Math 101 Syllabus
Course: Fractal Geometry and Chaos for the Liberal Arts
Term: Fall 2001
Time: T-Th: 4:00-5:15
Location: STT314
Instructor: Dr. Ken Monks
Office: STT163A
Phone: (570) 941-6101
Email: monks@scranton.edu
Office Hours: T-Th 5:15-6:00, 7:15-7:45 and by appointment or email
[Note: Office hours may be held in either STT314 or STT163A. Check both
locations.]
Recommended reading:
- Peak, D. and Frame, M.; Chaos Under Control, W. H. Freeman, ISBN:0-7167-2429-4
- Mandelbrot, B.; Fractal Geometry of Nature, W. H. Freeman, ISBN:0-7167-1186-9
- Peitgen, H.,Jurgens, H., Saupe D.;Chaos and Fractals, Springer-Verlag, ISBN: 0-387-97903-4
Prerequisite: High school mathematics only. Students cannot have taken any math course numbered above Math 101, nor can they be currently enrolled in such a course. This course is not intended for science, mathematics, or engineering students. (Science, math, and engineering students who wish to take a course on fractals and chaos should consider Math 320). A basic familiarity with computers to send email and browse the web will also be helpful, but it is something you can easily pick up in the course if you do not already know it.
Course Objective: To introduce the student to the beauty, magic, and applications of fractal geometry and chaos theory, with emphasis on the mathematics behind it all. This will accomplished primarily by covering the material in the lectures presented by the instructor. See the online lecture notes for a detailed list of the topics to be covered.
A fractal tree (from pg 59 in Chaos Under Control)
Attendance Policy: You will be expected to both attend and participate in every scheduled meeting of this course.
Email and the Web: All students in this course are required to have a university email account and are expected to check their email frequently for announcements and other information I may send to you. I will use email and the internet quite extensively in the course. If you prefer to check your home email instead of your university email you can forward your university email to you home account by following these instructions. I will not change your email address in my email address book from its default university account so you must either read your university email or forward it to your home account. Each student is also expected to be able to access any information that I post on the world wide web which is related to your course (which you apparently can do since you are reading this!).
Homework: I will post your homework assignments here. Due to the large volume of homework I assign and the large number of students in all of my courses, I must insist that all homework satisfies the following criteria:
- All homework must be done on 8.5"x11" paper. The paper must have straight smooth edges, not the jagged edges that are obtained when paper is removed from a "spiral bound" notebook. The paper should not be folded.
- All homework that consists of more than a single sheet of paper must be stapled in the upper left hand corner. Corners should not be folded or "dog eared".
- All homework must have the
following information written legibly in the upper right hand corner
of the first page:
- Name
- Course and time
- Assignment number (this is the assignment number given on the assignment sheet, not the number of assignments you handed in).
Thus, the first page of every homework assignment should look like this:
Any homework that does not conform to the above format will be discarded!
The homework that you hand in will not be
returned to you until the end of the semester, so if you want to keep a copy for
yourself you should make a photocopy before handing it in. If you are handing in
more than one Assignment number on a single day, each assignment must be stapled
and labeled separately. Failure to follow these procedures will result in
you not getting credit for all of your assignments.
Late Assignments: Don't even think about it. I have yet to accept one
and don't want to spoil my record. You will receive no credit for late
assignments. There are NO exceptions.
Grading: I may have an assortment of quizzes in class and/or online. I will also assign some homework sets which will be collected. Some may be graded for completeness only and others may be graded for correctness (my decision). The total of all of the points obtained on quizzes and homework assignments will be divided by the total number of points possible after dropping the lowest quiz grade and the lowest homework grade, and this percentage will determine 25% of your final grade for the course. We will also have a midterm exam, a final exam, and a term project that will each be worth 25% of your grade. In summary your grade will be determined as follows:
Final Exam - 25%
Midterm Exam - 25%
Homework and Quizzes - 25%
Term Project - 25%
Remember that the only way to really learn mathematics is by doing it yourself. This is the best way to prepare for your exams.
I hear and I forget.
I see and I remember.
I do and I understand
- Chinese Proverb
Schedule: We should have time to cover all of the material in the textbook. The following is a crude outline of what I hope to be able to cover. Naturally this schedule is not cast in stone. In particular, the date of the midterm may change, so don't plan on it.
| Topic Number |
Activity |
| 1 | Introduction |
| 2 | Overview |
| 3 | Iteration: Sets, Rules, Seeds, Orbits |
| 4 | Iteration: Functions, fixed points, cycles |
| 5 | GeeBie and HeeBie GB Fractals |
| 6 | IFS theory: Affine Transformations |
| 7 | Affine Transformations |
| 8 | IFS Fractals I |
| 9 | IFS Fractals II |
| 10 | Collage Theorem |
| 11 | Guess my IFS |
| 12 | The Chaos Game |
| 13 | Random IFS method |
| 14 | Testing for Randomness |
| 15 | Addresses I |
| 16 | Addresses II |
| 17 | Base n Rulers via IFS I |
| 18 | Base n Rulers via IFS II |
| 19 | Logarithms |
| 20 | Fractal Dimensions: Similarity Dimension |
| 21 | Box Dimension |
| 22 | Chaos: Dynamical Systems |
| 23 | Defining Chaos |
| 24 | more on Chaos |
| 25 | Chaos meets Fractals |
| 26 | Controlling Chaos |
| 27 | Intro to Complex Numbers |
| 28 | Fractals from the Quadratic Family |
| 29 | Julia and Mandelbrot sets I |
| 30 | Julia and Mandelbrot sets II |
| 31 | Cellular Automata I |
| 32 | Cellular Automata II |
| 33 | Cellular Automata III |
| 34 | Cellular Automata IV |
| 35 | Extra Topics |
| 36 | Extra Topics |
| 37 | Extra Topics |
| Class | Date | Day | Activity/Topic Number |
| 1 | Aug 28 | T | 1-2 |
| 2 | 30 | Th | 2-3 |
| 3 | Sep 4 | T | 4-5 |
| 4 | 6 | Th | 5-6 |
| 5 | 11 | T | 7-8 |
| 6 | 13 | Th | 8-9 |
| 7 | 18 | T | 10-11 |
| 8 | 20 | Th | 11-12 |
| 9 | 25 | T | 13-14 |
| 10 | 27 | Th | 14-15 |
| 11 | Oct 2 | T | 16-17 |
| 12 | 4 | Th | 17-18 |
| - | - | - | Fall Break! |
| 13 | 11 | Th | 18-review |
| 14 | 16 | T | Midterm Exam |
| 15 | 18 | Th | 19-20 |
| 16 | 23 | T | 21-22 |
| 17 | 25 | Th | 22-23 |
| 18 | 30 | T | 24-25 |
| 19 | Nov 1 | Th | 25-26 |
| 20 | 6 | T | 27-28 |
| 21 | 8 | Th | 28-29 |
| 22 | 13 | T | 30-31 |
| 23 | 15 | Th | 31-32 |
| 24 | 20 | T | 33-34 |
| - | - | - | Thanksgiving break! |
| 25 | 27 | T | 34-35 |
| 26 | 29 | Th | 36-37 |
| 27 | Dec 4 | T | 37-review |
| 28 | 6 | Th | review |
Adaptability: I retain the right to modify or change any of the policies stated in this syllabus during the term if I feel it is in the best interests of the students and the course.
