teacher is good and knows how to explain complex things well.
Date published: 2009-10-10
Rated 5 out of 5 by from A Wonderful Course This is a terrific exploration of chaos. It is a challenging topic and Dr. Strogatz found marvelous ways to explain chaos without losing a non-scientific listener in the math. He finds this field to be fascinating and he shares that enthusiasm with clarity. The information is valuable, interesting, and well-presented. Loved it.
Date published: 2009-07-31
Rated 5 out of 5 by from Outstanding!!! This is among the best. Professor Strogatz does a remarkable job with an intoxicating subject. This is truly as good as it gets.
Date published: 2009-06-02
Rated 4 out of 5 by from Chaos I agree with the social worker. I hoped more time spent on how chaos applies to everyday life. The subject was fascinating and well delivered, just more from the theorist point of view.
Date published: 2009-05-08
Rated 5 out of 5 by from Gentle Introduction to Chaos Dr. Strogatz does an outstanding job introducing the science of chaos and fractals. I personally would've appreciated more math, but there's plenty of fascinating qualitative concepts which did not require a more technical treatment. This course is a great way to gain a basic understanding of the key ideas of the subject, and hopefully The Teaching Company and Dr. Strogatz will consider making a Volume 2 of the course which digs deeper into the technical, mathematical details of this very fascinating field, perhaps using Dr. Strogatz's books as a basis.
Date published: 2009-05-03
Rated 5 out of 5 by from BEST PRESENTATION EVER ALL THE COURSES ARE FULL OF WONDERFUL INFORMATION: AND ALL THE PROFESSORS ARE EXTREMELY KNOWLEDGEABLE : BUT NO ONE IN THE 30-OR-SO COURSES I'VE MONITORED COMES NEAR PROFESSOR STROGATZ'S PRESENTATION SKILLS.......WELL PREPARED, ENTHUSIASTIC, WITH GREAT EYE-CONTACT RATHER THAN EVIDENT NOTE READING. VERY PERSONAL. THE MOST COMPELLING COURSE SO FAR. THANK YOU, PROFESSOR STROGATZ!!!
Date published: 2009-04-20
Rated 5 out of 5 by from The clearest way to visit Chaos I have used this in running a seminar on Chaos at a Learning in Retirement setting. Using Gleick's book, and computer demos was my original plan until I became aware of this series of lectures. They have been a God-send! We view a lecture, then have discussion, additional computer demos, and fit it into reading from Gleick. The class really likes the clarity of the presentations; they point out that Strogatz doesn't get interrupted by questions and comments as he talks and so can give his pitch with continuity (as opposed to the "live" instructor or seminar "leader"). This has been invaluable.
Date published: 2009-04-18
Rated 4 out of 5 by from Let's have a sequel! Dr. Strogatz was enthusiastic for this beginning course on chaos but let's have a sequel for those of us with stronger math skills. The course was well presented although he was not as smooth and comfortable at the beginning. Good survey course for beginners with no knowledge of chaos theory. I enjoyed it because I was familiar with chaos theory but would like to deepen my understanding of the subject.
Date published: 2009-04-18
Rated 5 out of 5 by from Who knew ? A spectacular course ! I have 2 points to make" (1) View this on a modern HD screen. On an older (or should I say ancient ) TV you lose half the detail in those extraordinary diagrams the Professor produces. (2) With the diversity of viewers, we'll never solve the problem of too much math/ too little math. Embrace what's there and enjoy !
Date published: 2009-04-09
Rated 5 out of 5 by from A great overview of Chaos I really enjoyed this series of lectures and felt it was a good introduction to Chaos. Prof Strogatz has obviously worked very hard to plan a coherent course. Also, he presented lots of analogies to help us make connections with everyday life and some of the abstract notions of Chaos. I felt he was an excellent teacher. The initial lectures were a little disjoint, Prof Strogatz seemed a little nervous, but he then got into a rhythm that i enjoyed. At times, he can labor the point, but i guess there are a wide variety of interests and abilities he has to cater for. I read with interest the other reviewers who wanted more mathematics, and i guess, i would like to go down that track too. But really that's for another course. This course certainly got my attention and has motivated me to learn more.
