Instructor: Dr. Tim Howard
Office: 215
Faculty Office Building
Phone: 706-568-2172
Email: thoward@colstate.edu
Web site: http://math.colstate.edu/thoward/
Office Hours: Please find my office hours listed on my
web site at http://math.colstate.edu/thoward/schedule.html
. If those times aren't suitable, I'll be happy to arrange an alternative
time.
The policies in this syllabus may be subject to change. Check the
above www address weekly for the latest version.
Most recent update to this syllabus: June 7, 2000.
Text. Introduction to Fractals and Chaos: Mathematics and Meaning, by Crayton W. Bedford. Published by Venture Publishing.
Prerequisites. Math 1131, Calculus with Analytic Geometry 1.
Calculators. You must have a graphing calculator for this course (I'll be using a TI-83). You may rent one from the math department for $50, with a $25 refund if you return it on time.
Grading.
Course grades will be based on
homework assignments, email journals and attendance, a midterm exam, and
a comprehensive final exam according to the following weights:
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| Homework assignments |
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| Email journal and attendance |
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| Lesson plan |
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| Midterm exam |
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| Final exam |
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To receive an "A" or a "B" as a course grade, the student must earn a passing grade in each separate category listed in the above table. Letter grades will be based upon the following percent ranges:
A: 90-100%
B: 80-89% C: 70-79%
D: 60-69%
Homework Assignments.
Your homework grade may be based upon problems
assigned from the text, possibly occasional quizzes (which may
or may not be announced), and other assigned work. Exercises
will be assigned daily from the text or from supplementary materials.
These assignments usually will be collected at the beginning of class each
Monday. Do NOT expect to have time in class for completing exercises.
Some of the homework assignments may require
use of computer software available for student use on campus at the Woodall
Hall computer labs and the mathematics computing lab in Arnold Hall (room
204). Some assistance in the use of the software will be available
in the mathematics computer lab; see the hours of operation posted on the
lab door for more information.
You are expected to see to it that homework
submissions are legible, neat, in order, and organized.
If they are not, you may be asked to re-write them and receive a penalty
for late submission.
LATE HOMEWORK: The penalty for
late homework submissions will be one point out of ten for class each day
elapsed since the due date. Once a graded homework assignment has
been returned in class, late submissions of that assignment will no longer
be accepted.
Email journal.
Each week, you must submit a journal entry by email to thoward@colstate.edu with the subject "Chaos Journal"; the subject must appear exactly in this way (observe the same use of upper and lower case letters). The purpose of the journal entries is to help me determine how class is going, determine whether or not concepts have been clear, learn what material has been enjoyable for the students, and check the work load on students. Journal entries must be submitted no later than 10:00 a.m. each Friday.
Each weekly journal entry should consist of one or two paragraphs summarizing your thoughts on the class since your previous submission. You must include the following:
Lesson Plan.
Those students taking this course for graduate level credit will be required to submit a lesson plan. The lesson plan topic must be submitted to me in writing and approved by me no later than Midterm (July 3). You should make your submission as soon as possible in case I do not approve your first proposal. Details of the required format of the lesson plan will be made available later in the term. The finalized lesson plan must be submitted no later than Tuesday, July 25.
Noteworthy Dates
Course web page.
Any modifications to the course policies and/or course syllabus will be announced on the course web page. You are expected to check the web page at least once per week. If you miss a class day, you should take special care to check the course web page and check with me as soon as possible in case you missed an assignment or an announcement.
Absentee Policy.
You are expected to attend every course meeting. Five or more absences may lead to a student getting dropped from the course with a grade of "WF" assigned.
Respectful Conduct
I intend to treat all student with respect and fairness. Since I expect the same respect from students in my courses, please observe the following policies:
Arriving late for class. Late class arrivals are disruptive and inconsiderate; moreover, they may be regarded as absences. Students who frequently arrive late may be asked not to return to class.Academic Withdrawal. The student handbook states the following:Pagers and cell phones. Use of cell phones in the class room will not be permitted; you may not bring one into the classroom unless the ringer is turned OFF. If you carry a pager, it must be set on silent mode or left outside of the classroom. Students in violation of this policy may be asked not to return to class.
To leave the university with a clear record at times other than at the end of a semester students must complete a "withdrawal form." This form, which includes instructions, is available in the Office of the Registrar, Richards Hall.Any course dropped after June 12 becomes a part of your academic record. From that date until mid-term (July 3) a grade of "W" will be assigned for withdrawal forms submitted to the Registrar. A grade of "WF" will be assigned for withdrawal forms received after mid-term. The student is responsible for completing the paperwork and submitting it to the Registrar’s Office.
Students with Disabilities: If you have a documented
disability, as described by the Americans with Disabilities Act (ADA),
it is recommended that you contact the Office of Disability Services at
(706)568-2330. The office will assist you in arranging appropriate
accommodations with the instructor.
1.1 Dynamical Systems
1.2 Sequences
1.3 Series
1.4 Programming the TI-83
1.5 Infinite Sequences and Series
2.1 What is a Fractal?
2.2 Similarity Dimension
2.3 Boxcount Dimension
3.1 Deterministic Chaos
3.2 Fixed Points
3.3 Periodic Points
3.4 The Attraction Criterion for Fixed Points
3.5 The Attraction Criterion for Cycles
4.1 The Logistic Function
4.2 Period Doubling
4.3 Universality
4.4 Properties of Chaos
5.1 A Review of the Basics
5.2 Graphing Complex Numbers
5.3 Polar Form
5.4 Complex Functions
6.1 What is a Julia Set?
6.2 Filled Julia Sets
6.3 Unfilled Julia Sets
6.4 Properties of Julia Sets
6.5 The Mandlebrot Set
6.6 Properties of the Mandlebrot Set
7.1 Differentiation
7.2 The Quadratic Route to Chaos
7.3 The Mandlebrot Structure
7.4 The Doubling Function
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