This seminar will focus on what the mathematical field of probability theory says about our everyday experiences of chance and randomness. We will survey a wide variety of topics, in which the primary interest is the way that mathematics can describe, and be used to analyze, the real world. Emphasis will be on situations in which testable hypotheses can be formulated (and actually tested!). Students will do projects in which they produce a hypothesis related to some occurrence of randomness in everyday life, gather data to test their hypothesis, analyze the data, and discuss their conclusions. Specific topics to be treated may include: perception and psychology of chance and randomness, randomness and the stock market, coincidences and rare events, game theory, political predictions, and randomness in evolution.
All course information is posted here; Blackboard is used only for grades. (See Dave Noon's take on Blackboard.).
Date | Reading | Other |
---|---|---|
M 1/11 | Chapter 2 of Pinker, through pg. 35 | Gather some data to test my prediction of 37.9% probability of a birthday match within a grop of 19 |
W 1/13 | Read the opening and sections 1, 7, and 8 of this paper | Exposition of the matching problem |
W 1/20 | Reread sections 7, 8 of the Diaconis—Mosteller article | Exposition of the matching problem: Take 2 |
M 1/25 | The two-part series called "The Laws of probability": Part 1 is in this issue, and part 2 is in this one. | Exposition of the matching problem: Take 3 |
W 1/27 | Reread both parts of "The Laws of probability", and skim the Wikipedia article on the central limit theorem | Small paper project proposal (guidelines) |
M 2/1 | none | Exposition: The Law of Small Numbers |
W 2/3 | none | Peer-review on expositions |
M 2/8 | none | Final draft exposition: The Law of Small Numbers |
W 2/10 | none | Draft of small paper |
M 2/15 | Reread Part 2 of "The Laws of probability", and skim the Wikipedia article on the central limit theorem | work on revising small paper |
W 2/17 | Read the structured abstract
of
this paper, and this blog
post This podcast from 10:30 to 21:00 would be good, too | work on revising small paper |
W 2/24 | Posts on The Upshot blog: #1, #2; also read the Nevada caucus part of this piece | none |
M 2/29 | Reread assigned readings from last time | Poisson approximation exposition; articulation of question/plan for large project |
W 3/2 | Understanding Uncertainty posts on breast cancer screening and HIV screening | articulation of question/plan for large project |
M 3/14 | Review Understanding Uncertainty posts from last time, plus this one | work on data gathering/analysis for large project |
M 3/21 | Skim sections 4.2, 4.3, 4.5 of Aldous's notes and Hypermind posts #1, #2 | Data and analysis,
first and last paragraphs of large project due 3/23 Conditional probability/testing exposition will be due next Monday 3/28 |
W 3/23 | Reread Hypermind posts from last time, plus this one. Also, this Upshot post | Conditional probability/testing exposition is due next Monday 3/28. First draft of long paper should be ready Monday 3/28 as well. |
M 3/28 | Emailed paper on ECT | Outlines and Transitions for long paper (first and last
sentences of each paragraph, bullet points for paragraph
contents) Video links: Neuroskeptic on p-hacking, Numberphile (tons of good choices) |