2021 Fall Course Syllabus - Mathematics 4096.001

Course: Mathematics 4096.001.

Course Title: Geometry of Tilings / Senior Problem Solving.

Credits: 3.0.

How this course will be taught: In person.

Time: Tue/Thu 3:30-4:50.

Place: Wachman 010.

Instructor: David Futer.

Instructor Office: Wachman 1026.

Instructor Email: dfuter@temple.edu

Instructor Phone: 215-204-7854.

Course Web Page: https://math.temple.edu/~dfuter/teaching/math4096_21/

Office Hours: Tue 11:00-12:00, Tue 1:30-2:30, Thu 11:00-12:30, and by appointment.

Prerequisites: Some background in Real Analysis and Modern Algebra.

Course Materials: The Tiling Book, by Colin Adams. The book is a PDF preprint, available from the course Canvas page.

Course Goals: Learn the mathematics of tilings and symmetry. Gain proficiency at writing mathematics and explaining it orally.

Topics Covered: We will study the geometry and symmetry of tilings. After developing an appropriate language to describe tilings and the patterns that generate them, we will learn to describe their symmetries in the language of group theory. We will then prove that there are exactly 17 different groups that arise as symmetries of tilings of the plane. (Why 17? You will have to stick around to find out!) In the second half of the semester, we will study aperiodic tilings - those with no symmetry at all - as well as the types of tilings that arise in curved geometry.

Course Grading: Class Participation: 30%. Homework: 30%. Oral presentation (including written outline): 20%. Final exam: 20%.

Exam Dates: Final exam: Thursday, December 9, from 1:00-3:00pm.

Attendance Policy: Participation is fundamental in this course, hence attendance is mandatory. Absences will only be excused by documentation from a doctor or other health professional, Student Health Services, other University office, etc. Every unexcused absence will lower your class participation score by 1/3 of a letter grade (A- to B+, B+ to B, etc).

Attendance and Your Health: To achieve course learning goals, students must attend and participate in classes, according to your instructors' requirements. However, if you feel unwell or if you are under quarantine or in isolation because you have been exposed to the virus or tested positive for it, you should not come to campus or attend in-person classes or activities. It is the student's responsibility to contact their instructors to create a plan for participation and engagement in the course as soon as they are able to do so, and to make a plan to complete all assignments in a timely fashion, when illness delays their completion.

Course structure: This course will differ from most math classes. The rough structure of a class day will be 50% lecture from the instructor and 50% inquiry-based learning. In particular, students will spend significant class time working together in groups of 3 or 4 trying to work out important examples and prove results that are central to developing the theory. The goal is to learn mathematics by doing mathematics rather than listening to a lecture with the prepackaged correct answer. More specifically, the point is not only to know what is true, but to discover why. You will learn the material the way a research mathematician solves a problem: through experimentation, trial and error, discussion with your peers, and a lot of hard work. Another key component of this is presenting your work to your peers.

Writing-intensive details: Math 4096 has been designated a "writing in the disciplines" course. This means we will devote a lot of attention to writing (and also oral communication). This will be visible in a few ways: * Classwork. During inquiry-based blocks of class time, we will practice working out and writing proofs of important results. You will also be asked to explain the results and ideas to your classmates. To encourage trial-and-error exploration, classwork will not be graded for correctness. (However, actively participating in these activities will be the key component of the participation score.) * Proofs in the homework. Homework assignments will mostly consist of proofs. They will be graded both on correctness and on clarity of exposition. * In-class presentation. At the end of the semester, every student will give a 15-20 minute presentation on a topic of their choice, chosen from a menu of options. Two weeks before the presentation, you will need to turn in a detailed outline, for discussion and revision. You are likely to find that presenting difficult mathematics orally is just as critical as presenting it in a written form, and involves somewhat different emphases.

Homework policy: Homework assignments will be posted on Canvas, and will typically be due on Thursdays. No late homework will be accepted, but I will drop your lowest homework score. I encourage you to start early and work in groups. There are only a couple of caveats to group work: * You should try to do all of the problems on your own before getting together with others. It does not benefit you (on exams and in the real world when you need to use math) to simply get solutions from your classmates! In fact, there is research suggesting that group work is much more productive when everyone has thought about the problems before getting together. * Everyone must turn in their own solutions. In other words, all written work must be your own, and written in your own words. Here are a few guidelines for how to write up the proofs: * Write up the problems in order, using only one side of the page and leaving lots of space for comments. Please staple your sheets together. * Begin each problem with a statement of that problem. * Proofs should be written in complete sentences, with appropriate mathematical notation where appropriate. Pictures can certainly be used to illustrate the text, but the text still needs to make sense. * Proofread what you've done to be sure that it's complete and makes sense. Remember that proof-writing is above all an act of communication, and that the ultimate goal is clarity. * Start early! This way, if you are stuck, you can still discuss the problem with the other students, or with me.

