MATH 521: The Real
Number Sysytem
Syllabus - Fall 2003
Instructor: Marianne Korten
Office: Cardwell 234, 532-0567
Office Hours: Mondays 11:30-12:20
Textbook:
Main textbook: Numbers: Rational and Irrational, Ivan Niven, The
Mathematical Association of America, New mathematical Library.
For additional readings and work I will use the following books:
1. The Number Devil, Hans Magnus Enzensberger, Henry Holt & Company.
2. The Man Who Counted, Malba Tahan, W. W. Norton & Company Ltd.
3. Matemax, Alicia Dickenstein (if I can get my hands on it!).
4. Peripheral Visions, Mary Catherine Bateson, HarperCollins.
5. Mind and Nature, Gregory Bateson, Hampton Press Inc.
6. How to Read and Do Proofs, Daniel Solow, John Wiley & Sons.
Course description:
An extensive developement of number systems, with emphasis upon
structure. Includes systems of natural numbers, integer numbers,
rational
numbers, and real numbers.
The course will introduce some formal logic, enough to understand and
be able to do elementary proofs (additional reading 6 above). We will
read some epistemology, inorder to place our work within the thought of
structuralism (5 above); 4 above is largely a reflection about informal
learning using the thoughts of cultural anthropology. The other three
books will further illustrate the subject we are woking on, while
providing you with material you may later use in your own classroom.
Grading policy:
Attendance and participation are requiered. Final grades will be
based on witten work and participation, as follows:
60% of the grade can be earned for mathematical work, in the following
way: 15% for homework, 15% for the midterm, 30% for the final.
40% can be earned for work on the additional materials, in the folowing
way: 20% for an essay due during the last third of the course,
20% for your work in the discussion of the assigned additional
readings.
Here I will post your (roughly weekly) assignments.
By August 27 you will need to have chosen the book you will focus on
for the additional reading and discussion, from
the list above, excluding 6. Peripheral Visions will
appeal to people with an inclination toward humanities. Mind and Nature
will be slower to read but is extremely interesting. 1,2, and 3 will
have many pleasing problems and explanations suitable
for use in the classroom; 2 is almost storytelling. To work with 3 you
will need to be able to read elementary Spanish .
Except 3, they are available through bookstores.