Date published: 2009-03-05
Rated 4 out of 5 by from A little more in depth could be better Don't get me wrong, this is a great course for the general layman, but if you are a scientist you'll be left feeling like you learned "about" something (as opposed to learning something). It's entertaining, and Professor Strogatz is a lot of fun, and makes everything clear and nice, but unfortunately, the course assumes the student doesn't know anything about math or science, and so it's pretty dumbed down. Watch it for entertainment value or to learn "about" chaos, but not really understand in any meaningful depth.
Date published: 2009-02-28
Rated 4 out of 5 by from Excellent but needs more math Given my background as a math and physics major as an undergraduate and a math-related Mater's degree I thought the course was a little light on the math. Other than that Prof. Strogatz did an excellent job of using props, computer simulation, thought experiments, analogies and other visula cues to explain the complex ideas underlying chaos and how non-linearity can cause organized disorder.
Date published: 2009-02-04
Rated 5 out of 5 by from Eyeopening - more than you think When I ordered this course, I hoped it would answer specific questions about chaos in quantum mechanics and hopefully thermodynamics. I got some of that, but not what I expected. Instead, I got more. A LOT more. To my surprise, the scope of chaos theory is a whole lot bigger than just those two topics. It is, in fact, everywhere, and I really got an eye-opening experience. In physics alone, Prof. Strogatz describes three cracks in Newton’s shield. Two of these (relativity and quantum mechanics) I already knew about. What I wasn’t prepared for was the third one, chaos theory. As it turns out – and this floored me – Newton’s seemingly-simple F=ma has chaos built in! The description of the three-body problem – and you’ll probably have to go through this more than once – is categorically mind-boggling. (I need to anticipate the professor by saying that chaos and randomness are not the same thing. Random is a total lack of determinism, but chaos – this is not a typo – is deterministic. This seems like a contradiction, but it’s not.) Most of the above is covered in the first half of this course, but there’s more. You’ll also find the difference between linear and non-linear processes (no math!) is quite a bit more than you might think, and how linear function don’t go chaotic, but non-linear ones almost always do. You’ll also be introduced to things that are ‘periodic’, those that aren’t, and how this plays into the hand of chaos. Through computer video, you’ll see how a process can start out as periodic and ‘degenerate’ into chaotic – even though the process is well-defined (deterministic). This is quite a show! You’ll also be introduced to weird things like the butterfly effect, strange attractors, and iterative maps. The third quarter of the series is devoted to fractals. Now, I’m not all that interested in these things, but I did find the lectures interesting and enjoyable. What I did find surprising is that these things propagate themselves in such a way that, in a chaotic manner, they reproduce themselves. I found this interesting; you may find more. As with most Teaching Company science and math courses, the math itself is sparse and totally optional – nothing more than high-school algebra is needed and again, even this is optional. The objective is not to give you problem-solving skills in this subject. Rather, the objective is give you a high-level view (looking from above) of the entire subject and you can decide for yourself whether you want to move on to a formal course or text-study in this subject. You may need to go through lectures, or even the whole course, more than once. But that’s the advantage of the DVD medium. The only real problem (and criticism) of this course is the professor’s use of the terms “differential equations” and “integration”. This assumes you know enough about calculus to know what these are and mean, and the implications of these processes. I would prefer the professor offer more explanation. But, if you don’t know these things and are willing to let these concepts bounce off (or research them on your own), this detracts little from what the course has to offer. Consider it a distraction and just move on. Understanding the concept of chaos does NOT require you to know the mathematical implications of calculus. As a teacher, you’ll find Prof. Strogatz enthusiastic and fast-moving. I enjoyed each and every one of these lectures. Again, this course is a looking-down view of chaos theory. You won’t come out of this course knowing everything that is to know about it – that would not be realistic – but you’ll gain an excellent high-level and conversational knowledge of the subject. In other words, if the subject comes up, you’ll be able to understand what’s being said and participate in the discussion. Even though this course wasn’t, strictly speaking, what I was looking for, I’m glad I went through it, and in my opinion, it was worth the price of admission.
Date published: 2009-01-25
Rated 3 out of 5 by from chaos I guess I am a little less enthusiastic then the other reviewers. Dr Strogatz is clearly excited about this topic. His attempts at humor are pretty corny, but he tries hard. This is a difficult topic to organize into a coherent presentation. I would recommend only to those very interested in this material.
