APICS competition for undergraduate students  
The APICS Math competition is a mathematical problem solving competition
written at the annual APICS Mathematics and Statistics meeting. 

Mathematical Contest in Modeling  
The Mathematical Contest in Modeling is an international contest administered by the Consortium on Mathematics and its Applications (CoMAP) and sponsored by CoMAP, the Mathematical Association of America (MAA), the Society of Industrial and Applied Mathematics (SIAM), the National Security Agency (NSA) and others. Each team of three students is given two realworld problems, one involving the mathematics of continuous change and the other involving discrete mathematics. The team picks a problem and works on it over an extended weekend. Their entry is a paper which applies mathematics to the problem and explains why they took their approach, how they tested their ideas and the limitations of their ideas. In 1999, a second contest, the Interdisciplinary Contest in Modeling was introduced; the ICM does not offer a choice of problems, but the two contests are otherwise comparable.  
Putnam Competition  
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 selfcontained 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 selfcontained
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.
