  In recent years, various notions of algebraic independence have emerged as a
central and unifying theme in a number of areas of applied mathematics,
including algebraic statistics and the rigidity theory of bar-and-joint
frameworks. In each of these settings the fundamental problem is to determine
the extent to which certain unknowns depend algebraically on given data. This
has, in turn, led to a resurgence of interest in algebraic matroids, which are
the combinatorial formalism for algebraic (in)dependence. We give a
self-contained introduction to algebraic matroids together with examples
highlighting their potential application.