Date published: 2009-01-19
Rated 5 out of 5 by from A fantastic journey along a fractal landscape Chaos and fractals are important and fascinating topics as they find application in science, mathematics, and society. Dr. Steven Strogatz, long at the center of this cyclone, has produced a wonderful and educational lecture. No one should pass up the experience of listening to Strogatz in order to learn about the beautiful and complex world currently being explored by mathematicians, computer scientists, and researchers in virtually all disciplines. Dr. Strogatz's superb communication skills and sense of humor – such as when he takes a bite out of the fractal broccoli – make for a compelling experience and stimulating odyssey. Buy this DVD and feed your brain!
Date published: 2009-01-16
Rated 5 out of 5 by from Eye-opening course on the Omnipresent Nonlinear Chaos is part of your life, whether you like it or not, and that is a great insight provided by this course. If you doubt it, then you might want to try to explain what happened to your 401k account last year. Steve Strogatz does a great job of preparing you to learn more on your own. Now, The Teaching Company needs to hire him (or one of your other terrific math lecturers like Michael Starbird or Ed Berger) to do a course on linear algebra.....
Date published: 2009-01-15
Rated 5 out of 5 by from Chaos Theory I enjoy viewing courses in areas that are far afield from my profession. Professor Steven Strogatz's presentation of Chaos Theory was first rate. He explained this complex theory in a way that was both undertandable, yet rigorous.
Date published: 2009-01-14
Rated 3 out of 5 by from Disagreement I was not as pleased with this course as most others are. I come to these lectures as a Ph.D. social scientist, wanted to learn about chaos theory/complexity theory. Many of these concepts are being alluded to in my field and I wanted to be able to work with them. While the lecturer is fairly good, the course was presented on a straight mathematics basis (or at least as far as I got because my interest waned near the end). There are many demonstrations, which could be a plus, but they were fairly technical in my opinion. I would rather some allusion to chaos/complexity in relation to philosophy, psychology and other human behavior topics, as well. Some applications are being developed currently and this course could benefit from a contextual discussion rather than in the confines of the sciences. Thus it had a sort of "nerdy" quality that kept it from being as approachable as it could be. If it had this approach, he'd have gotten A+ from me!
Date published: 2009-01-13
Rated 5 out of 5 by from Chaos and More from a Master A few days ago, I finished listening to Professor Steven Strogatz’s 24 lectures on chaos on four DVDs produced by The Teaching Company (TTC) in their series on Science and Mathematics in 2008. The course appears to be extremely important for a number of reasons. The first reason is that chaos theory is one of the fundamental stepping stones to our understanding of complex systems (i.e., dynamical systems with many interacting agents). The inherent nonlinear foundation of chaos brings us a bit closer to understanding emergent behaviour through its self-organization in nature (i.e., spontaneous pattern formation, without any central authority). The second reason is that the course includes fractals not only as elegant and pleasing pictures, but also as a critical concept to develop multiscale metrics that are necessary to characterize the complexity of chaos, thus allowing us to harness and control chaos. The third reason is that the course provides a number of applications of chaos, reflecting its pervasive presence in nature and artifacts. The selected applications address many nonlinear problems that could not have been handled by linear methods before. The fourth reason is that Professor Strogatz is an excellent teacher; he is a passionate and wonderful story-teller, with a vast knowledge and experience in addressing the critical issues of chaos, including synchronization of chaotic systems, while being careful to explain many inherent limitations of the present-day chaos models. Each lecture was presented in a delightful, gentle, and clear manner. Professor Strogatz appears to be a friend explaining important but difficult topics, rather than an instructor of facts and procedures. In fact, it was always easy to return to each successive lecture with a sense that something important would happen. The course was a journey and an experience. Although very few equations have been used in the course explicitly, the critical concepts have been explained in a way that is linked closely to the differential and difference equations behind them. Rather than impressing the viewer with his formidable skills in handling such mathematics, Professor Strogatz impresses us with his insightful comments related to the dynamics of chaotic systems. The actual dynamics and structure of such systems are illustrated and demonstrated using several techniques, including (i) physical models (e.g., a dual double pendulum, and synchronization of two metronomes — Wittner’s taktell wood super-mini metronomes), (ii) simulations using Java applets available on the Web, (iii) animations and videos, as well as (iv) many diagrams and still pictures. The course is also supported by many references selected according to their seminal influence and impact on the development of chaos and fractals. It is also evident that Professor Strogatz has known many of the pioneering authors personally. The Course Guidebook (148 pp.) included with the DVDs, and the Lecture Transcript Part 1 (229 pp.) and Part 2 (234 pp.) sold separately, are very good companions to the course. I have read the Guidebook prior to viewing the lectures, while the Lecture Transcript was useful in checking some facts after viewing each lecture. The course consists of three parts. It starts with 12 lectures on chaos (Part 1), followed by six lectures on fractals (Part 2), and six lectures on applications of chaos (Part 3). I have been teaching a postgraduate course on Fractal and Chaos Engineering (FCE) since January 1994, with a slightly different organization. I start from fractals and fractal dimensions as the essential measures of self-similar and self-affine objects, followed by chaos analysis and characterization through a variety of metrics, including Lyapunov exponents. As with this course, applications are emphasized throughout my FCE course. In the first part of FCE, I provide a unified theory of fractal dimensions suitable not only for monfractals, but also for multifractals (i.e., mixture of fractals). The FCE course used several textbooks, including the 1994 Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering by Professor Strogatz. In closing, I would recommend the Chaos course very highly to those who are just starting in the area, and to those who enjoy listening to a Master of the topic.
