Complexity Science seems to be advancing frontiers in many conventional subjects. For example, network (graphs) have become important tools in chemistry, biology and sociology to name a few. Ergodic theory, Tsallis entropy and non-Gaussian statistics seem just as important. While it may be difficult to develop a curriculum, Thurner's recent text, Complexity of Complex Systems, might provide a starting point.
A second suggestion related to the "physics" idea Carl mentioned... Squigglology. That's what I call the study of how to interpret and repurpose a variety of notations found in physics texts. Wolfram Language treats many of these cogently, once you 'break the code'. Tensor notation is a difficult but notable example.
