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Mathematics 13: CHANCE is a new, experimental math course that is being offered at UCSD for the first time this semester. The standard elementary math course develops a body of mathematics in a systematic way and gives some highly simplified real-world examples in the hope of suggesting the importance of the subject. In the course CHANCE, we will choose serious applications of probability and statistics and make these the focus of the course, developing concepts in probability and statistics only to the extent necessary to understand the applications. The goal is to make students more literate in statistics and probability, and to motivate them to continue their study of mathematics.

The journal Chance, started by Springer in l988, is the inspiration for this course. In its brief existence, Chance has attracted some of the leading workers in probability and statistics to write articles on subjects of current interest in a way understandable by a reader with little previous knowledge of probability and statistics. Topics that have been covered in Chance include:

• Air safety

• Scoring streaks and records in sports

• Health risks of electric and magnetic fields

• The effectiveness of aspirin in preventing heart disease

• Statistics, expert witnesses, and the courts

• The undercount problem in the 1990 U.S. Census

• Extraterrestrial communication

• The use of DNA fingerprinting in the courts

• Maintaining quality of manufactured goods in the face of variation

• Randomized clinical trials in assessing risk

• The role of statistics in the study of the AIDS epidemic

• The use of statistics to detect cheating on exams.

Other topics that have been recently discussed in the press and popular journals such as Nature, Science, and Scientific American are:

• Paradoxes in probability and statistics

• The work of Kahneman and Tversky on fallacies in human statistical reasoning

• The stock market and the random walk hypothesis

• Demographic variations in recommended medical treatments

• Informed patient decision making

• Coincidences

• Random and pseudo-random sequences

• The reliability of political polls

• Card shuffling, lotteries, and other gambling issues.

In the course of the term, we will choose six to ten separate topics to discuss with special emphasis on topics currently in the news. We will start by reading a newspaper account of the topic. In most cases this will be the account in the New York Times. We will then study the treatments in journals like Chance, Science, Nature, and Scientific American. These articles will be supplemented by readings on the basic probability and statistics concepts relating to the topic. We will use computer simulations and statistical packages to better illustrate the relevant theoretical concepts.