Discourse is an online discussion forum similar to math.stackexchange. A key difference is that it is distributed under an open source license making it easy for anyone with a server to host their own forum.
Put another way - this instance of Discourse is ours.
It's got some great features. You can log in securely, participate in discussions, and start new ones. You can upload images to illustrate your ideas and enter groovy typeset mathematics as described in our aptly named "How do I enter groovy, typeset mathematics" question.
How fun is that?!!?
Note that participation in Discourse is a course requirement and it will affect your grade! The software keeps track of your participation and, as you use it, your "trust level" increases. This translates directly to points in the class as described in our trust levels question. I will also be creating a special badge or two indicating significant accomplishments. Again, with these come actual points.