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I am teaching an undergraduate course which consists entirely of exploratory projects on any interesting mathematical topic. I'm looking for projects where a first-year student who has only taken calculus can make discoveries within an hour, and an advanced undergraduate thinking about graduate school can continue even after twenty hours. I prefer projects where students can do short investigations, make conjectures, and then try to prove them (or run computations).

So far I have found the book The Joy of SET, which I think is ideal for such projects. I am also thinking about projects on prime numbers, cellular automata, and lattice paths.

I would like additional resources that I can work from, where the authors have already thought out how to prompt students to explore topics with particular low-hanging fruit in mind, and tons more fruit beyond it.

To be clear, I'm not looking for textbooks for students to read themselves as in Recommendations for inquiry based/aided discovery textbooks, although I got some ideas there (Indra's Pearls). I also got some ideas from Topics for Discovery-based Projects, such as Julia Robinson Mathematics Festivals.

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  • $\begingroup$ (At first I thought this was a calculus course, but then it sounded like a problems course. It's not completely clear.) I am loving the book Measurrement, by Paul Lockhart. It has so many questions, and each one can take you to others. (It is not a textbook.) The JRMF has has much material, I'm curious that it's not providing you enough for the whole course. $\endgroup$ – Sue VanHattum Jan 16 '17 at 16:01
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    $\begingroup$ I edited to clarify that this is not a calculus course, but has just calculus as a prerequisite. Thanks for the ideas @SueVanHattum! The JRMF does have some great ideas (and I have not gone through them all yet). Many of them are too small for my course, but I have found some gems so far. $\endgroup$ – Jordan Jan 16 '17 at 20:44
  • $\begingroup$ 'Computations' made me think of projecteuler.net $\endgroup$ – Sue VanHattum Jan 17 '17 at 22:03
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Student Research Projects in Calculus

Cameos For Calculus

I particularly like the first one because the authors include with each project a description of how long it may take a student, any issues they've encountered, and (sometimes) how it can be explored further.

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Nice question and I should say Inquiry-based Project is taking my attention. So, I really like these books:

Tanton, J.(2001). Solve this: math activities for students and clubs. Cambridge University Press.

Cofman, J. (1990). What to Solve?: Problems and Suggestions for Young Mathematicians. Oxford University Press, New York.

I hope these resources could help you.

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