Professor: Jeff Johannes
Section 1 MF 2:30-3:45p
Office Hours: Monday 12:00N-1:20p, Tuesday 8:00 - 9:00p,
Wednesday 11:30a - 12:30p, Thursday 4:30 - 5:30p, Friday 10:00 - 11:00a, or
by appointment or visit.
Email Address: Johannes@Geneseo.edu
The Symmetries of Things by John Conway, Heidi
Brugiel, and Chaim Goodman-Strauss, AK Peters, 2008
Almost all beauty is because of symmetry. There are
amazing patterns all around us in art and nature. In this course we
will classify and analyse many diverse symmetries … from kaleidoscopes
and wallpaper patterns to more exotic patterns on spheres and beyond.
Upon successful completion of Math
380: Symmetry a student will be able to:
- Compute signatures of given symmetry patterns on the plane and
- Produce symmetry patterns on the plane and sphere with a given
- Write presentations of symmetry patterns.
- Discover and analyse symmetry patterns in broad non-mathematical
Upon successful completion of Math 381: Algebraic Symmetry a student
will also be able to:
- Identify isomorphisms between symmetry groups and canonical abstract
Your grade in this course will be based upon your
performance on participation (on-line and in person), problem sets, take
home exams, and a final experience. The weight assigned to each is
Field Trip Report
If you are present and engaged in class you will receive
one participation point that day. If you also participate to the class
as a whole (answer a question, present a solution, ask an insightful
question or offer important relevant commentary) you will receive two
participation points for that day. Working each day and never speaking
in class will earn 80%. Speaking every other day on which there is an
opportunity to speak will earn 95%. Scores between will be scaled
Field Trip Report
One week after we take a field trip out of town, please
write a report about what you saw and learned and how you felt about it.
Create examples of symmetry as discussed in class.
Examples will be valued based on mathematical sophistication and something
perhaps about artistic effort (not necessarily artistic success).
Find examples of symmetry in "real life" and analyse them
as discussed in class. By "real life" we mean anything that does not
have a reference to mathematics. More appreciation will be shown
toward examples encountered in your actual physical life. More
appreciation will also be shown toward more sophisticated examples.
These two are likely to be at odds.
You will give a 11-13 minute presentation on a symmetry topic not covered
in class. A topic proposal will be worth 5%,
each of two rehearsals will be worth 20%, critiques of other students'
presentations will be worth 10%, the 11-13 minute presentation will be
worth 35%, and a reflective essay will be worth 10%.
Occasionally you will be given anonymous feedback
forms. Please use them to share any thoughts or concerns for how the
course is running. Remember, the sooner you tell me your concerns, the
more I can do about them. I have also created a web-site
accepts anonymous comments. If we have not yet discussed this in
class, please encourage me to create a class code. This site may also
be accessed via our course page on a link
feedback. Of course, you are always welcome to approach me
outside of class to discuss these issues as well.
SUNY Geneseo will make reasonable accommodations
for persons with documented physical, emotional, or cognitive
disabilities. Accommodations will be made for medical conditions
related to pregnancy or parenting. Requests for accommodations including
letters or review of existing accommodations should be directed to Ms.
Heather Packer in the Office of Disability Services in Erwin Hall 22
or email@example.com or
585-245-5112. Students with letters of accommodations should submit a
letter to each faculty member at the beginning of the semester and discuss
specific arrangements. Additional information on the Office of Disability
Services is available at www.geneseo.edu/dean_office/disability_services.
It is my policy to give students who miss class because
of observance of religious holidays the opportunity to make up missed
work. You are responsible for notifying me no later than February 8 of
plans to observe the holiday.
Tentative Schedule subject to significant changes as we go forward.
This schedule and details are a work in progress actively negotiated with
January 25 Introduction
and through p. 18 of §2
February 1 Kaleidoscope field trip
Read §3, Select topic for presentation.
Field trip report
Discuss exercises and start §4
Complete §4, §5
§6, found symmetries due.
March 1 9 (includes part II preview)
17 Final title & abstract due
18 Deadline for GREAT Day proposals and for student
talks at Seaway
Part II prelude + 10
29 Memorial Art
April 1 Seaway Rehearsals
Seaway meeting - Field trip report due
6 MAA Seaway
Meeting at St. John Fisher College, Rochester.
8 GREAT Rehearsals
11? 3 Found hyperbolic symmetries due
Presentation reflections due
May 3 Created
examples of colourings due
Thursday, May 16 final experience 3:30 - 6:00p Show and tell of discovered
and created examples.