Math 150: The History of Chance

Michael W. Trosset

The following information is for Fall 2003:

General Description
Gambling is an ancient human activity; efforts to understand this activity led European philosophers to modern notions of chance and risk. This seminar will explore the historical development of probabilistic and statistical modes of thought. The first half of the course will emphasize developments in the 15th, 16th, and 17th centuries, focussing especially on the celebrated correspondence between Blaise Pascal and Pierre de Fermat. In the second half, each student will explore a related topic of interest.

Basic Information
Math 150 will meet on Tuesdays and Thursdays, from 11:00 a.m. to 12:20 p.m., in Room 4 of Morton Hall.

Tentative Office Hours
Tuesdays, 3:30-5:00 p.m., Wednesdays, TBA, or by appointment, in Jones 127.

Attendance is Required
This is a seminar. Most classes will be dedicated to discussing the readings. It is absolutely essential that you read all assigned material and come to class prepared to discuss it.

Texts
There are three primary texts: P.L. Bernstein's Against the Gods: The Remarkable Story of Risk, F.N. David's Games, Gods and Gambling: A History of Probability and Statistical Ideas and I. Hacking's The Emergence of Probability.

Reading Assignments

  1. Chapters 1-2 in Bernstein, Chapters 1-3 in David
  2. Chapters 1-5 in Hacking
  3. Chapter 3 in Bernstein, Chapters 4-7 and Appendix 2 in David, Chapter 6 in Hacking
  4. Chapter 4 in Bernstein, Chapter 8 in David, Chapter 7 in Hacking
  5. Chapter 9 and Appendix 4 in David
  6. Chapters 8-10 in Hacking, plus handout
  7. Chapter 11 in David, Chapter 11 in Hacking
  8. Chapter 5 in Bernstein, Chapter 10 in David, Chapters 12-13 in Hacking
  9. Chapter 12 in David, Chapters 14-15 in Hacking
  10. Chapters 6-7 in Bernstein, Chapter 13 in David, Chapters 16-17 in Hacking

Writing Assignments
This course fulfills the College's writing requirement. Each student will write three response papers and one term paper.

Response Papers (approx 2 pages each)

  1. I will provide a circumscribed assignment, e.g., "Discuss the use of Pascal's Wager in Eric Rohmer's Ma Nuit Chez Maud."
  2. Each student will have one week to produce (a) a draft of the response paper, and (b) a commentary that explains the draft. The commentary will consist of short (typically one-sentence) statements that describe the paper's primary thesis and the role of each paragraph in supporting that thesis.
  3. The students will peer-review each other's drafts. Each student will receive one other student's draft plus commentary. I will provide a checklist of review criteria. Each student will have 5-7 days to write a brief reaction paper (approx 1 page) that offers constructive suggestions on how to improve the draft.
  4. Each student will have one week to produce the final paper.

Term Paper (approx 10 pages)

  1. Each student will submit a brief written proposal (approx 1 page) for a term paper. I will reserve class time for discussion of the proposals.
  2. After a proposal is approved and research has commenced, the student will submit an annotated bibliography (approx 2 pages) of materials on which the term paper is likely to draw. I plan to devote one class meeting to exploring library resources relevant to historical research in mathematics. This meeting will take place at the SWEM library. I hope to work with one of the research librarians in introducing the students to the resources that they are likely to use in researching their term paper.
  3. Each student will submit a draft of the term paper.
  4. The students will peer-review each other's drafts. Each student will write a brief reaction paper (approx 2 pages) that offers constructive suggestions on how to improve the draft.
  5. Each student will submit a final paper.

Grades
Your semester grade will be based on the grades that you receive on your writing assignments (70%) and on your contributions to class discussion (30%). Grades on writing assignments will be weighted in proportion to the approximate numbers of pages indicated above.

Response Papers

  1. Discuss the speech by Cicero's fictional character Quintus, reproduced on page 24 of David. In essence, Quintus is arguing that: If an alleged coincidence seems too implausible, then we tend to believe that it wasn't really a coincidence. Provide a modern example of this type of reasoning. Propose a way to use a fair die to determine if a self-proclaimed psychic has extrasensory perception.

  2. Compare Galileo's essay, Sopra le Scoperte dei Dadi, and the letters between Pascal and Fermat with respect to the probability concepts implicit and explicit in each. The letters are often cited as the birth of modern probability. Do you agree? Argue one of the following perspectives: either (1) compared to Galileo's essay, the Pascal-Fermat letters contain important conceptual advances in the study of probability; or (2) the Pascal-Fermat letters merely elaborate on probability concepts previously articulated by Galileo. Neither perspective is "correct"---Hacking writes that "not until the correspondence between Fermat and Pascal do we find expectation well understood," whereas David contends that the Pascal-Fermat contribution "was in effect the extension of the idea of the exhaustive enumeration of the fundamental probability set, which had already been given by Galileo." Support your argument with quotations from Galileo and Pascal-Fermat.

Reaction Papers
Here are some things to consider when critiquing a paper.

The purpose of your critique is to provide constructive criticism that will help the author write a better second draft. Be fair. If you discover something that you like, don't hesitate to compliment it. If you discover something that could be improved, don't hesitate to note it. And be nice! No matter what you think privately, find a way to communicate your thoughts in a neutral, objective style that respects the author's feelings. I trust you to write critiques with maturity; I will not tolerate use of this forum to insult other students.

Global Issues

Local Issues