Instructor: Frank Thorne, Coliseum 1022D, thorne@math.sc.edu.
Classes will be 9:40-10:30, MWF, in 300 Main, Room B112. When necessitated by the Covid-19 situation, they will simultaneously be live-streamed through Microsoft Teams.
Covid-19 Safety:
- Don't come to class if you have Covid-19 (confirmed or suspected).
- Masks are required in university buildings.
- Classes will be livestreamed over Microsoft Teams for the initial surge, and later
as needed. If you wake up with Covid symptoms let me know, stay home, and participate online.
- I will bring a HEPA air purifier to improve Covid safety in the classroom.
- Please spread out in class, to the extent possible.
- (Not required) The vaccine is strongly recommended. You can get it
on campus (walk-up, M-F, 9:00-3:00) or
off campus.
If you suspect Covid-19, the university requests that you go through official channels:
contact the COVID-19 Student Health Services (SHS) nurse line (803-576-8511), complete the COVID-19 Student Report Form and select the option allowing the Student Ombuds to contact your professors.
When talking with the SHS nurse, be sure to ask for documentation of the consult as you will need this to document why you missed class. You will also use the COVID-19 Student Report Form if you have tested positive for COVID-19 or if you have been ordered to quarantine because of close contact with a person who was COVID-19 positive. In each of these situations you will be provided appropriate documentation that can be shared through the Student Report Form.
Attendance Policy:
- A seating chart will be kept, to facilitate contact training.
- Attendance of at least 80% total is expected, other than excused absences. A grade penalty may be enacted
if you miss more classes than this.
- During periods of high transmission, all lectures will be streamed over Microsoft Teams. Documentation
is not needed if watching online instead of in-person. Documentation and advance notice are
expected if you need to miss class entirely or need an extension on the homework.
- During periods of low or moderate transmission, lectures will be live-streamed as needed.
- The Provost has asked that classes not be recorded, except under special circumstances. If you need a recording,
please bring this to my attention.
Course objectives/learning outcomes:
Successful students will:
-
Master the foundations of projective geometry from a classical point of view -- i.e., as an attempt
to depict three dimensions in two.
-
Master the foundations of projective geometry from a synthetic point of view -- starting with the
"extended Euclidean plane".
-
Understand the application of these principles to visual art, and dabble in the creation of artwork
applying them.
-
Master the basics of complex numbers, both algebraically and geometrically.
-
Demonstrate the utility of both approaches in proving classical theorems in plane geometry.
-
Compare and contrast the projective and complex approaches with each other and with the classical
approach to Euclidean geometry.
Texts :
Microsoft Teams : The course will heavily use Microsoft Teams for announcements,
discussion, file sharing, and chat. During periods of high transmission, and later as needed, lectures will be livestreamed
over Teams as well.
Please either check Teams daily, or have it forward new announcements to your email. You can ask me questions directly via Teams. Although private questions are okay, please ask your question publicly if you are comfortable doing so -- maybe others will be interested in the answer as well!
Exam schedule : The exams will be take home and pledged, of two hours duration.
You will have at least a 72 hour window to complete them, at a time of your choosing.
Dates will
be announced at least a week in advance.
Homework :
Warning. I assign a lot of homework.
The homework will be posted either here or on Microsoft Teams, and is intended to take 5-8 hours a week. That is a lot. Please
count on making a consistent effort to do well in this class! Starting the night before is a bad idea.
If homework takes you more than 10 hours on any given week, then that is more than I intended;
please let me know.
There will be at least one bonus problem on each homework.
Please note. You will be graded both on correctness and on quality of exposition. Indeed, a major
focus of Math 532 is the ability to communicate mathematical ideas clearly.
The standard is that someone who doesn't know the answer should be able to easily follow your work.
In particular, please write in complete English sentences and draw pictures where needed.
Pictures should be clearly drawn and labeled.
Any work that is confusing, ambiguous, or poorly explained will not receive full credit.
You get one "free" homework extension, of up to one week, with no excuse needed. Beyond that, extensions will only
be given in case of documented illness or emergency.
Final project :
Instead of a final exam, this course will ask you to do a final project on an aspect of geometry
related to the course.
The project will consist of an initial proposal, a term paper, and a 20-minute presentation during the final exam period.
Group work is encouraged. More details will be announced.
Grading scale: You are guaranteed at least the following grades: A = 88+, B+ = 83+, B = 75+, C+ = 70+, C = 60+, D = 50+.
| Grade component |
% of grade |
| Two midterm exams |
20% x 2 |
| Final project: |
20% |
Homework: |
40% |
Contacting me :
Please contact me if you have any questions about the course, about my expectations, about my lectures,
about the homeworks, about the reading, or about anything else. The syllabus is demanding and it is my
job to help you succeed.
Office Hours :
- Mondays and Tuesdays, 4:00-5:00, in COL 1022D (eventually) or via Teams (all semester).
At the beginning of the semester office hours will be held via Teams only, or in-person on the Horseshoe by request.
- Tuesdays, 9:00-10:00, outdoors on the Horseshoe. (Via Teams in case of inclement weather.)
Accommodations:
If you have a disability, have particular Covid-related concerns, or otherwise need special accommodations, please be in touch with me and I will do my best to accommodate your needs. If requesting extra time on exams
or an exception to course rules, requests should go through the
Student Disability Resource Center at least one week in advance of the relevant assignment.
Academic integrity is expected of all students.