Disability Statement: Any student who has a need for accommodations based on the impact of a documented disability or medical condition should contact Disability Resources and Services (DRS) in Howard Gittis Student Center South, Rm 420 (drs@temple.edu; 215-204-1280) to request accommodations and learn more about the resources available to you. If you have a DRS accommodation letter to share with me, or you would like to discuss your accommodations, please contact me as soon as practical. I will work with you and with DRS to coordinate reasonable accommodations for all students with documented disabilities. All discussions related to your accommodations will be confidential.

Academic Freedom: Freedom to teach and freedom to learn are inseparable facets of academic freedom. The University has adopted a policy on Student and Faculty Academic Rights and Responsibilities (Policy # 03.70.02) which can be accessed here (opens in new tab/window).

Add/Drop Policy: Students will be charged for a course unless dropped by the Drop/Add deadline date. Check the University calendar (opens in new tab/window) for exact dates.

During the Drop/Add period, students may drop a course with no record of the class appearing on their transcript. Students are not financially responsible for any courses dropped during this period. In the following weeks prior to or on the withdrawal date students may withdraw from a course with the grade of "W" appearing on their transcript. After the withdrawal date students may not withdraw from courses. Check the University Calendar (opens in new tab/window) for exact dates. See the full policy by clicking here (opens in new tab/window).

Incomplete Policy: The grade "I" (an "incomplete") is only given if students cannot complete the course work due to circumstances beyond their control. It is necessary for the student to have completed the majority of the course work with a passing average and to sign an incomplete contract which clearly states what is left for the student to do and the deadline by which the work must be completed. The incomplete contract must also include a default grade that will be used in case the "I" grade is not resolved by the agreed deadline. See the full policy by clicking here (opens in new tab/window).

Expectations for Class Conduct: The best way to maintain a safe and focused learning environment is for everyone to get vaccinated. Masks must be worn by vaccinated and unvaccinated people in all indoor or in enclosed spaces (including classrooms, the Library, the TECH Center, the Student Center, shuttles/buses, administrative spaces, common areas in residence halls, etc.). For your general health and well-being, hand washing and monitoring your health is still highly recommended.

Student Support Services: The following academic support services are available to students (all links open in a new tab/window):
    The Math Consulting Center
    Student Success Center
    University Libraries
    Undergraduate Research Support
    Career Center
    Tuttleman Counseling Services
    Disability Resources and Services
If you are experiencing food insecurity or financial struggles, Temple provides resources and support. Notably, the Temple University Cherry Pantry and the Temple University Emergency Student Aid Program are in operation as well as a variety of resources from the Division of Student Affairs.

For courses in remote mode:

Technology specifications for this course: A working computer with a reliable internet connection, a Webcam, and audio capability. Recommended Internet Speed: 8mbps download & 5mbps upload. You can test your connection at https://www.speedtest.net. Please note: Hard-wired connections are more consistent than Wi-Fi for Zoom sessions. A scanning app such as AdobeScan or CamScanner is required as is access to Zoom and Canvas (the Canvas app is also recommended).
Limited resources are available for students who do not have the technology they need for class. Students with educational technology needs, including no computer or camera or insufficient Wifi-access, should submit a request outlining their needs using the Student Emergency Aid Fund form. The University will endeavor to meet needs, such as with a long-term loan of a laptop or Mifi device, a refurbished computer, or subsidized internet access.

Remote proctoring statement: Zoom, Proctorio or a similar proctoring tool may be used to proctor exams and quizzes in this course. These tools verify your identity and record online actions and surroundings. It is your responsibility to have the necessary government or school issued ID, a laptop or desktop computer with a reliable internet connection, the Google Chrome and Proctorio extension, a webcam/built-in camera and microphone, and system requirements for using Proctorio, Zoom, or a similar proctoring tool. Before the exam begins, the proctor may require a scan of the room in which you are taking the exam.

Online Classroom Etiquette: It is expected that each student attends every class on time for the full duration of each class and behaves, in the same professional manner, as if you are in a regular classroom. This refers in particular to your location and attire. It is not appropriate to eat a large meal, drink alcohol, smoke, or get up often during an online class.

Statement on recording and distribution of recordings of class sessions: Any recordings permitted in this class can only be used for the student's personal educational use. Students are not permitted to copy, publish, or redistribute audio or video recordings of any portion of the class session to individuals who are not students in the course or academic program without the express permission of the faculty member and of any students who are recorded. Distribution without permission may be a violation of educational privacy law known as FERPA as well as certain copyright laws. Any recordings made by the instructor or university of this course are the property of Temple University.