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Participants in World Math Day are commonly referred to as mathletes.
The Putnam Exam: The William Lowell Putnam Competition is the preeminent undergraduate level mathletic competition. Administered by the Mathematical Association of America, students compete as individuals and as teams (as chosen by their Institution) for scholarships and team prize money. The exam is administered on the first Saturday in December.
The GRE Subject Test: While some may think of the Mathematics GRE Subject Test as an individual examination, it is truly a struggle of one versus many. When graduate programs evaluate an individual they are not considered apart from every other student. Teaching fellowships and other funding can only go to a limited number of students and each institution seeks to maximize its return on investment by selecting the best available candidate for their program.
Mathletic Off-season Conditioning
The academic off-season (traditionally referred to as "summer") can be especially difficult on mathletes, though various training regimens have been proposed to keep mathletic ability at its peak. Publications such as the MAA's The American Mathematical Monthly and the AMS's Notices of the American Mathematical Society are widely read to maintain and hone mathematical ability. Some coaches suggest seeking research internships or grants, many of which are funded by the National Science Foundation.
At higher levels, mathletes can obtain funding from host institutions to work on summer research projects. For example, the University of Delaware offers the Groups Exploring the Mathematical Sciences project (GEMS project) to first year graduate students. The students act as the principal investigator and work with a undergraduate research assistant and a faculty adviser who will oversee their summer research.
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