In this class, we focus on general problem-solving skills in mathematics. There are a number of unusual features of the course, including:
Each one of the above features of the course is a carefully thought-out, deliberate and crucial part of the the structure of the course.
For example, having beginning, intermediate and advanced students work together concurrently in the same room will capitalize on peer instruction, as well as make for a positive and potentially exciting learning environment. There is precedent for this type of instruction - it is often done that way in studio art and dance courses. But it is an approach seldom tried in mathematics. Indeed, in a traditional mathematics course based on lectures and the linear accumulation of knowledge and skills, such an approach is likely to be frustrating for all concerned. But it seems to be a perfect vehicle for a problem solving course which is not based solely on structured lectures.
Furthermore, the absence of a text or a predetermined set of problems allows the class to evolve according to its interests and skills. The freedom so obtained is well worth the uncertainty accompanying such an approach. By working on journal problems, the class has the potential for added versatility and excitement - the instructor will usually not know the solution of a particular problem in advance. In this way the instructor is brought closer to the student - more of a collaborator than a professor, and the role of the instructor will be like the navigator of a ship sailing in uncharted waters. This approach has many potential benefits for the student, such as getting a more realistic feel for the daily life of a mathematician than what can be obtained from any lecture-based course.
Finally, there is the added incentive of having your solutions ackowledged publicly in the journals, and possibly even published. The rewards seem more substantial than the typical letter grade at the close of a course. Of course, because the turnaround time is so long for these journals, the public response to the submitted solutions will most likely happen after the course ends. This is part of the reason why it is graded on an S/U basis only. The other reason is to encourage collaboration over competition.
The learning process can be a slow one. Since the problems we look at each semester are different, students may (indeed, they are encouraged to do so) repeat the course for credit as often as they like. Since it is only 1 credit, it should be easy to fit into your schedule most semesters. The benefits should only increase with time. Hopefully, with one or more experiences in this course, your increased problem-solving skills should help you both understand and appreciate many of your other mathematics courses.
The course is structured as follows: first-year students enroll at the 100-level, and are required only to have passed the QRI requirement. Sophomores enroll at the 200-level, juniors and seniors at the 300-level. At or above the 200-level, students will be required to also have completed the QRII requirement (which usually means having just one course with a substantial quantitative component under their belts). However, the QR prerequisites are the only ones. A sophomore, for example, is not required to have already taken this course at the 100-level before enrolling at the 200-level. Honors Forum credit is available for this course, and may be eligible for HF credit even upon subsequent repeated enrollment in the course (for repeated HF credit, the student will have to petition the Honors Forum Council for permission.)
Prior to the existence of this course, there was an ad-hoc group of students who worked on these journal problems (as an extra-curricular activity without course credit!) much in the same way as we plan for the course. This group, called the Skidmore College Problem Group, has been in existence since 1992, has had dozens of correct solutions acknowledged by the journal editors, and has had 5 of its solutions published by the Pi Mu Epsilon Journal. The members of this course will automatically become members of this group (which may or may not have members from outside the course). You are invited to examine the website for this group and look over some of their solutions.
Members of the Skidmore College Problem Group usually participate in the annual William Lowell Putnam Competition, commonly known as the Putnam Exam held each year on the first Saturday of December. The members of this class are also invited to participate in this competition. In fact, occasionally the class will look at problems from previous Putnam exams as examples of challenging and interesting problems. It goes without saying that the practice in problem-solving you will obtain in this course will make you natural candidates for Putnam contestants. However, it should be emphasized that this course is not specifically designed as preparation for that exam. For more information about the Putnam exam, visit the following website.
