Ajaxify scheduling checks

This is a thing we keep wanting, so I went and did it.  We do lose some efficiency from reusing data that gets computed for multiple checks, but I think that's worth it.

I decided to do this in [React.js](https://facebook.github.io/react/).  I've mentioned React to several other people on web-team after using it this summer, and I think we should start using it, especially for new JS development.  It makes making interfaces like this really easy -- you don't have to manage the DOM yourself, you just have to say what it should look like when.  Unfortunately this does mean adding a new library, but it should play well with other things when we need it to, and I really hope we can phase out a lot of the other ones, because I think React is way better.

Because we don't do any JS preprocessing or packaging or anything, I used React's in-browser JSX transformer.  It's a little slower, but not much.  Ideally sometime we will actually package our JS reasonably and then we can use the server-side transformer.