HP 300: Chaos and Coherency (Honors Course)
Course Syllabus - Fall 1999

Professor : David Kaup (office : SC 353, phone : 268-2360, email : kaup@clarkson.edu)

Office Hours : MWF 11:00 - 12:00, TTh 10:00 - 12:00. I'll also be glad to make an appointment for some other time - just let me know when (call or send email).

Professor : J.A. MacDonald (office: Snell Hall 329 Ext. 3870, email: macdonaj@clarkson.edu

Office Hours: 10AM-2PM TTh (1-2PM after Nov. 17), 1-4PM W, 1-2:30PM F, and by appointment.

Professor: Hayley H. Shen (office: Rowley Lab 132 Ext. 6614, email: hhshen@clarkson.edu

Office Hours: 9:30-12:00 TTh and by appointment.

Goals: The goals of this course will be to i)improve the student's ability to communicate, ii) to give him a through understanding of the scientific method, and an ability to apply the scientific method in his career and life, and iii) to give him an understanding of how it relates to critical thinking.

Approach: For the purpose of achieving these goals, the subject of coherency and chaos will be used as a means to an end. It would be unreasonable to expect all students, regardless of their major, to achieve a given high mathematical level of competence in chaos theory. However, we shall strive to give each student an understanding of what the phenomena of coherency and chaos are, and will give examples of where these phenomena occur. We do have a wide background of students to accommodated in this course. We will try to communicate the same ideas and concepts to one and all.

The first part of the course will lay down basic concepts, such as observation, truth, causation, and effect. We shall discuss the various criteria for, and definitions of each. Key to the scientific method is how does one test for the truth of something. We shall present and discuss various means for testing for truth, or the truth of something. After the basics are introduced, we shall examine applications in the field of the financial markets (Prof. MacDonald), and in the field of granular flow (Prof. Shen).

One of the primary purposes of this course is to give the student training in the scientific method. It will also operate as an open seminar, with discussion and questions encouraged from the students. In the process of this course, you will observe your classmates, and maybe even the professors, at times, violating the scientific method. You may also observe the scientific method being subtly altered to fit the agenda of the speaker. If you observe these points, consider that you have learned something and have gained an ability in observation. Feel free to comment on them, if you wish. However, as we all know, such comments can lead to very {\it exciting} discussions. We professors will encourage such, to the extent that time will allow.

Textbooks: Required: CHAOS: Making a New Science , James Gleick [Penquin Books (1987)].
Recommended: EXPLORING CHAOS , Ed. Nina Hall [Norton & Co. (1993)].
Recommended: CHAOS And ORDER In The STOCK MARKET, Edgar E. Peters [Wiley & Sons (1991)].

Proposed Outline:

  • Week 1 -- Scientific Method, Critical Thought, and Truth. What are they? When to use what? How are they best used?
  • Week 2 -- Solitons and Coherence: What are they? What can one do with them?
  • Week 3 -- Chaos: What is it? How does one test for it? How does it differ from Coherency? Why is it not Randomness?
  • Weeks 4-7 -- Prof. MacDonald's material on Chaos in the Financial Markets.
  • Weeks 7-10 -- Presentations by Students.
  • Weeks 11-1 } -- Mixing and Chaos by Prof. H. Shen.
Seminars The textbook chosen for this course, is a descriptive book, with few mathematical equations. Thus all students are expected to be able to follow and understand it. During weeks 7-10, all students will be expected to present a seminar from some chapter in these textbooks. You may do this in pairs, in which case, your seminar would be expected to cover one period ( < 40 mins. + 10 mins. for questions). If you want to work alone, then your seminar would only cover one half of a period ( < 20 mins. + 5 mins. for questions). I suggest that you select your topic as soon as possible, before someone else selects it. Simply submit your topic to me, on a full sheet of paper, with that day's date, our course number, your name(s), and any {\it necessary} restrictions on the date of your seminar. It is expected that students whose major belongs to the topic chosen, would (or could) expand in deeper depth on the topic, than the textbook does. HOWEVER, from past experience, I would recommend that you avoid complexities, and keep it simple, but {\it through, and understandable} to your classmates.

Of course, these seminars will be graded by Profs. MacDonald, Shen and myself. The grade will be based on how well you presented the material, how understandable it was to the audience, and how much interest it generated. Each member of your audience will also critique your seminar, and submit recommended grades to the professors, based on how well they felt that you presented the material.

Research Paper: All students will prepare a research paper, somehow related to the topics of this course. It could be on an application of the Scientific Method, or a critique of some "scientific result". Prime candidates for the latter are any area where claims or predictions by authorities and/or experts of that area can be demonstrated to be untrue.

The rules for this is as follows:

  1. You must find a possible topic, go to the library and prepare a bibliography. You may (but are not required to) ask the professors in your department for suggestions. Before the end of the third week of classes, you must submit your bibliography. If it is approved, then you may continue.
  2. Before the end of the sixth week, you must submit an outline of your research paper. The outline must be somewhat detailed, defining what topics you will cover in each section of the paper. It must be approved before you can continue. It is expected that your paper will be more than just a literature survey. It must require some application of the scientific method on your part, whereby you are to present your case and then draw an independent conclusion.
  3. Before the end of the eleventh week, your research paper must have been submitted.
  4. All research papers will also contain a glossary, which will define {\bf all} technical terms used in the paper. What terms must be included? Well, if most of your classmates could not define a given term in your paper, then that term must be included in the glossary. The definition(s) of any term in the glossary must be in your own words, and must be sufficiently clear such that any of your classmates could read the definition and understand the meaning of the term. I also require that when I read your definition, then I would understand the term.
  5. The research paper must be a minimum of ten pages, excluding any title page or table of contents, in 12 pt. font, double spaced, with no more than one inch side and bottom margins, and a 1.5 inch top margin.
  6. You are expected to use correct English and to have no misspellings in your paper. You are also expected to compose the paper so that all sections and paragraphs flow easily from one to the next, with the expressed ideas and concepts being easily followed and understood by the reader (be that reader one of your classmates, or Prof. MacDonald, or Prof. Shen, or me).
  7. The grade of a research paper will be based, in part, on how well you can meet the above deadlines and criteria. Each day an item is late, will mean a 1 point penalty. Thus one week late will be a penalty of almost one letter grade.
Exams and Grades: There will be a midterm exam (15 %) and a final exam (15 %). Profs. MacDonald and Shen will each assign 15 % of the grade, based on any work that they assign during their 4 weeks of presentations. The seminar presented will count 15 % of the grade. The research paper will account for 25 % of the grade. The grading scale will be A=90-100, B=80-89, C=70-79, and D=60-69. The two exams will be based on anything covered in the course, up to that time. Emphasis will be on the material presented in the seminars, key definitions, and anything else that you would be expected to know. After all, this is an Honors Class. On the final exam, you may be asked questions from any seminar presentation, and even from your own research paper.