Mathematical exposition

Lectures: 2 sessions / week, 1 hour / session

In this course, participants will gain experience in presenting and writing mathematics. In particular, the lectures will be given by the students! For each lecture, the student lecturing will provide written notes to be handed out to the class, and there will also be several writing assignments throughout the semester. Mathematically, the class is an introduction to chaotic dynamical systems theory, covering topics such as iterated function systems, the transition to chaos, symbolic dynamics, fractals and Sarkovskii's Theorem.

Devaney, Robert L. A First Course in Chaotic Dynamical Systems. New York, NY: Addison-Wesley Publishing Company, The Advanced Book Program, 1995. ISBN: 0201554062.

Before delivering each lecture, students will meet with the instructor and present part of their lecture, along with a "time plan" outlining where in their lecture they plan to be after each 10 minute interval, and what material they will exclude or include if time adjustments are necessary. Students will receive detailed feedback on their lecturing style and on their lecture notes.

Homework assignments will be handed out each Wednesday, and will be due the following Wednesday. No late homework will be accepted.

Solutions to many homework exercises are available. Students are not permitted to consult these solutions before handing in homework. Working together on homework assignments is permitted, but should be acknowledged at the top of the homework, and each student must write up their homework assignments by themselves.

There are no exams in this class.

Chaotic dynamical systems will be explored through three computer experiments. Students are strongly encouraged to work together on these experiments. In each computer lab, students will be asked to write an essay describing their findings; feedback will be provided on these essays before they are rewritten into final form.

There will also be a more substantial essay project on Sarkovskii's Theorem, divided into several parts. Students will receive feedback on their writing and will be asked to rework the assignments on Sarkovskii's Theorem into sections of a single paper. Of course, this paper will require an introduction and in any paper the introduction is the section where good writing matters most, so we will also give students feedback on drafts of their introduction.

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