I get some very interesting emails through my international work. The one copied below came from Maria Droujkova, one of the most charismatic and active characters in on-line collaberative maths learning. I just thought I'd share it in the vague hope that someone might have an interest in following it up and might feed back on this thread. If you have a gifted and enthusiastic student, perhaps you could ask them to consider it? The courses seem to be free, places are very limited. As the are based in the US some of the colloborative sessions may be in the middle of the night. Her email follows: Peer to Peer University opens its virtual doors to the next round of courses next week, and you are invited! I think these courses will be interesting and accessible for teens. There is a great international community of course facilitators and students. Here are short descriptions of the math courses, from their leaders: ~*~*~*~*~* SHORT CALCULUS http://p2pu.org/math-future/short-calculus The plan for this course is to work together, using various free learning tools, to create a repository of solved problems in Calculus 1.The plan for the course is based on the outline at http://www.sosmath.com/calculus/calculus.html -- see this link for some more details, but note that we will certainly not be restricting ourselves to this resource! The high-level outline for the course is: * Week 1: sequences & series * Week 2: limits and continuity * Week 3: differentiation * Week 4: integration * Week 5: techniques of integration * Week 6: taylor polynomials and power series ~*~*~*~*~* MATHEMATICS FOR GAME DESIGNERS http://p2pu.org/math-future/mathematics-game-designers The initial outline (subject to change) is as follows. This is developing in a conversation with Stefan Kreitmayer and Daniel Chiquito. The idea is to take the basic concepts of "games" and explore them using mathematics. In this course we will focus on two mathematical ideas: discrete differential equations (difference equations, differential equations on graphs, whatever you want to call it), and strategy/proofs. The course is emphasizes the needs and interests of game designers, but programmers or math fans are welcome to enroll. We will expect to meet for voice conversations twice a week. Budget at least a couple of hours for homework as well. Exercises are optional (but encouraged) and are structured in such a way that they can be done with or with out programming. Feel free to invent your own exercises or projects and share them with the group! We will particularly aim to support development in Python with examples and tools being added during the course. ~*~*~*~*~* INTRODUCTION TO MATH ART http://p2pu.org/math-future/introduction-math-art This is a hands on course where participants will create mathematical art and share it. We will use a computer language I co-designed with my colleague David Rosenthal. The language can be downloaded from: https://docs.google.com/Doc?docid=0AbZ0ZAK7RTghZGhnajNia3FfMTg5NmhuOHh4NGM2&hl=enParts of the course will cover chapters in the book that is available in a PDF format Using the link: http://www.ithaca.edu/dani/APGS/MathArt_Winter2010.pdf Depending on the student skills and interest it may touch other topics like Math and Music, Creating Games and dynamic Mathematical Art.