Maybe this should be a comment under Darij Grinberg's or Terry Tao's answer, but anyway: the discriminant of a monic polynomial is the square of the Vandermonde determinant evaluated at roots of the polynomial. Undergraduate students who advanced to a linear algebra course must have encountered at least the discriminant of a quadratic--although in this case the relation between the Vandermondian and the discriminant is not so wonderful...
This relation between Vandermondian and discriminant also determines the relation between Euler class and Pontryagin class: http://en.wikipedia.org/wiki/Splitting_principle
