主题目录

  • 课程介绍( Course Introduction)

    University: Massachusetts  Institute  of  Technology

    Instructors: Dr. Emma Carberry

    Course Number: 18.091

    Level: Undergraduate

    Course Description

    This course provides techniques of effective presentation of mathematical material. Each section of this course is associated with a regular mathematics subject, and uses the material of that subject as a basis for written and oral presentations. The section presented here is on chaotic dynamical systems.

  • 教学大纲(Syllabus)

    Course Meeting Times

    Lectures: 2 sessions / week, 1 hour / session

    Course Description

    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.

    Textbook

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

    Pre-Lecture Meetings

    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

    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.

    Exams

    There are no exams in this class.

    Computer Labs and Writing

    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.

    Grading

    ACTIVITIESPERCENTAGES
    Lab Reports/Essays 35%
    Paper on Sarkovskii's Theorem 25%
    Oral Presentations and Lecture Notes 25%
    Homework 15%
  • 课程影音(Audio and Video)

  • 作业(Assignments)

    The assignments are taken from the main text:

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

    Assignments were handed out in the sessions noted in the table below.

    SES #ASSIGNMENTS
    1 Homework 1: p. 26: problems 5, 10, 11aceg, and 12-14
    3 Homework 2: p. 34: problems 1f, 4f, 6; p. 50: problems 1c, 2b, 4f, 5, 6, and 9
    5 Homework 3: p. 67: problems 1ab and 2-13
    7 Homework 4: p. 80: problems 9-19
    9 Homework 5: p. 95: problems 15, 17, and 18
    10 Homework 6: p. 111: problems 6, 7, 9, 13, and 17
    12 Homework 7: p. 151: problem 3
    13 Homework 8: p. 152: problem 9
  • 考试(Exams)