Mathematical Economics

After some brief discussion of the course's scope and aims, and using the overview of the familiar case of the real numbers, we begun with the definition of a distance function (metric) w.r.t. a non empty set of reference as a real function defined on the product of this set with itself that satisfies positivity, separation, symmetry and triangle inequality. The example of the discrete metric showed that any such set bears at least one such function, and further examples implied that more than one metrics can exist, possibly inside structured families of metrics, some of which attribute possibly different properties to the reference (or carrier) set. The structured set comprised of the carrier set with the metric was defined as a metric space.  We begun examining of several examples of metrics and subsequent spaces, including the Hamming distance, as well as distances defined on sets of real finite dimensional vectors. We also examined a new example regarding finite simple connected and undirected graphs. We constructed a metric defined on the set of vertices that represents (part of) the graph structure.

Procedural details can be found at the course's syllabus, notes on the previous here, and a counterexample of a metric here. The graph-theoretic example can be found here. The whiteboards from the analogous previous year's lectures (please keep in mind that those are not necessarily identical to the current lectures but they contain some common elements) can be found here and here.