Spring 2010 Course Syllabus
Course: Mathematics 0824.005.
Course Title: Mathematical Patterns.
Time: Tuesdays and Thursday from 2:00 to 3:50.
Place: BE160 (That's Beury Hall.).
Instructor: Paulos, John A.
Instructor Office: 540 Wachman Hall.
Instructor Email: paulos@temple.edu
Instructor Phone: 204-5003.
Office Hours: by appointment.
Prerequisites: a willingness to think, an openness to a broader conception of mathematics.
Textbook: Notes (Past lectures will be videotaped and available to students.).
Course Goals: to induce critical thinking about matters mathematical.
Topics Covered: Mathematical Patterns by John Allen Paulos There will be two units in the proposed course: Basic Numeracy, and Probability. The approach will be primarily via suggestive stories that illuminate the ideas in question rather than through general principles or excessive computation. This means that the course will focus on mathematical ideas, not computation and formulas, and on the vignettes and applications to everyday life and social issues that illustrate them. I. Basic Numeracy We'll start out discussing certain essential numbers: coast to coast distance, population of the US, the population of the the world, approximate number of deaths annually from various common diseases contrasted with the number of deaths in more dramatic contexts, the difference between a million, billion, and trillion, and so on. Incidentally, a million seconds takes approximately 11 1/2 days to tick by, a billion seconds is about 32 years, and a trillion seconds 32,000 years. We'll talk about estimating and comparing: How much human blood in the world? How many homeless in NYC, how many battered women, and so on. Related to this are so-called Fermi problems. Physicist Enrico Fermi was known for challenging his classes with problems that, at first glance, seemed impossible. One such was estimating the number of piano tuners in Chicago given only the population of the city. Dimensional analysis, basic conversions, scientific notation come next. For example, how fast does human hair grow in miles per hour? Cost of beef in drachma per kilogram, many disparate conversions. May seem irrelevant until one starts talking of the equivalents of the one trillion dollars spent in Iraq, for example (130 EPA's, 170 NSF's, 200 NCI's). Voting: Olympics (judges, precision), presidential elections, Lani Guinier, Oscars, Enron. Example of Borda, Condorcet, with the five actors or movies. Application to primaries. More Examples. Puzzles and paradoxes. One example: You find yourself in a room with three light switches. In a room upstairs stands a single lamp with a single light bulb on a table. One of the switches controls that lamp, whereas the other two switches do nothing at all. It is your task to determine which of the three switches controls the light upstairs. The catch: once you go upstairs to the room with the lamp, you may not return to the room with the switches. There is no way to see if the lamp is lit without entering the room upstairs. How do you do it? II. Probability and Statistics Psychological aspects of statisitics: The very important anchoring effect, availability error, and confirmation bias. Examples from Tversky, Kahneman, and other cognitive psychologists. Relevance to the stock market. Sample spaces, examples (coins, dice, heights, incomes) Probability rules (sum rule, product rule, at least one rule). Expected value. Conditional probability. Racial profiling and false positives. Bayes' theorem. Cancer test (98% accurate, 1 out of 200 with cancer, 10,000 tests administered.). Surveillance programs. OJ Simpson verdict. Lie detector tests. Expected value, insurance, blood tests, Pascal's wager, etc. correlation versus causation. Coincidences and birthday problem. Probability of a particular event vs probability of some event of a general sort. JFMAMJJASOND, MVEMJSUNP. Significant? No. And, of course, the birthday problem and the optimal strategy for picking the best spouse when meeting candidates sequentially. (Pass up the first 37% and then pick the next one better than of his or her predecessors. Various classic puzzles and stories: the Monty Hall problem, gambler's ruin, the gambler's fallacy and gambler's ruin, the Banach match box problem, the drunkard's random walks, the St. Petersburg paradox, the random chord problem, the hot hand, monkeys randomly typing on a typewriter, the Buffon needle problem, and many others. Lotteries, a tax on innumeracy. Rare events in general. How likely to inhale a molecule exhaled by Julius Caesar in his dying breath? Finally, among the news stories covered will be many of the following: air safety, relative risks; scoring streaks, "hot hands," and records in sports; health hazards of all sorts; statistics, expert witnesses, and the courtsl; the U.S. Census; redistricting, elections, especially 2000 and 2004 presidential election; use of DNA and, more generally, (conditional) probability in the courts; randomized clinical trials; "studies show," "many," and "may be linked"; epidemiology, AIDS; the stock market and the random walk hypothesis; economic statistics and reporting; environmental concerns, contamination reports; conspiracies, hoaxes, especially on the internet; demographic variations, social work issues; reliability of political polls; lotteries and other gambling issues; junk science of all sorts.
Course Grading: There will be two or three quizzes, a final, your section work, and your compiled notes.
Exam Dates: TBA.
Attendance Policy: Attendance is strongly encouraged since the lecture notes will be the basis of the course.
Any student who has a need for accommodation based on the impact of a disability should contact me privately to discuss the specific situation as soon as possible. Contact Disability Resources and Services at (215) 204-1280, 100 Ritter Annex, to coordinate reasonable accommodations for students with documented disabilities.
Freedom to teach and freedom to learn are inseparable facets of academic freedom. The University has adopted a policy on Student and Faculty Academic Rights and Responsibilities (Policy # 03.70.02) which can be accessed here.
Students will be charged for a course unless a withdrawal form is processed by a registration office of the University by the Drop/Add deadline date given below. For this semester, the crucial dates are as follows:
- The first day of classes is Tuesday, January 19.
- The last day to drop/add (tuition refund available) is Monday, February 1.
- Spring recess is the week of Monday, March 8.
- The last day to withdraw (no refund) is Monday, March 29.
- The last day of classes is Monday, May 3.
During the first two weeks of the fall or spring semester or summer sessions, students may withdraw from a course with no record of the class appearing on the transcript. In weeks three through nine of the fall or spring semester, or during weeks three and four of summer sessions, the student may withdraw with the advisor's permission. The course will be recorded on the transcript with the instructor's notation of "W," indicating that the student withdrew. After week nine of the fall or spring semester, or week four of summer sessions, students may not withdraw from courses. No student may withdraw from more than five courses during the duration of his/her studies to earn a bachelor's degree. A student may not withdraw from the same course more than once. Students who miss the final exam and do not make alternative arrangements before the grades are turned in will be graded F.
The grade I (an "incomplete") is reserved for extreme circumstances. It is necessary to have completed almost all of the course with a passing average and to file an incomplete contract specifying what is left for you to do. To be eligible for an I grade you need a good reason and you should have missed not more than 25% of the first nine weeks of classes. If approved by the Mathematics Department chair and the CST Dean's office, the incomplete contract must include a default grade that will be used in case the I grade is not resolved within 12 months.