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Jessika Richter
Jessika Richter
(Lund - Sweden)

The short and sweet: I have been a passionate teacher since 2001.  I first worked with the National Park Service in Washington (state), then moved to Australia where I completed my DipEd at the University of Melbourne and then taught at Hailebury  ...

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Similarities and Differences

Students will use WolframAlpha to make a query comparing the similarities and differences between two animals. The will identify attributes to compare and contrast.

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1. SUBJECT:  Mathematical chaos




The course will demonstrate chaos in physical experiments and in simple mathematical terms (only high school algebra). We will discuss the role of chaos in topics such as astronomy, rhythms of the heart, and pinball machines. Computer demonstrations will also be utilized to show the principles. Presentations by class members will be encouraged. Video DVD presentations will also be utilized from The Teaching Company disks on chaos.

Readings: James Gleick. Chaos: Making a New Science (Penguin reprint, 2008, original 1987), pbk $13.60 (also used). Other material will be placed on the Member Website or handed out in class. A course website has been established.



                        Weeks:             7

                        Sessions:         2 hours/week; Monday am 

                        Hours:  10-12


5. REQUIRED TEXT: James Gleick. Chaos: Making a New Science (Penguin reprint, 2008, original 1987), pbk $13.60 (also used). Other material will be placed on the Member Website or handed out in class. A course website has been established.


Retired chemical engineer, BS '52 and ScD '55 from MIT. Member of HILR since 1991.


8. COURSE GIVEN AT:HILR, Spring 2009




 Syllabus for the Chaos study group, Wednesday mornings, Spring 2009


Week 1, April 1 Reading: Gleick 1-56; Lorenz short paper on butterfly Subjects:

Use of computer programs to download and install -- Adobe pdf, Mathematica Player, Java

Lorenz Mathematica program; starting conditions, rotate figure,

What is a differential equation? (bottom page 46-47)

Experiments 3 magnet pendulum

Video of waterwheel (?)

What’s next week? (Logistic equation, difference or iterative equations.


Week 2, April 8 Reading: Gleick pages 57-80 should be read carefully; pages 81-118 are interesting but pages 98 -103 are the most relative in this section. Subjects:

Review Lorenz, differential equations(possibly video), sled program

Difference or iterative equations

Logistic equation (Mathematica program)(note fractal nature)

What’s next week? (strange attractors)


Week 3, April 15 Reading: Gleick pages 119-133 are background; 134-153 should be read carefully and are more difficult but will be discussed in greater detail. Subjects:

Strange attractors: Lorenz, Rossler, Henon (note fractal nature)(video?) (Mathematica programs)

Pendulum and double pendulum programs (Mathematica and Java) (also video)

Sled program and attractor (Mathematica programs)

What’s next week? (cobweb diagram, “universality”) 

Week 4, April 22 Reading: Gleick pages 155-168 are background; 169-181(top) read carefully; 181-211 are background. Subjects:

Logistic equations as cobweb (Mathematica programs)

Bifurcation and Feigenbaum numbers (“universality”). (video?)

What’s next week? (Famous Mandelbrot set)


Week 5, April 29 Reading: Gleick pages 213-240 are very interesting; pages 241-272 just background. Subjects:

Mandelbrot set (Mathematica, Java applets and Winfract)

Julia sets

Page 234, parameters, Sled model

What’s next week?


Week 6 , May 6 It is likely that we will fall behind this schedule so that Week 6 and week 7 will not be programmed more fully. Reading: Gleick pages 273-317 background; Afterword: page 319-324. Subjects:

Video on where chaos is going.


Week 7, May 13

Syllabus for Chaos, Spring, 2009

In this syllabus I have listed the reading to be accomplished prior to the week where it is listed. Thus the reading in Gleick, pages 1 to 56 should be read before the first session. Other readings may be listed on our course website; and I will suggest priorities for these other readings. I also will list the subjects that we will discuss in each week. During the class, I will also outline the topics to be covered in the subsequent week.

You may have questions, suggestions and/or comments. Please email these to me as they arise and I will answer by email and/or bring them up in class. Please make sure that I address any and all questions and any issues that come up. I have asked you, in this syllabus, to download and install several programs. These are all from well-recognized and reliable sources and they should install easily. I suggest using whatever the programs recommend as to where they are installed and any recommended options, that is, the “default” settings. Please let me know if you have (or don’t have) any problems with these.

