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I teach at a smallish (~2000 undergrads) liberal arts college. The math department is small and we have only about 8-10 majors per year. As far as I know, the Putnam exam has not been offered here for at least a few years, due to lack of interest. But a student recently asked me about it, saying he knew of at least one other student interested in doing it. To register, we need at least 3 students to take the exam.

Note: Here is the website for the William Lowell Putnam Competition. And here is an archive of past years' problems and solutions. In the USA, this is the premier mathematics competition for undergraduates. It is notoriously difficult, and graded very stringently; quite often the median score is 0.

Question 1: How do I drum up interest in studying for and, ultimately, taking the exam? Seeing that participation has been nonexistent, is there anything special I can do to make students not only aware of, but also enthusiastic about it?

Question 2: Is there anything I can do to help coach these students? Of course, going over old problems can be effective; what else do you suggest? Keep in mind that these students might not be willing to put in that much extra time outside of coursework. How can I maximize their enjoyment/benefits?

I'm interested in experiences with this kind of environment, a small liberal arts college, and especially if you started this "from scratch", as it were. However, I'm interested in any more general experiences you might have in working with students to study for this exam.

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    $\begingroup$ I created the "math-contests" tag for this, hoping it can be used for questions about Putnam, Olympiads, etc. I also created the "liberal-arts" tag since I'm especially curious about experiences at a similar institution, in terms of size (both of school and math department/majors). $\endgroup$ – Brendan W. Sullivan Jun 5 '14 at 19:46
  • $\begingroup$ I guess that explaining what a "Putnam exam" is might enhance this question... $\endgroup$ – mbork Jun 5 '14 at 20:15
  • $\begingroup$ @mbork: I added a paragraph with a description and some links. Thanks for the suggestion. $\endgroup$ – Brendan W. Sullivan Jun 5 '14 at 20:18
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    $\begingroup$ This is just a comment, not really an answer (hence being put in as a comment). I think this is very possible if you restrict the focus to solving the first two problems in each session's test, since those are designed to be much easier than the other 4 problems in each session's test. In other words, avoid looking at old problems that aren't among the first two (unless someone is REALLY interested in one of the others). It isn't all that unreasonable that you can get the two interested students to each get one or two of those easier problems on test day, I would think. $\endgroup$ – Dave L Renfro Jun 5 '14 at 20:18
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    $\begingroup$ @vonbrand I don't believe that is allowed. But someone should correct me if I'm mistaken. That could be a possibility for me, but it might be quite difficult since I currently have no interaction with students at other schools nearby... $\endgroup$ – Brendan W. Sullivan Jun 5 '14 at 22:19
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There are a lot of resources for problem solving online.

One place to look is MIT's OpenCourseware; see their Problem Solving Seminar:

Course Description

This course, which is geared toward Freshmen, is an undergraduate seminar on mathematical problem solving. It is intended for students who enjoy solving challenging mathematical problems and who are interested in learning various techniques and background information useful for problem solving. Students in this course are expected to compete in a nationwide mathematics contest for undergraduates.

You might also be interested in some of the Art of Problem Solving (AoPS) resources. The site also has recommended books for a variety of mathematics contests; see here.

Ideally you would find someone with experience doing MathCounts, IMOs, or (since you are in the Boston area) PROMYS. You might look specifically into contacting the people with PROMYS for Teachers.

If none of your prospective participants has experience with problem solving competitions: I will second Dave L Renfro's comment about focusing on the first couple of problems in each session, i.e., A1, A2, B1, and B2. It is quite possible for a mathematics major who has no experience with these competitions to rack up points on these problems: usually the scoring would be 1 (something of relevance), 2 (partial solution), 9 (almost a full solution), or 10 (a full solution). With a fair bit of practice, first time test takers should be expected to score a 10 or 11 on the examination (and, as you said, even scoring a single point can be enough to surpass the median).

A word of caution: More than helping students to do well, I would emphasize that a poor performance on the Putnam does not entail an inability to do mathematics (or even be a professional mathematician). Like all things, doing well requires practice, and students who have not competed in MathCounts, IMOs, etc in the past are unlikely to score very high in this competition. Moreover, you write:

Keep in mind that these students might not be willing to put in that much extra time outside of coursework.

If the students are unwilling to put in a lot of time and are not experienced in this type of problem solving, then they may well be shut out.

Final suggestions: Free food is one way to entice students. Another method is to see if some sort of prize (even if it is just a certificate) can be awarded to the student who scores the highest at your institution on the Putnam. Note that the highest scorer might not be a mathematics major: See if those with other majors - e.g., Computer Science, Economics, Physics - have any interest in participating (especially with the free food). Separately, I know of at least one other small, MA liberal arts college that offers its own internal problem solving award: see more on Amherst College's Walker Prize Examination here and links (without solutions) to tests from 2009-2012 and 2013.

And if you do manage to get (non-graduating) students interested enough to take it: Try and see if they will help out with the preparations the next year. Doing well on this competition and maintaining student interest are both matters of school culture in addition to some raw talent and a lot of practice.

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