I looked through your code and you are trying to load js modules via require calls. E.g. :
https://github.com/odytrice/RequireAngular/blob/dev/RequireAngular/Scripts/app/modules/app.ts
require("angular-route");
require("angular-resource");
require("angular-animate");
This will not work since TypeScript does not know about these require calls and cannot add this to the define
section. To tell typescript about this you need to use the /// <amd-dependency
PS: I have a video on the subject : http://www.youtube.com/watch?v=4AGQpv0MKsA&hd=1