Suggested downloads:

1. I assume you have the Adobe reader for reading “PDF” files. This is available at:


2. There are programs that are available or that I will make available based on mathematical programming from “Mathematica” which is made by Wolfram.com. These programs require a “player” which is available at: http://wolfram.com/products/player/

You will be asked to fill in a form with your name, etc. but there is no advertising, etc. that is used from this information. Wolfram is a very reliable company.

Once you download and install this player, you may wish to explorer their site with over 4000 demonstrations that can be run with the player: http://demonstrations.wolfram.com/

An interesting demonstration related to our first readings is the “Butterfly” by Edward Lorenz. :http://demonstrations.wolfram.com/LorenzAttractor/

click on “Download live version”.

If you put your mouse icon on the figure and hold down the left button, you can rotate the figure to see different views.

3. I have also placed under the first week a more elaborate version of the Lorenz equation with the ability to vary the initial conditions ; this will work with the Mathematica Player. The full code is shown, but cannot be edited in the Player; just ignore this.

You will note that I have listed this and other information under the first week (below). If the first week (or subsequent weeks) are changed after being announced (by email), another email will be sent to make you aware of any changes.

This email was sent out to the group members on 2/3/09.

Welcome to our chaos study group. I hope it will be interesting, informative and stimulating. I have attached the class list although Lydia believes that there may be additional members.

One of the notable aspects of "chaos" is that its recognition as a wide spread phenomenon only appeared in the late 1970's and became widely recognized in the 80's. The history of its roots, of those who first "discovered" chaos, and of the discovery and reception of the results and implications makes a fascinating story. It is this story that Gleick presents in his book, "Chaos: Making a New Science".

I picked this book by Gleick since it is the best available general presentation of the subject and with only elementary math required. It was originally published in 1987 and reissued in 2008; the reissue is identical to the original but has added a six page "afterword" that tells what happened to some of the principal players. If you have an older edition, I will give you copies of this "afterword".

In the last twenty years there has been a considerable amount of work that utilizes the concepts that we will discuss. These efforts are generally of a very technical nature well beyond our capabilities. A series of lectures were given in 2008 by an expert in this field and are available on a set of DVDs that I will be using selectively in our class discussions. It is worth noting that the expert, Dr. Steven Strogatz formerly at MIT and now at Cornell, recommends Gleick's book as essential reading for his lectures.

There is a lot of excellent material available on the internet. In order to best utilize these resources, I would like you to answer the following questions. Please send me an email with your answers. Some of the questions might be "worrisome", but I am only trying to get a feel of what can be done as an assignment versus being done in class. There may be optional additional reading or web based demonstrations.

1. Are you "comfortable" sending and receiving email?

2. Do you use the internet for reading news and/or searching for information?

3. Are you aware of the HILR Member Website (isites.harvard.edu/hilrmembers)? Do you go to it on occasion? Have you used a course website in any previous study group? I plan to have a course website where the syllabus, some additional documents and some web links will be located. (We will cover this in the first session if needed.)

4. What computer system do you use? (Windows XP, Vista, MAC). If you use a MAC, can you use Windows programs on your system?

5. What browser do you use? Some web sites may act differently, so I would like to test them in advance. (Internet Explorer, Firefox, Safari)

6. How do you connect to the web? (telephone "dial-up", DSL (Verizon), cable (Comcast or others))

7. Do you have a spreadsheet program like Excel? Have you used it at all? There are some simple programs that can be run; but you would not have to "program" them yourself.

8. Have you ever "downloaded" a program from the web and "installed" it? There are a couple of programs that I would like us to use. I will demonstrate in class how to obtain and install these. I can also provide the programs on a CD for those who have very slow connections to the internet. I expect to have them installed on the computer in the HILR Dunlop library. Again, these are all programs that demonstrate various aspects of chaos which are described in our reading and will be used in class. However, it is very interesting and helpful for the class members to explore these themselves.

Finally, I plan on putting up our syllabus on our course web site in the next few weeks. For any that desire it, I can send it by email or US Post. When it is on the web, I'll send out an email. Of course, if I don't get a reply to this email, ---.

If you have any questions, comments or suggestions, please do not hesitate to write.

Best regards to all,

Bob Lurie


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