Foundations of Math (Logic)
Please feel free to come by my office any time during scheduled
You are welcome to come at other times, but in that case you
might want to make an appointment, just to make sure that I will be
there then. You can make an appointment simply by talking to me
before or after class, by calling me at my office or at home, or by
You may also ask any questions directly via phone or e-mail. If I'm
not in when you call, please leave a message on the voice-mail or
answering machine with your name, number, and a good time for me to
call you back. I will try to repond to your phone or e-mail message
as soon as possible.
Upon successful completion of the course, you will be able to
solve in-depth problems from several areas of mathematics. These
solutions will require clearly-written explanations instead of, or in
addition to, calculations. In order to find the solutions, you will
have to gather data (this may or may not involve a computer), look for
patterns, make conjectures, test your conjectures against the data,
and, if necessary, revise your conjectures.
You will also be proficient at solving shorter "routine" problems
from the mathematical areas we investigate.
We will spend about two weeks on Mathematical Induction and Number
Patterns; and then four weeks on each of Modular Arithmetic; some area
of Geometry; and a third topic to be decided later, possibly Continued
Approximately weekly, I will distribute notes covering material from
the previous week or so of class.
You will also each take your turn writing student versions of the
notes for one class period. These will also be distributed.
- Problems (8% each):
For each of the four topics we discuss, after about one week of class
discussion of one or two open-ended problems, you will choose one of
several comparable problems to investigate yourself. You will have
two to three weeks to work on this problem, with a preliminary draft,
to be checked by me and/or other students, due midway. You are
encouraged to consult with me on a regular basis about your ideas and
progress on this problem.
- Journal (8%):
You will keep a journal recording all your ideas for the course,
especially on the in-depth open-ended problems we discuss in class,
and the ones you solve (see above). I will check your journal periodically.
- Participation (6%):
I expect you to be actively engaged with the material during the
entirety of each class period. Your participation grade will be my
subjective evaluation (on a 0-6 point scale) of how well you meet
this expectation. Active engagement does not require you to have all
the answers all the time, but to make an honest effort at all times.
You can demonstrate this engagement in several ways.
I expect you to take part in class discussions. This means
contributing your ideas, and explaining why you believe them; and
commenting (constructively!) on other students' ideas, asking
questions about points you do not understand.
There will be some in-class group activities, and I expect you to do
your share towards making your group effective.
- Homework (8%):
Homework will be assigned periodically (approximately weekly), and
announced in class and on the course website. Assignments will be due
at the beginning of class. No late homeworks! (Incomplete
homeworks will be accepted, though.) If an emergency prevents
you from delivering your homework on time (or having someone else
deliver it for you), please let me know as soon as possible. Your
lowest homework score will be dropped.
You are encouraged to work together on your homework, but you must
write up your solutions by yourself.
- Tests (8% each):
There will be three in-class, closed-book tests.
You will have to solve shorter ``routine'' problems, similar to the homework.
These tests will be on the following days:
- Modular Arithmetic: Fri., 26 Feb.
- Geometry: Wed., 31 Mar.
- Continued Fractions?:Fri., 30 Apr.
Makeup tests can be given only in unusual and unavoidable
circumstances, and with advance notice.
- Final (16%):
The final exam will be comprehensive over all
the topics we discuss in class, and resemble the in-class tests. The
final will be on
Fri., 7 May, 4:00-6:45 p.m.
- Quizzes (6%):
There will be a few in-class quizzes, announced ahead of time.
While I will not take roll, I do expect you in class every day
(realizing that emergencies do arise). Attendance will not directly
affect your grade, but it will be hard to get a good participation
grade if you are absent too often.
The deadline for droping the course with a
W is Fri., 5 Mar. After this date, you can only drop with the
Dean's approval, which is granted only under extenuating
Course drops are now student-initiated only.
I hope everyone will complete the course successfully, but if you are
having doubts about your progress, I will be happy to discuss your
standing in the course to help you decide whether or not to drop.
You are only allowed three enrollments in this
course, so please exercise the drop option judiciously.
Occasionally our class will be videotaped, as part of the process of
assessing this course and its effectiveness. I will also ask you to
take part in some brief videotaped interviews, also for assessment
purposes. Video segments will be shown publicly only
with the consent of everyone appearing in the segment.