Assignments for Week 1

R = Readings ._._. W = Writings

  1. (W) Send me an e-mail message telling about yourself: I hope that you will write this self-introduction in a form that will be suitable for distribution to the other students in the class. If some or all of it is for my eyes only, please so indicate.

  2. (R) In our online textbook read the introductory sections and the first two chapters. Also read my "lecture" for the week.

  3. (RW) STANDING ASSIGNMENT EVERY WEEK: Read the parts (if any) of your "general history" book corresponding to this week's material. You are encouraged to mail in ("report to the class") anything interesting or important that you found in your reading that's not in the online material. (This could be a general comment like "Kline's discussion of Indian mathematics is much more detailed than Allen's," or it could be a specific bit of pertinent information.)

  4. (W) In order to do some real mathematics this week, let's delve further into "magic squares".
    1. Construct a magic square of order 2, or prove that no such thing exists.
    2. Choose one:
      • Without peeking (or memorizing the algorithm in Theorem 1) construct a magic square of order 3.
      • Prove that the algorithm in Theorem 1 is correct.
    3. (Extra credit) Take up Dr. Allen's challenge of generalizing the algorithm to the case where n is not prime.

  5. (R) Our text material discusses Indians North of Mexico and says a bit about the Inca, but it does not cover the Maya, whose mathematics seems to me to be the most impressive in ancient America. Fortunately, Maya math is very popular in precollege education right now, so there is a lot on the Web. Type "Maya mathematics" into SCIRUS; browse and enjoy. (Don't feel obliged to read all 11,000 hits; even the relevant ones quickly become repetitive.) If you're in too much of a hurry to play the Web game, here are two good sites I noted down: Michiel Berger ._. St. Andrews. (The second one has a link to a reference list (things on actual paper!).)

  6. (R) Here is a very interesting article on modern inhabitants of (very) North America that I found while doing my own Maya browse. I should point out that the development of "culturally appropriate" pedagogy for minority populations is highly controversial. I highly recommend (but this part of the assignment is optional)

  7. (RW) (Optional; could turn into a term paper topic) Some of Dr. Allen's remarks are rather sketchy -- more a suggestion that a topic exists rather than a source of information about it. (I have in mind, for example, page 3 of The Scope of Ancient Mathematics.) Research one of these things and write a report on it. (This does not need to be submitted this week; but if it drags past the end of September, you ought to enlarge the report and make it your term paper.)

  8. (R) (Optional) Here's another site that was brought to my attention: Geometry Step-by-Step from the Land of the Incas. Great music and pictures.