Math 28 Course Information
Winter Term 2002
Instructor. The instructor for the course is Professor Bogart. His office hours for the term will be announced on the course web page, www.math.dartmouth.edu/~m28w02.
Organization of the course. Math 28 is a course in combinatorial mathematics. This year the course is being taught as a "guided discovery" course. This means that the primary text for the course is a set of problems with just enough prose so that the problems will make sense. It is available at the course web page www.math.dartmouth.edu/~m28w02 in the form of course notes. You should expect that these notes will be revised from time to time during the term. By working these problems, students will discover for themselves the main theorems of combinatorial mathematics (and their proofs) and examples of how these theorems are used. Students are encouraged to work together on the problems. Students are expected to work as many of the problems as they can and submit them. Certain problems will be designated each week in advance as "mandatory" problems. These problems will be graded by the instructor and returned to the student for revision as necessary. A student is expected to work on these problems until they are essentially correct. When students write the final draft of a problem they should not work together with other students. For mandatory problems, students should turn in their final draft without showing it to anyone else. For other problems, students are expected to ask for feedback from other students on their final drafts. There will be a form available for giving feedback. Students will then turn in their first final draft, the feedback form from another student, and their revisions based on that feedback. A random sample of these nonmandatory problems and feedback will be graded. Students doing the problems will be graded on the basis of their first final draft and their revisions; students giving the feedback will be graded on the usefulness and correctness of their feedback. Students should, to the extent possible, continue to revise and turn in a non-mandatory problem until they have (and believe) feedback that it is correct.
Although there is a practical reason for getting feedback from other students (namely this makes it unnecessary to limit the class size to eight students) there are important cognitive reasons as well. Students learn to explain their work more carefully when they have to explain to someone else why his or her work is unclear. They also learn better how to find mistakes in their own work by learning how to detect mistakes in other people's work.
Class time will be devoted largely to a discussion of the problems and the broad themes in combinatorial mathematics that the problems illustrate. This discussion will be split between whole class discussion, including possible student presentations of their ideas, and small group discussions. Students will be graded on class participation. Unfortunately, coming late to class may disrupt small group discussions, and so this will have to be reflected in the class participation grades of students who habitually come late to class. Of course it is difficult to participate if one does not come to class at all, and so habitual absence will also be reflected in the class participation grade.
Careful grading of the problems is a very time-consuming process. Students are asked to facilitate the process by keeping their problems in a loose-leaf notebook with a table of contents (an appropriate form will be provided) that shows when problems were submitted, what page they are on, when revisions were submitted and what page they are on. Revisions should not be made by writing on the original problem because part of the grading process will be comparison of the original and revised versions of the problems. Grades on the mandatory problems and the random sample of feedback problems will also be recorded on the table of contents so that a student can tell at a glance what her or his status is. Problem notebooks will generally be collected on Wednesdays. Problem notebooks will be collected on the last day of classes, which is a Wednesday, so students may want to make "backup" copies!
Grading of the course. Students' problem solutions (including both mandatory problems and others) will count for 50% of the grade. There will be a midterm exam that is intended primarily to show students how well they are learning so it will count for only 5% of the grade. The final exam, to be scheduled by the registrar, will count for 20% of the grade. Feedback will count for 15% of the grade and class participation will count for 10% of the grade. The notes have appendices on mathematical induction and on functions and relations. Students who need to work through these appendices will not need to submit so many problems from the regular chapters. It is unlikely that anyone will complete all the problems in the notes. Completing 90% of the problems (and not systematically avoiding the most challenging 10%) in the regular chapters will count for the full 50 points. (The 90% level is tentative and the instructor reserves the right to revise the percentage downward if that seems appropriate in the interest of fairness.) The instructor expects to award A's and A-'s to everyone who earns at least 90 points, B-'s, B's and B+'s to everyone who scores between 80 and 90 points, C-'s, C's and C+'s to everyone who earns between 65 and 80 points and D's to everyone who earns between 50 and 65 points. Again the instructor reserves the right to move the borderlines between grades downwards if that seems appropriate in the interest of fairness.
The honor principle. The honor principle applies to the course as follows. Students may not give or receive assistance from anyone (except the instructor) on exams. If there are "take-home" problems on an exam, students may not consult references in working on these problems. Students are to write the final draft of any work they turn in or give to someone else for feedback on their own without consulting anyone else. Similarly, when giving formal written feedback, students may not consult with anyone else. At all other times, both before and after work has been turned in, students are encouraged to discuss the problems with other students.
Grading of the problems. Problems that are correct and well written will be awarded ten points. Problems that are almost correct or almost well written will be awarded nine points, and a student need not continue working on that problem to get ten points if her or she chooses not to. Problems on which a student has made significant progress will be awarded five points, but students will be expected to continue working on such problems. In the case of multipart problems or problems with multiple questions, points will be allocated proportionally among the parts or questions, so fractional grades are possible. It is especially valuable to find more than one solution to a problem, and so students will receive bonus points (typically up to ten) for additional (distinctly different) solutions to a problem. Exceptionally interesting extra solutions may receive more than ten bonus points.
X-hours. The X-hour for the course is 8:45-9:50 Thursday morning. X-hours will be used when the instructor has to be out of town and miss a class, when the class needs additional time working together, for review and for other purposes. However the use of an X-period will be announced in advance. Since the advance notice may be short, students are expected to keep the X-period open.
Students with disabilities. Any student with a documented disability needing academic adjustments or accommodations is requested to speak with the instructor by January 16. All discussions will remain confidential, although the Academic Skills Center may be consulted to verify the documentation of the disability. Students who think they may have a disability but are not sure are encouraged to consult with the Academic Skills Center.