Time and Location: MWF period 5, Little Hall, Room 201
Office Hours : MWF period 7 and by appointment made 24 hours in advance.
Note on Email: I often check my email just in the early afternoons on weekdays. So if you need a reply by a certain time, plan ahead accordingly.
Text: The course will be based on Gerald A. Edger, Measure Topology, and Fractal Geometry, Springer-Verlag, 1990. (An online version is available through the UF library.) though you are not required to buy it.
Other books of interest:
Michael Barnsley, Fractals Everywhere, Academic Press, 1988.
Kenneth Falconer, Fractal Geometry (second edition), Wiley, 2004.
Prerequisites: Calculus sequence and curiosity.
Brief Course Description: Here’s a quote from the Wikipedia article on what fractals are and what they are used for:
“There is some disagreement amongst authorities about how the concept of a fractal should be formally defined. Mandelbrot himself summarized it as “beautiful, damn hard, increasingly useful. That’s fractals.” The general consensus is that theoretical fractals are infinitely self-similar, iterated, and detailed mathematical constructs having fractal dimensions, of which many examples have been formulated and studied in great depth. Fractals are not limited to geometric patterns, but can also describe processes in time..Fractal patterns with various degrees of self-similarity have been rendered or studied in images, structures and sounds and found in nature, technology, art,and law. Fractals are of particular relevance in the field of chaos theory, since the graphs of most chaotic processes are fractal.”
We will start with many examples of fractals, then explore a general way of constructing them via Iterated Function Systems. We will then study the mathematical structure of fractals in more detail using various notions of fractional dimensions.
Homework: Home work will be assigned every other Friday and due the next Friday. Late homework will be accepted the next Monday at 2/3 credit. After that, no late homework will be accepted. Homework page here. All HW is due in hard copy and at the start of class. I do not accept electronic submissions.
Final Homework or Project: You have a choice of a final homework or project. Details are here.
Grades: Grades will be based on 80% for homework and 20% for the final project/homework.
Class Attendance and Protocol: Most students benefit a great deal from attending class regularly. Arriving late and/or leaving early, reading the newspaper, talking, texting, etc. disrupts the class and is rude and unprofessional. As far as I know it is impossible to take math notes on a laptop, so please don’t open yours in class. You are responsible for all information given in class and posted on the course websites, for example, changes to the exam schedule, etc.
Excused Absences: In certain circumstances a student will be able to make up a missed exam. These circumstances could include medical situations, family emergencies, travel for University activities (eg. band, debating club, etc), and religious observances. In these cases the student must inform me before or within one week after the missed work and provide written documentation.
Honor Code: In this course authorized aid on homework consists of talking to me, other students, and looking at the text for this course. This means that you are not allowed to look in other books for solutions to the homework or at the written solutions of other students.
Additional Information:
Grades: Grading will be in accord with the UF policy stated at https://catalog.ufl.edu/ugrad/current/regulations/info/grades.aspx.
Honor Code: “UF students are bound by The Honor Pledge which states, “We, the members of the University of Florida community, pledge to hold ourselves and our peers to the highest standards of honor and integrity by abiding by the Honor Code. On all work submitted for credit by students at the University of Florida, the following pledge is either required or implied: “On my honor, I have neither given nor received unauthorized aid in doing this assignment.” The Honor Code specifies a number of behaviors that are in violation of this code and the possible sanctions. Furthermore, you are obligated to report any condition that facilitates academic misconduct to appropriate personnel. If you have any questions or concerns, please consult with the instructor or TAs in this class.”
Class Attendance: “Requirements for class attendance and make-up exams, assignments, and other work in this course are consistent with university policies that can be found at: https://catalog.ufl.edu/ugrad/current/regulations/info/attendance.aspx.”
Accommodations for Students with Disabilities: “Students with disabilities requesting accommodations should first register with the Disability Resource Center (352-392-8565, https://www.dso.ufl.edu/drc/) by providing appropriate documentation. Once registered, students will receive an accommodation letter which must be presented to the instructor when requesting accommodation. Students with disabilities should follow this procedure as early as possible in the semester.”
Online Evaluations: “Students are expected to provide feedback on the quality of instruction in this course by completing online evaluations at https://evaluations.ufl.edu. Evaluations are typically open during the last two or three weeks of the semester, but students will be given specific times when they are open. Summary results of these assessments are available to students at https://evaluations.ufl.edu/results/.”
Contact information for the Counseling and Wellness Center: https://counseling.ufl.edu/, 392-1575; and the University Police Department: 392-1111 or 9-1-1 for emergencies.