The last three or four decades have seen a remarkable evolution in the institutions that comprise the modern monetary system. The financial crisis of 2007-2009 is a wakeup call that we need a similar evolution in the analytical apparatus and theories that we use to understand that system. Produced and sponsored by the Institute for New Economic Thinking, this course is an attempt to begin the process of new economic thinking by reviving and updating some forgotten traditions in monetary thought that have become newly relevant.
Three features of the new system are central.
Analytic Combinatorics is based on formal methods for deriving functional relationships on generating functions and asymptotic analysis treating those functions as functions in the complex plane. This course covers the symbolic method for defining generating functions immediately from combinatorial constructions, then develops methods for directly deriving asymptotic results from those generating functions, using complex asymptotics, singularity analysis, saddle-point asymptotics, and limit laws. The course teaches the precept "if you can specify it, you can analyze it".
A revolution is underway in science classrooms. The demands of the new workplace and the ready access to information afforded by new technologies have radically changed the way we define a scientifically literate society.
More than ever teachers need professional development that provides them with the resources they need and empowers them to take the action required to build classrooms where the next generation of scientifically literate students will flourish.