Welcome to Chance!
Chance is an unconventional math course. 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 you better able to come to your own conclusions about news stories involving chance issues.
Topics that might be covered in Chance include:
During the course, 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 read other accounts of the subject as appropriate, including articles in journals like Chance, Science, Nature, and Scientific American, and original journal articles. 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.
The class will differ from traditional math classes in organization as well as in content: The class meetings will emphasize group discussions, rather than the more traditional lecture format. Students will keep journals to record their thoughts and questions, along with their assignments. There will be a major final project in place of a final exam.
The class meets every morning from 9:00 to 10:15 and from 10:45 to 12:00 in room 142. Afternoon sessions will be held in room 531 from 1:00 to 2:30 and 3:00 to 4:00, and will be used for discussion of material in the text, questions about homework, use of the computer, or anything else relating to the course.
We want to enable everyone to be engaged in discussions while at the same time preserving the unity of the course. From time to time, we will break into discussion groups of 3-4 people.
Every member of each group is expected to take part in the discussion and to make sure that everyone is involved: that everyone is being heard, everyone is listening, that the discussion is not dominated by one person, that everyone understands what is going on, and that the group sticks to the subject.
After a suitable time, we will ask for reports to the entire class. These will not be formal reports. Rather, we will hold a summary discussion between the teachers and reporters from the individual groups.
The required text for the course is Freedman, Pisani, Purves, and Adhikari, Statistics, 2nd edition. We strongly encourage you to buy the book; it is available at the U of M bookstore for about $40. If you cannot buy the book, please see one of the instructors. There will be 10-15 copies on reserve at the Geometry Center. The supplementary text, Data Desk by Velleman, is available for $10, also at the Geometry Center.
Each participant should keep a journal for the course. This journal will include:
A good journal should answer all the questions asked, with evidence that some time has been spent thinking about the questions before answering them. In addition, there should be evidence of original thought: evidence that you have spent some time thinking about things that you weren't specifically asked about. This might take the form of: finding and commenting on news articles about topics relevant to the course; asking us challenging questions; making connections between what went on in class and experiences in your own life; going to a casino and winning a lot of money.
In writing in your journal, exposition is important. If you are presenting the answer to a question, explain what the question is. If you are giving an argument, explain what the point is before you launch into it. What you should aim for is something that could communicate to a friend or a colleague a coherent idea of what you have been thinking and doing in the course.
You are encouraged to cooperate with each other in working on anything in the course, but what you put in your journal should be you. If it is something that has emerged from work with other people, write down who you have worked with. Ideas that come from other people should be given proper attribution. If you have referred to sources other than the texts for the course, cite them.
Your journal should be kept on loose leaf paper. Journals will be collected periodically to be read and commented on. If they are on loose leaf paper, you can hand in those parts which have not yet been read, and continue to work on further entries. Pages should be numbered consecutively and except when otherwise instructed, you should hand in only those pages which have not previously been read. Write your name on each page, and, in the upper right hand corner of the first page you hand in each time, list the pages you have handed in (e.g. [7,12] on page 7 will indicate that you have handed in 6 pages numbered seven to twelve).
Journals will be collected and read as follows: Wednesday 22 June; Friday 24 June; Tuesday 28 June; Thursday 30 June.
We will not have a final exam for the course, but in its place, you will undertake a major project. The major project may be a paper investigating more deeply some topic we touch on lightly in class. Alternatively, you could design and carry out your own study. Or you might choose to do a computer-based project. To give you some ideas, a list of possible projects will be circulated. However, you are also encouraged to come up with your own ideas for projects.
At the end of the course we will hold a Chance Fair, where you will have a chance to present your project to the class as a whole, and to demonstrate your mastery of applied probability by playing various games of chance. The Carnival will be held from 1:30 to 3:00 on Friday, July 1.