Date published: 2009-01-03
Rated 5 out of 5 by from Fascinating Subject Professor Strogatz is an excellent teacher. The practical applications of chaos, from art to health and disease, are especially interesting and often surprising. This is a great introduction to a relatively new area of science.
Date published: 2008-12-21
Rated 5 out of 5 by from Great Subject, Leading Instructor Strogatz is a leader in this field and has written one of the leading textbooks on the subject, so TTC has really scored in getting him to prepare this course. Overall, I found the course to be excellent and among the TTC courses I've enjoyed most, though I have to confess that I've dabbled in this subject since it first became hot about two decades ago. I thought that Strogatz chose a reasonable technical level for the course, and made good use of graphics, though I would have preferred somewhat more math. In that respect, the course has to be considered strictly introductory, and limited to a basic conceptual level. If you want an understanding of chaos at the advanced layperson level, you'll need to read some papers and/or books, and Strogatz provides good references in that regard. Highly recommended for anyone interested in science, and among TTC's best science courses.
Date published: 2008-12-20
Rated 5 out of 5 by from Thoroughly Exciting! This course grabbed my attention right from the start and held me in wrapped awe until the very end. Then I bought all the books. Professor Strogatz was terrific. I am not a mathematician nor a scientist and yet I understood his lectures. His book is used as the textbook for teaching this course in many colleges. After finishing this course I find myself seeing chaos theory in very many different aspects of life, from economics to migraine headaches to music, etc. Makes me wish I were a young student again and could get involved in this discipline as a career.
Date published: 2008-12-17
Rated 5 out of 5 by from Excellent Course Professor Strogatz does a beautiful job of transmitting both his knowledge and his enthusiasm for the subject of chaos. He gives thorough coverage of the topic, and he uses extensive visuals to demonstrate what might be difficult to understand in the abstract. I thorougly enjoyed this course.
Date published: 2008-12-17
Rated 3 out of 5 by from A thorough introduction to chaos Strogatz is undeniably a giant in the field of chaos. His "nutty professor" personality is fun to watch, and he's taken special care to prepare this course in a way that doesnt require the viewer to have an advanced mathematics background [although a basic understanding of high school algebra and geometry will be a big help]. The second half of the course highlights cutting edge applications of chaos theory across an impressively broad array of fields. That said, the pacing felt a little uneven at times; this course probably could have worked just fine as 12 lectures instead of 24.
Date published: 2008-11-30
Rated 5 out of 5 by from Excellent Excellent introduction to a complex but fascinating area. Very personable professor who is able to get across essential concepts clearly, interestingly, and with little need for formal math. Most importantly, does not talk down to students. This course is challenging, but worth it. (Also very highly recommended: the book "Chaos" by James Gleick.)
Date published: 2008-11-06
Rated 5 out of 5 by from Quirky Professor but he makes it work This is SUCH a fascinating subject and Professor Strogatz (although not your orthodox,play by the rules lecturer) makes the experience all the more enjoyable! He is almost as chaotic as the topic itself! (I suspect he is so by design) He made every point very well and with much clarity. I can now appreciate all the Chaos that surrounds my life, where before it was just frustrating! Thank You TTC for another life changing course!
Date published: 2008-10-26
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