MATHEMATICS 1: Fall, 2003. Tu Th 1:15-2:30

Office: Fletcher 224 Phone: x 73160; Secretary x. 621-8218.
Email: jgrabiner@pitzer.edu
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

Central Question:

What is the role of mathematics in the rest of thought and the rest of the world?

Key Illustrations: (1) Probability and Statistics (2) Geometry

Required Books:

For Part (1): Darrell Huff, How to Lie with Statistics (Norton), Second Edition
Warren Weaver, Lady Luck: The Theory of Probability (Dover)
Plus selections from the course anthology, Readings for Math One, including readings from Laplace and Maxwell, various newspaper articles on public opinion polls and public-policy issues, and other handouts.

For Part (2): Euclid, Elements, vol. I (Dover paperback)
Plato, Meno (Bobbs-Merrill) (you can use another edition if you own one already)

Plus more selections from Readings for Math One, including selections from Plato, Voltaire, Descartes, Jefferson, Kant, Spinoza, Gamow. Also various handouts

Assignments:

 

(a) "Real-world problems" This is to get us all into the habit of seeing mathematics in the world. Each week (unless announced otherwise), every student will find and hand in ON THURSDAY, at the START of class, a real-world problem and its solution.
ONE PAGE is all that's needed. Each completed assignment will include three parts.

(1) A description of the real-world situation that gives rise to the problem
(2) A statement of the mathematical problem you have abstracted from the situation. What makes it "real"? Somebody needs to care about the solution!
(3) The solution to the problem stated in part (2). (See the examples on both sides of the handout to get the idea.)
Make this fun! Look around you at situations, and try to abstract problems from them. Use any mathematics you know--even simple arithmetic sometimes produces valuable knowledge.
(Note: late work will be docked one point per calendar day. Exceptionsonly on grounds of illness or similar compelling reasons)
(b) 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.
(c) Occasionally: finding statistical fallacies in ads and in the news, analyzing public-opinion polls and advertisements, problem sets.
(d) Short in-class report and 3-4 page written version of it. Near the end of the course,
each student will report on how mathematics is used in some area of interest to the student.
In the past, topics have ranged from sports to painting to pathology to social work; please
talk with me to find material on your topic. You provide your interest; I'll help you find the mathematics. Students in past years have found listening to other students' reports a highlight of the course. Attendance at others' reports, and written responses to them, will be required.
This assignment will be worth 15% of your course grade.
(f) Exams: Midterm in class, Thursday, October 16. Final: Wednesday, Dec. 17, 2 PM.
(g) Grading: Midterm 22%, daily responses 10%, project 15%, all other assignments 20%,
Final 33%.
 

(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.

CALENDAR for Math One, Fall 2003
  Dates & Assignments:
Sept. 4. Introduction to the course
Pascal's "Wager," from the Pensées [Thoughts] (written in the 1650's) and Stephen Jay Gould, "The Median Isn't the Message" (from his Adam's Navel (1995).
Question from L. A. Times (August 31, 2003) about polling.
(All three readings will be handed out on Sept. 2. For the first two, identify the key philosophical points being made, ask yourself why the author chooses to use mathematics to make these points, and try to figure out the mathematics-we'll discuss it further in class.).
Sept. 9: Read Huff, How to Lie with Statistics, 2d. ed., first half. Start working through the Huff handout (for you; NOT to be handed in).
Sept. 11: Second half of Huff. Note: We will also be looking at public opinion polls, especially about the California recall, as they come about.
We may deviate from this calendar if events promote it.
Sept. 16: Weaver, Lady Luck: The Theory of Probability, 21-101. Do not miss this class; it will be your first introduction to probability theory.
Sept. 18, Sept. 23, 25: Weaver, 102-117, 132-135, 149-156, 304-323. More probability theory, applications, and philosophical implications. There will also be a problem set.
Sept. 30: The problem of free will. Laplace and Maxwell (in packet).
Oct. 2: Moving from "probable" to "certain": Plato, from Republic, selections from Books 6 &7. These are in the reading packet (or, if you own another edition of Plato, on Greek page numbers 509-end of 528).
Oct. 7: If you're registered in California, don't forget to vote. Read: Plato, Meno.
Oct. 9: Reflections on the election. Second discussion on the Meno.
Oct. 14: Review of all material to date
Oct. 16: Midterm exam. Study questions will be provided.
Oct. 21: No class Tuesday (Fall Break).
Oct. 23: Euclid, Elements, pp. 241-242 (Proposition I), up to the paragraph that starts "Zeno..." also, read and understand the definitions, postulates, common notions, on pages 153-155. Be able to construct an equilateral triangle yourself with straightedge and compass, following the description in Proposition I. Note: The English used by Heath is old-fashioned, with subjunctive mode and complex words. Translate it into 21st-century English for yourself, but make sure you understand it, and ASK ME if you don't.
Oct. 28: Euclid, Elements, Statements and proofs of propositions 13-16, pp. 275-280; master the proof of prop.15.
Handouts: "Informal remarks on proofs, " and "Logic Handout." These are important assigned readings.
Oct. 30: Begin Euclid's theory of parallels. Reread Postulate 5, and skim the notes following it, esp. pp. 202-204, 220. Read the statements, and try to master proofs, in Book I, Propositions 27-28.
Nov. 4: Continue with the theory of parallels, trying to master the proofs of Book I, Propositions 29-32.
Nov. 6: Catch-up on logic and parallels. Also, practical geometry: Euclid, Book I, Prop. 26, and the note on p. 305 and diagram. See if you can figure out how Thales, on the shore, found the distance of a ship at sea.
Nov. 11: Philosophy influenced by geometry: Descartes, selections from Discourse on Method (1637), in packet
Nov. 13: Benedict Spinoza, selections from Ethics, (1675), "On God," in packet. Thomas Jefferson, The Declaration of Independence, in packet. (Also, you should be thinking about your project topic. Please ask me if you would like help or advice.)
Nov. 18: George Gamow on non-Euclidean Geometry (in packet). Exhibition, in class, of 2-dimensional and 3-dimensional non-Euclidean spaces.
DO NOT MISS THIS CLASS: It's cool.
Nov. 20: Kant, Prolegomena and Critique of Pure Reason (selections), in packet.
Nov. 25: Voltaire, selections from the Dictionary (in packet). Helmholtz, "Geometrical Axioms," in packet.
Nov. 27: Happy Thanksgiving
Dec. 2-4. Student reports. Everyone must be ready on Monday. Responses to be handed in each day. 5 homework points for each response; no makeups.
Dec. 9-11. Student reports. Responses, as in previous week. A review will be scheduled for the final, and study questions will be made available.
Dec. 17 Final Examination, Wednesday, December 17, 2:00 P. M.