**Instructor:**Dr. Ken Monks**Email:**monks@scranton.edu**Web:**monks.scranton.edu

**Course:**Math 320 – Chaos and Fractals**Term:**Spring 2022**Time:**TR 6:00-7:15**Location:**LSC 316

**Office Hours:** T-Th 5:15-6:00pm, 7:15-8:00pm and beyond (or following the end of Math 320, whichever comes last) and by appointment or email. All office hours will be held in LSC 316.

**Highly Recommended Textbook:**
Peitgen, H.,Jurgens, H., Saupe D.;*Chaos and Fractals, *Springer-Verlag (second edition) ISBN: 0-387-20229-3

**Recommended reading:**

- Mandelbrot, B.;
*Fractal Geometry of Nature,*W. H. Freeman, ISBN:0-7167-1186-9 - Barnsley, M.;
*Fractals Everywhere*, Academic Press, 1988, ISBN:0-12-079062-9 - Devaney, R.,
*A First Course in Chaotic Dynamical Systems*, Addison-Wesley, 1992, ISBN: 0-201-55406-2

**Course Prerequisites:** One math course beyond MATH 221 and one CMPS course or equivalent experience

**Highly Recommended Software:**

*Maple* – we will use Maple extensively in this course. Maple is available in most public computer labs on campus and via remote.scranton.edu. However, it may be more convenient for you to purchase your own copy. Math majors will find it to be quite useful in other courses beyond our own. You can purchase it for about the same price as a mathematics textbook. (You can think of it as the textbook expense for the course.)

**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 course is designed for students in mathematics, science, computer science, and engineering majors and related fields who have had some calculus and basic linear algebra. This will be accomplished primarily by covering the material in the course lecture notes and any supplementary material presented by the instructor. See below for a list of topics we hope to cover.

We will use a mixture of hand computations, computer experiments, and mathematical proofs to explore the topics at hand. As a result, students will be required to do calculations, computer projects, and read and write some mathematical proofs. Exams will generally be designed to see if these three objectives are being met.

**Covid Classroom Protocol and Attendance Policy.** The university lists the current campus policies for dealing with the covid pandemic on their Royals Safe Together website. Please read all of the information there. We will also be following some additional protocols in our course to keep everyone as safe as possible.

*Masks*: must be worn at all times in the classroom by all students and faculty. The masks must meet the current university requirements for masks on campus. If you come to class with an unapproved mask you will have to leave to get an approved one. Approved masks might be available at your Dean’s office as well as other locations on campus.*Speaking up*: It is harder to understand someone who is speaking while wearing a mask. If you didn’t hear something I said, ask me to repeat it. Conversely, try to speak more loudly than usual when asking or answering a question in class.*Mask Slipping*: Sometimes a mask will slip below the nose, especially while talking. You should let me know if my mask slips below my nose and I will remind you of the same.*Instructor illness or isolation*: if I become ill or have to isolate or quarantine due to exposure to covid, you will still attend class in one of two ways:*In person*: if I am not well enough to teach via Zoom and a substitute teacher fills in.*Zoom*: if I am well enough to teach via Zoom, we will use the Math 320 Zoom meeting room. We will also use this Zoom meeting room if the university pivots to remote teaching at some point during the semester.

*Student illness or isolation*: if you are feeling ill (whether or not due to covid), tested positive for covid, have to isolate or quarantine, are immunocompromised or want to reduce your in-person class time to minimize your risk, or have some other valid reason for missing class, you should not attend class. Your fellow students and I will be very much more understanding if you miss class than if you come and put everyone else at risk. I will be quite understanding with not letting absence due to a pandemic affect your grade. To repeat,Do not come to class if you are sick, exposed to covid, quarantining, or isolating.

*Exams*: must be taken in person in LSC 316 unless they are take-home exams. You cannot take an exam asynchronously, via Zoom, or in CTLE.- No cell phone or other unapproved computer use is allowed during in-person classes.
*Social Distancing:*We will try to maximize social distancing in the classroom and office hours as follows.*Sit in the correct seat.*The student desks in LSC 316 seat two students, one on the right and one on the left, facing the front of the room. When you come into the room, sit only in the seats that are on the right hand side of the two person desks in the second and fourth rows (with the first row being closest to the front of the room) and sit on the left hand side of the desks in the third row. This will increase the minimum social distance between the students and between the instructor and the students.*Do not approach the instructor.*If you have a question, ask it from your seat in the classroom. Do not come up to the podium. All office hours will be held in our classroom, LSC 316.*Conversely, I will not come to your seat*or look over your shoulder at your work while you are seated.

**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. Each student is also expected to be able to access any information that I post on the web that is related to your course. Contact the Help Desk if you need assistance.

**Homework:** I will post your homework assignments on our course web page. Due to the large volume of homework I assign, I must require that all homework satisfies the following criteria. Each assignment must be in pdf format and submitted via your shared Dropbox folder. If it is handwritten is should be scanned to pdf, and if it in typeset in LaTeX the pdf output should be saved, not the LaTeX source code (no MS Word!). I will specify whether a particular assignment has to be typeset with LaTeX or handwritten and scanned.

- All homework must have the following information at the top of the document:
**Name****Assignment number**(this is the assignment number given on the homework assignment web page, not the number of assignments you handed in).

