Introduction to Order

The work of a curious fellow
The beginning...

Hello. My name is J. D. Jones . To find out more about me and my background just click on my name which should appear underlined and in a distinct color. That underlined and colored name is an example of a "link". I will use links throughout this on line textbook to let you jump to new topics. I assume that since you have arrived at this page you are somewhat familiar with navigating around web sites so I will not spend more time on that subject. If you need additional help, use the Help menu item on your browser.

Welcome to this on-line version of the program "Order"by M. Casco Associates. The program is intended to introduce the mathematics of chaos to non-mathematicians, in plain language, assuming only a solid high school math background. Chaos theory is finding its way into many professions, among them market analysis, medicine, manufacturing and ecology, as well as science and engineering. A person completing the program's lessons will be able to understand the references to chaos appearing in their own field and apply the principles in their work. You will find images from the science of chaos scattered around on this page, and possibly some others. Just pause your cursor over any image for its caption.

Iteration Spider Web
The Java War

Those of us who write online material including Java applets, and those of you who need to run those applets are caught in the crossfire of the Java war. Microsoft tried to take over the Java virtual machine business a few years ago and failed. Sun Microsystems, the original Java company, won that battle and Microsoft is giving up, abandoning their Java technology and their support for Java. All new computers will now be shipped with the Sun Java runtime environment (JRE). That means that when websites are updated, the authors must make a choice about whether or not to move up to the modern Java language, not constrained by the limitations of the Microsoft virtual machine. At M. Casco we have decided to move on, since the move will be have to be made sooner or later. Consequently if you have a computer shipped before 2004, you will probably need to download a free Java plugin from Sun and install it on your computer in order to use the applets included on this website. We apologize for any inconvenience. It seems that this is one of the prices we have to pay as customers for progress in the technology marketplace.

This is probably a good place to talk a bit about the organization of this course and some of the symbols you will see. There is a main thread to this story which is carried by the series of pages of which this is the first. These pages are linked together so that when you are at the end of one you may click on "Next" to go to the next one or on "Previous" to go back to the previous one. You may also click on a link to "Other" which gives you access to the course outline from where you may jump to any page. The links within the main thread are marked by a green ball like this.
main threadNext
When new terms are introduced, they will be linked to a glossary entry so if you find underlined and highlighted words in the text, just click on them to get to the definition. At the end of each page will be a link like this to jump to the glossary so you can browse for any term in which you are interested.

Regions of Order and Chaos
Section of Complex Set Boundary

Some things are easier to understand than others. Probably we will not always agree on what the hard stuff is but I may mark things that I found confusing when I was learning, with a little devil like this to alert you to trouble.
devilish hard
You might want to take extra time going over that section.
Occasionally I will include a link to my email box which looks like this to make it easy for you to leave questions for me.
Are there any questions?

This email interaction is an important benefit of this online textbook over a printed book.
From time to time I may have a tidbit of information which some folks might find interesting but which is not required to understand the material. I will use a symbol like this to indicate a link to that stuff.
extra stuff

We will begin with a review of concepts from algebra and develop the topic in such a way that we maintain its connection to "ordinary" mathematics. The presentation is compact but do not try to rush through it. These concepts will require some soak time. Take time to play around with the displays. This material is well supplemented by the book "Chaos" by James Gleik, published by Penquin Books in 1988.

Iterated Transform Image
Cross-Sections of an Attractor

During this course we will be working with fractals such as the last few images in this page. These images arise from the repeated application of less than a half-dozen lines of computer code. This program provides an introduction and some capability to produce fractal graphics for the purpose of illustrating the mathematics.

The style of the text is intentionally conversational. The concepts we present are exciting and learning them should be fun. Nothing is gained by obscuring this material in a fog of four-dollar words.

Click on the Next link to continue with this course. Click on Other to go to the list of all the lessons in the course outline.

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Page Last modified: 17-Feb-2011 09:21 AM
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