Problems for Submission MAT301 Guidelines Submission These problems are due each Thursday morning at 10 a.m. We are planning to use Crowd- mark for submission of assignments. It will be linked on the course website. You should prepare the problems separately (on separate pages, in separate files).1 Make sure that you save all of your files as a pdf. Other formats are not readable to graders are will not be graded (that is, they will be treated as if you had not submitted it). Grading & Feedback of Problems Each problem will be graded according to the following scale: • Proofs – 1 point = mastered (generally, mastered means that it is (a) a correct proof and (b) the grader can understadn it) – 0 points = not yet mastered • Explore – 1 point = complete and demonstrates engagement – 1/2 point = complete but doesn’t show engagement (i.e. – 0 points = incomplete The way to think about the scores is a measure of your progress, not potential. Be aware that this usually results in a lower percentage grade than students are used to - unless you get a perfect assignment, students often get 50% at first. This can seem shocking to some students! This is why we believe in revisions instead of partial grades - this way, you show us how you can master it, we don’t guess how close you are to mastery. 1This is because you will be allowed to resubmit problems that are not correct and complete. 1 MAT301 Winter 2024 Prof. Mayes-Tang Revisions Generally, Explore problems will NOT be eligible for resubmission. Exceptions to this policy will be announced during the term. We will accept revisions to a limited number of problems on a posted schedule (TBA ac- cording to TA scheduling). Academic Integrity There will be a student contract outlining the “rules of engagement” that must be submitted prior to or along with the homework problems. It is consistent with the rules outlined during the first day of class and on the syllabus.2 1 Week 1 (due 10 a.m. on January 16) These problems do not need to be prepared in LATEX. You can draw the images required for this problem set. Along with your first homework, you must submit the Student Contract.3 1. Explore: Frieze Patterns As a (very large!) class, you will build a database of frieze patterns across campus. A question you will answer is: what is the most common type of frieze pattern? Is there a most common type of frieze pattern in modern buidings vs. older buildings? a) Take pictures of frieze patterns across campus (Make sure that you record where you’ve found the patterns). Find four of them from different buildings across the UofT campus that have four different symmetry groups. Write down the sets underlying their symmetry groups (that is, the symmetry actions for each frieze group) b) Sketch the Cayley diagrams of each frieze pattern. c) Enter your frieze pattern and its information into your section’s spreadsheet.4 On the assignment page, give the ID number of the entry. 2. Proof: Symmetry groups of regular n-gons 2As of January 9 it is not yet prepared. But it will be very similar to Dana Ernst’s contract https: //danaernst.com/teaching/StudentContract.pdf. I will post it shortly. 3Undecided if it will be required every week, or only some weeks. 4We’ll provide a basic link to the spreadsheet on the course website on the weekend, and you can build it out. If someone has already entered your frieze pattern but you have conflicting information on it, make a new row and indicate that it is a conflict under a “conflict” column. If someone has already entered your frieze pattern and you have the same information, just enter your name at the end of the row. 2 ©No copying, sharing, or posting without written permission MAT301 Winter 2024 Prof. Mayes-Tang (a) Based upon all of the investigations you have done, make a conjecture about how many actions will be in the symmetry group of the regular n-gon, if n is an integer greater than 1. (b) Write a paragraph giving as convincing an argument as you can in favor of your conjecture. Try to anticipate the counterarguments of a skeptical reader. 3 ©No copying, sharing, or posting without written permission 51作业君版权所有