- File names should also contain your name and the assignment number.
- All individual problems should be clearly labeled by writing the problem number and the problem itself at the start of the problem.
- Formal and semi-formal proofs must have only one statement per line. Expository English proofs should be in word-wrapped paragraph form and follow the conventions for standard mathematical writing that we discuss in class.
- Problems must occur in your document in the same order that they are assigned, e.g. problem #3 must appear before problem #4 which must appear before problem #7, etc.
- Some assignments must be typeset. For those assignments, in addition to meeting the criteria above, you must also use some form of LaTeX to typeset your work. This can be done with raw LaTeX code compiled on your computer, or by using an online LaTeX editor such as
*Overleaf*.*You cannot use Microsoft Word under any circumstance.*See below for information about Overleaf. - Homework files that you hand in may be edited and marked up by me, so if you want to keep a copy for yourself you should make a backup copy of your original file. If you are handing in more than one Assignment number on a single day, each assignment must be handed in separately (i.e. in separate files). Failure to follow these procedures may 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. Assignments must be handed in by saving them in Dropbox, on the day they are due, before the start of class, as indicated by the file time-stamp. You may not place paper homework assignments under my office door or hand it to me in the hall or mail it to me or have an uncle deliver it to my house. No paper assignments will be accepted.

**Missed assignments:** In order to allow for sickness, bad days, other exams, scheduling conflicts, etc. I will compute the average number of problems graded in each assignment and quiz at the end of the term and drop this number of points from the total possible points when computing your homework average (this is similar to “dropping” one homework assignment for everyone).

**Collaboration:** All questions on each assignment can be done either individually or collaboratively as teams of two or more. If you discuss a problem with another student, that student becomes your collaborator on that question and you must write their name at the start of your solution like this:

#5 (Team: John Doe, Mary Smith)

This indicates that you spoke to John Doe, and Mary Smith about problem #5 (do not include your own name in the ‘Team:’ list, since your name is on the top of the assignment). Similarly, John and Mary would list you, and each other, on their problem #5 as team members. Note that it does not matter how much or how little you discuss on a particular problem. Whether you work out the solution entirely together and read each other’s write ups, or simply ask for a small hint from another student, each of you must list the other as a collaborator on that problem. When working on a problem as a team, each member of the team must still write up their own solution in their own words and notation.

It is in your best interest to follow the following guidelines regarding doing your homework. If you can get a question entirely correct on your own, you should do so without talking to anyone else, otherwise your credit for that question will be considered to be shared by the members on your team. However, if two or more students are really stuck on a question and are not going to be able to get it by themselves and want to team up to try to answer it together, then it would be in their best interest to do so since they would receive at least some partial credit instead of no credit at all. So if you can get it by yourself, you should, and if you can’t, find someone else who can’t and work together.

You should attempt to do all assigned problems completely on your own (or with members of your team) without using any outside resources beyond our book and course materials. In every case you should write your own solution in your own words and symbols.

No two students should send me the same .pdf file or use the same LaTeX file. Just like paper assignments, you should each do your own write ups even if you collaborate.

Any acts of cheating on assignments or exams which come to my attention will be dealt with in the most severe manner possible under University guidelines. Plus I will be really upset!

**Quizzes:** There may be unannounced quizzes in some classes which will consist of problems from the homework you are handing in on that day. These quizzes will be graded the same way as the homework assignments, except that you cannot collaborate with other team members on the quizzes.

**Grading:** There will be a midterm exam and a final exam unless I determine that it is in the best interests of your education to not have them. There will be a lot of homework which will not be graded, and a lot of quizzes. Quizzes can either be in-class or a random selection from the homework handed in on that day and will consist of zero or more problems selected randomly by Maple or intentionally by me from the homework assignments that you hand in, or a problem or two that I give you in class to work on. When selected at random, the selection process will be as follows: a random sequence of problem numbers will be selected (this sequence can contain duplicates) and graded in the order they appear on the list. If a problem has more than one part the part will then be selected by a second random sequence of part letters. Which problems are are on the quiz will not be announced before you hand in the homework assignment, thus you should strive to get all of the homework problems correct. There might also be some bonus problems assigned which you can solve for extra credit. I will keep a tally of the number of these optional problems that you solve during the semester and take that into account when determining your final course grade. Each part of each quiz problem will be worth $n$ points (specified in the problem), with points awarded as follows:

Points awarded | Awarded if: |

$n/k$ | Your response is complete and correct and there are $k$ members on your team. |

0.1 | You made a significant attempt at the problem which is either incomplete or incorrect, and you clearly write (or type) “NOT CORRECT” at the very top of your solution. |

0 | Your response is either incomplete or incorrect. |

There will be no partial credit for any solution, especially on proofs (but I do sometimes give a score of ‘+1ce’ which means ‘one point because you were close enough’). Exam problems will also be graded the same way that quiz problems are graded. Thus you should strive to get as many problems entirely correct as possible rather than wasting your time trying to get partial credit on a lot of problems but have them all be wrong.

At the end of the term I will compute your grade as follows:

Let $x$ be a student.

Let $p(x)$ be the total number of points earned by $x$ on all exams and quizzes.

Let $T$ be the total number of points possible.

Let $D$ be the number of points I drop for everyone in order to account for sickness and excused absence.

Let $K$ be a constant (the curve) to be determined by me at the end of the semester.

Let $G(x)$ be the student’s final grade.

Then $G(x)$ is computed by: $$G(x) = \frac{p(x)}{T-D}+K$$ and this number is converted to a letter grade in accordance with the following table:

If your numeric grade is greater than or equal to … |
Your letter grade will be at least … |
---|---|

93 | A |

89 | A- |

85 | B+ |

82 | B |

78 | B- |

74 | C+ |

70 | C |

67 | C- |

63 | D+ |

60 | D |

0 | F |

Remember that the best way to learn mathematics by doing it yourself.

I hear and I forget.

I see and I remember.

I do and I understand

– Chinese Proverb

**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. That includes the right to give letter grades which are not consistent with the numerical grades computed above.