Mathematics 10 Course Syllabus Fall, 2003, MW 2:45-4:00

Professor Judith Grabiner

Office: Fletcher 224 Phone: x 73160; Secretary x. 621-8218.
Office Hours: Posted on Office Door
Also by appointment--just ask!

Every reasonable effort will be made to accommodate students with disabilities. If you need to request accommodations or need additional assistance, please contact the Academic Support Services Office at 7-3553


All cultures have mathematics, though they may not have a class of people called "mathematicians." In this course, we will look together at the mathematical activities of a number of present-day cultures and of several historic cultures. We will concentrate on the mathematics, but will also try to gain some understanding of the cultural setting and to understand how culture and mathematics interact. Each student will do a project on a topic of his or her own choice, involving some mathematical subject in some cultural setting; more precise instructions will be forthcoming.

Responsibilities of the student:

(1) Know all the policies in the syllabus. (Assignment: Read this syllabus from start to finish by the second class!)

(2) This is a math course. Most people learn mathematics best in a communal setting, with the chance to ask questions and to share ideas. Most people also learn mathematics better when they do mathematics, rather than watch someone else do it. I want to be able to speed up or slow down according to the needs of the class, so I will make assignments as they seem warranted by our progress, rather than adhere to a rigid schedule. Accordingly, to get anything meaningful for you out of the course, please attend class regularly and to complete the assignments on time. If you miss a class, it is your responsibility to find out what we did, to get copies of any handouts, and to do any assignments as soon as you can. To help you, I will announce and post my office hours.

(3)This is a course in history and culture. Learning about other cultures requires an openness to new ideas, a willingness to ask questions, and free and full discussions. But it also requires the active pursuit of new knowledge. Accordingly, please do the readings for a day's class before the class, so that you can participate in the discussion and be able to build new knowledge on a foundation.

(4) Please ask questions whenever you think they're warranted, and I reserve the right to somewhat shift directions if it seems warranted. I promise you that, if you fulfill your responsibilities, you will come out of this course both knowing some interesting types of mathematics and understanding how mathematics has been part of many different cultures.


