Syllabus for MATH-400 Topics
in Mathematics, ARCHIMEDES
Dr. Wildenberg
C-103K (585)-385-8179
Home number: (585)-461-3495
(Please use this number if talking to me can save you a lot of grief. Otherwise, please respect my privacy).
Web page: http://sun1.sjfc.edu/~gwildenberg/ , links from http://home.sjfc.edu/
and http://www.sjfc.edu/
Office hours: See web page where my schedule
is posted. If you would like to see me at
other times, please make an appointment.
Main goals:
1.
Improve and
extend knowledge of Euclidean geometry.
2.
Understand and
appreciate how Archimedes anticipated integral calculus.
3.
Learn about how
the Greeks anticipated and expressed modern concepts such as limit.
4.
See formal
proofs in a relatively accessible context.
Prerequisites: A high-school course in Geometry.
Text: The Works of Archimedes, Edited by T. L. Heath,
Web sites: We will be able to keep
text costs down by using the web. In particular David Joyce has online a
complete copy of
Format: Though I will begin with a few lectures and other
presentations, most of the classes will consist of students “presenting” the theorems and
ideas from Archimedes book “On the Sphere and the Cylinder.” You will know in advance the earliest date on which you will
present. Being absent on the date you
are called on to present will result in an F for that presentation.
Presentations will be done by teams to be formed the first day of class. Please note that each member of the team is
expected to be prepared for the entire presentation but that I will choose who
begins and who follows at the time of the presentation. A presentation should take about 50-55
minutes. This will leave us with 5
minutes for a quiz (see below) and 20 minutes for discussion of the day’s
presentation and/or previous material.
Grading
of presentations: Here is what I expect to see in a presentation. Perforce these are the factors that are used
in grading the presentations (when applicable).
1. A clear statement of the theorem in modern language.
2. The proof, with all steps justified by reference to
a theorem or postulate from Euclid or an earlier theorem or postulate from Archimedes.
3. A list of questions that the rest of the class can
use to test their knowledge of the material you are presenting. These need to be sent to me, by email, in
electronic form at least 48 hours
before the scheduled presentation. I
will then post these questions to my web page.
4. A summary of “where we are”. This part is a bit sticky but here’s what
would be ideal. These theorems are not
isolated – they are part of a book which has a conclusion. Sometimes it will be possible to discern
where the author is going. Or to put it
another way it will sometimes be possible to see how the theorem prepares us
for what is coming.
5. Visual aids.
By these I mean slides, blackboard work, hand-outs, etc. There is not a specific requirement for these
but how skillfully you present the material is a factor.
Other grading: Most classes will begin with a short (5 minutes)
quiz on some work that has been recently covered. By “recently”, I mean that the
material asked about will normally be
from 1 week earlier. For example if we
meet on Jan 15, you can expect questions on that material on Jan 22. (F if
you’re not there to take it.) Note to the presenters: You are trying to prepare
your classmates for these quizzes. There will also be an in-class final or a
final project.
Attendance:
Regular class attendance is required.
Missing more than two classes will result in one FULL GRADE DROP for
each class missed. Missing a day on which you are scheduled to present will
result in an F for that presentation.
Students
with disabilities may be interested in the college’s policy:
In
compliance with St. John Fisher College policy and applicable laws, appropriate
academic accommodations are available to you if you are a student with a
disability. All requests for
accommodations must be supported by appropriate documentation/diagnosis and
determined reasonable by St. John Fisher College. Students with documented disabilities
(physical, learning, psychological) who may need academic accommodation are
advised to make an appointment with the Coordinator of Services in the