SCI 199Y: Large Numbers and Small Probabilities (2004-5)

How many molecules of water go over Niagara Falls each century? If we lined up all the grains of sand on Toronto Islands, would they stretch all the way to the sun? If you fly to Europe next summer, what is the probability that your airplane will crash? Is a medical treatment safe just because some study claims it is? How unlikely does a risk have to be before we can safely discount it? This course will examine such questions, including mathematical methods of estimating large numbers and small probabilities, and also philosophical discussions of what we can conclude when probabilities are small.

Instructor: Professor Jeffrey S. Rosenthal, Department of Statistics, University of Toronto. Sidney Smith Hall, room 6024; phone (416) 978-4594;; 'jeff' at ''

Time: Tuesdays, 2-4. First class Sept 14. Last class of first semester Dec 7. First class of second semester Jan 4. Last class of second semester April 5. No class Feb 15 (Reading Week).

Place: Sidney Smith Hall, room 2129.



  1. There is no textbook for this course. Instead, readings and small assignments will be distributed by the instructor as necessary.
  2. Classes will involve a combination of presentation from the instructor, student cooperative work in small groups, and whole-class discussion.
  3. To obtain class participation points, students are expected to punctually attend class each week, to enthusiastically participate in discussions and activities during class time, and to conscientiously keep up with readings and other (small) weekly assignments.
  4. The Minor Paper will be 5-10 pages (typed double spaced), and the Major Paper will be 10-20 pages (typed double spaced). You will have some freedom to choose your topics. Details will be discussed later.

For general assistance with writing essays, see the web page Writing at the University of Toronto.

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