Mathematics 5
Winter Term 2000
The World According to Mathematics


Mathematics and Knowledge: Models of Reality, draft manuscript by Dwight Lahr.

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The text is available in the College Copy Center, Thayer Hall, at a no-profit cost of


Dwight Lahr

410 Bradley
Office Hours:

MW: 2:00–3:00 (and by appointment)

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Josh Laison

1-S Bradley
Office Hours:

MW: 3:00–4:00 (and by appointment)

We both encourage you to contact us by e-mail for purposes of asking questions,
making comments, or setting up meetings.


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The course will draw upon both mathematical and meta-mathematical material. Each
week readings and exercises will be assigned that are intended to give you facility
with the concepts being developed in class. A good plan is to read the material
indicated for a given day before going to class and then to do the exercises listed for
that day after having attended the class.

Class Discussions:

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Each student will be expected to participate in the class discussions, especially those
that occur on Fridays. Some students may even want to volunteer—either
individually or as part of a group—to lead a discussion on a given day. The student
or students leading the discussion should be prepared to start off with a ten-minute
presentation. The presentation should have been developed in consultation with
either Dwight Lahr or Josh Laison and might include approximately three to five
questions that will be used to focus the discussion of the class following the
presentation. The Friday discussions will provide a good opportunity to review
homework exercises assigned in that week.

Examinations and Papers:

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There will be a mid-term examination and a final examination in the course. Each of
these examinations will involve a take-home mathematical problem-solving part and
a research-paper part. The mid-term writing assignment will be to write a five-page
double-spaced paper on an assigned topic based upon themes developed in class.
Approximately one week will be allowed to complete this part of the exam. The final
writing assignment will consist of a seven-page paper (double-spaced), for which
two and a half to three weeks notice will be given. Topics for the final paper will also
be from a list of possible topics. In the case of both the mid-term and the final, paper
topics that depart from those on the official list must be agreed upon in advance on
an individual basis in conversation with either Dwight or Josh. All papers must
involve mathematical ideas and should be used to demonstrate your understanding