Foundations of Math (Logic)

Spring 1999


Instructor: Dr. Art Duval

Please feel free to come by my office any time during scheduled office hours. 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 sending e-mail.

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.

Course Content:

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 Fractions.

Course Notes:

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:

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.

Attendance policy:

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.

Drop date:

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 circumstances. 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.