  (a) Readings: The course has three required books (available at Huntley now), and a Packet of xeroxed readings (also obtainable from Huntley).
The books are: Marcia Ascher, Ethnomathematics: A Multicultural View of Mathematical Ideas; Frank Swetz, Was Pythagoras Chinese? Right-Triangle Theory in Ancient China; and George Gheverghese Joseph, The Crest of the Peacock: Non-European Roots of Mathematics. The reading packet includes selections from J. L Berggren, Episodes in the Mathematics of Medieval Islam, R. Gillings, Mathematics in the TIme of the Pharaohs, N. L. Rabinovitz, Probability and Statistical Inference in Ancient and Medieval Jewish Literature, W. Feldman, Rabbinic Mathematics, D. E.Smith and Yoshio Mikami, A History of Japanese Mathematics, T. Crump, The Japanese Numbers Game, Aasger Aaboe, Episodes from the Early History of Mathematics, and C. Zaslavsky, Africa Counts: Number and Pattern in African Culture. All assigned readings not in the required books are in the reading packet, though not necessarily in the order assigned. Also, I will distribute handouts on the mathematics any time I think this is needed.
Handouts are required reading!
  (b) Homework Assignments: There will be problem sets and/or brief writing assignments, assigned as appropriate, and announced in class. The due dates will be announced at the time the assignments are handed out. I encourage you to discuss these assignments with each other, and to form study groups. The only caution is this: do NOT copy somebody else's writeup. Talk together all you wish, but write up your answers on your own. Make sure you understand any answers you've learned from your group--you'll see some of the questions again on the quizzes and midterm. Remember, the purpose of any such assignment is not to produce a page of answers, but for you to understand. Penalty for late assignments: one point per CALENDAR (not class) day (except Saturday & Sunday). (If you're sick or have a similar compelling reason, I'll generally waive the penalty, provided that you let me know BEFORE the assignment is to be handed in; leave a message on my machine at 73160 or email)
NOTE: Two weeks late is the absolute maximum, whatever the reason.ABSOLUTE DEADLINE FOR ALL HOMEWORK: Last day of class!
  (c) Daily responses: 10% of total grade. At the end of every class, hand one sheet of paper, explaining your view in one sentence of BOTH of these: (1) the most important point (2) a question you have, or an item of interest to you. No makeups on these.
  (d) Tests: The midterm is Wednesday, Oct. 15 in class. The final will be Thursday, December 18,, at 2 PM.
  (e) Project: Each student will do a project on a topic of his or her choice involving some mathematical subject in some cultural setting. This will result in a short (about 8 minutes) in-class report so you can share your findings with the class, and a written paper of about three pages. You'll be required to understand both the mathematics you are writing about and its cultural setting, but the emphasis of your report and paper (whether on the mathematics or the culture) will be up to you. I will be glad to have a conference with each of you before you get launched on your report to help you define your topic and get the most out of this assignment. I'll hand out further instructions closer to the time this is due.
There will be questions on the final exam on student reports. Also, there will be a brief written exercise due in class on each day of student reports.
  (f) Grading algorithm: Daily responses 10% of grade; Midterm 20% of grade, Homework 25% of grade, project 20% of grade, final exam 25% of grade.
Tentative Calendar: Math 10. Fall, 2003
    M. Ascher, Ethnomathematics; F. Swetz, Was Pythagoras Chinese?. G. G. Joseph, The Crest of the Peacock: NonEuropean Roots of Mathematics. These are available at Huntley.
Readings for Math 10:
    A packet, available at Huntley, including selections from J. L Berggren, Episodes in the Mathematics of Medieval Islam, R. Gillings, Mathematics in the TIme of the Pharaohs, N. L. Rabinovitz, Probability and Statistical Inference in Ancient and Medieval Jewish Literature; W. Feldman, Rabbinic Mathematics; D. E.Smith and Yoshio Mikami, A History of Japanese Mathematics, T. Crump, The Japanese Numbers Game, C. Zaslavsky, Africa Counts: Number and Pattern in African Culture, A. Aaboe, Episodes from the Early History of Mathematics.
Dates: Topic and Assignments
  Sept. 3: Introduction to the Course.
  Sept. 8, 10: A few number systems. Among non-literate peoples: Ascher, chapter 1.
Among the ancient Babylonians: Aaboe, pp. 5-10, 16- top of 19.
In Japan: Smith-Mikami, on the soroban, Chapter 3 (in packet). Crump (in packet).
  Sept. 15, 17: Graphs, in many cultures. Ascher, ch. 2 (pp. 30-65).
  Sept. 22, 24: Kinship & Group theory. Ascher, 66-83.
  Sept. 29, Oct. 1: Chance, Strategy, Combinatorics, and Expectation: in games, Ascher, 84-94; in medieval Jewish literature. Rabinovitch, 3-7, 76-77, 142-151, 161-164.
  Oct. 6: No class: Yom Kippur.
  Oct. 8: Number systems in African cultures and the history of the study of African mathematics.
Zaslavsky, 1-51.
  Oct. 13: Mathematics in ancient Egypt, Gillings, 4-23, 185-192.
Numbers in ancient Babylonia, Aaboe, 17-22.
  Oct. 15: Midterm examination
  Oct. 20: Fall Break
  Oct. 22, 27, 29:
Right-triangle theory in ancient China. Swetz, 7-25, 26-61, 62-68;
In packet: The Talmud: Feldman, 17-18, 35.
  Nov. 3, 5: Early Greek Mathematics. Aaboe, 35-37, 40
(last 2 paragraphs)-middle of 42. Also, Aaboe, 52-53.
  Nov. 10, 12: Mathematics in the medieval Islamic world. Berggren, 1-5, 21-26, 37-39,
124-5, 182-186; Joseph, 311-319, 324-328, 338-341.
  Nov. 17, 19, 24: Mathematics in Ancient and Classical India, Joseph, 215-263, 264-300.
  Nov. 26: No class; last-minute report preparation and conference day.
  Dec. 1, 3, 8, 10: Student Reports. (Note: Everyone must be ready on the very first day of reports!) Responses to be handed in each day: 5 homework points for each day.
No makeups on these responses.
Also on December 10: Grand and glorious review.
  Dec. 18 Final: Thursday, Dec. 18, 2 PM