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In my graduate courses, I often have my students write term papers on original mathematical topics. I explain the process in this answer over at MathOverflow. It works fairly well for me.

But I'd be very interested in hearing about other experiences or approaches to using term papers in mathematics. What has worked for you? What doesn't work so well? Do you have students pick their own topics? Do all students write on the same topic or from a list of topics? Do you meet with students individually to discuss their papers? Do you have them submit drafts and then revised versions? Do you insist on $\TeX$? Do you have students work in groups? Do you have students give talks on their research topics? Does it matter whether the course is introductory or advanced? What special issues arise for using term papers in an undergraduate course?

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    $\begingroup$ $\LaTeX$ is a must. Meeting all together helps with general topics, and general coordination. One on one meetings will be needed anyway. $\endgroup$ – vonbrand Mar 16 '14 at 13:44
  • $\begingroup$ @vonbrand In a graduate class, I agree that tex is a must, but for undergraduates, who may not be aiming at a math-publishing career, perhaps it is less relevant? I don't understand what you mean by "meeting all together", since of course any class meets together regularly as a class. $\endgroup$ – JDH Mar 16 '14 at 13:51
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    $\begingroup$ I mean a meeting specifically about the papers. And for any math-related text, $\LaTeX$ hurts much less than any alternative I'm aware of. $\endgroup$ – vonbrand Mar 16 '14 at 14:01
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One professor (who I greatly respect) did as follows:

  • He made the papers a part of the exam, the second part being the talk/presentation.
  • The papers had to be in some particular conference format (there were style files at the conference page).
  • There were two dates in which students could present, and it would be organized in a mini-conference form (20 minutes for the talk, 5 minutes for questions, 5 minutes for connecting laptop).
  • There were 8-9 topics listed that students could pick from (there were about 20 people in the class) which were simplified cases of some research problems.
  • You could do your own topic if you could persuade the professor (actually anything reasonable worked).
  • "I took the XYZ approach and failed" were valid results.
  • Students worked alone (but there were exceptions). They could discuss their project during office hours, but were not required to.
  • There were no drafts, but if you submitted a draft, your paper would get "peer reviewed" by the professor.
  • Some of the works were later submitted to student session of the said conference.

In my opinion it worked pretty well. One key thing was that each topic was assigned to more than one student and so it could be later compared, it made an interesting discussion and some funny discoveries. It is worth to point out that the professor would never use students' data against them (even if it was clear that one of them did something wrong). Finally, I think it is significant that it was a practical course, namely natural language processing, where there is a big supply of easy research questions (and is quite entertaining because of the "insights" of machine learning algorithms).

I hope this helps $\ddot\smile$

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    $\begingroup$ It sounds great! $\endgroup$ – JDH Mar 17 '14 at 1:25
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This was the term-paper assignment for the graduate class I took on differential geometry:

Take a paper in differential geometry published in the past 10 years. Explain what it draws on, what it means, and why it is important.

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