#### DESCRIPTION

The examination will be constructed to test originality
as well as technical competence. It is expected that the contestant will
be familiar with the formal theories embodied in undergraduate mathematics.
It is assumed that such training, designed for mathematics and physical
science majors, will include somewhat more sophisticated mathematical concepts
than is the case in minimal courses. Thus the differential equations course
is presumed to include some references to qualitative existence theorems
and subtleties beyond the routine solution devices. Questions will be included
that cut across the bounds of various disciplines, and self-contained questions
that do not fit into any of the usual categories may be included. It will
be assumed that the contestant has acquired a familiarity with the body
of mathematical lore commonly discussed in mathematics clubs or in courses
with such titles as “survey of the foundations of mathematics.”
It is also expected that the self-contained questions involving elementary
concepts from group theory, set theory, graph theory, lattice theory, number
theory, and cardinal arithmetic will not be entirely foreign to the contestant’s
experience.