Mathematical Modeling Challenge (MMC/Mammoth)
This is the main contest of the tournament. Its (single) problem is handed out to teams a few days before the official opening of MMT. Normally, teams have five days to write their solution papers.
By and large, the Mammoth task is close to the tasks of IMMC (International Mathematical Modeling Challenge). Examples of IMMC tasks can be found here. The main difference is that in addition to written papers, teams have to present their solutions orally at a conference.
Math Applied To Science (MATS/Primate)
This is an individual olympiad in which participants are given three problems to be solved in two hours. Problem sets may depend on the league. In these problems, mathematics is applied to situations from mechanics, physics, or other sciences and some knowledge of these sciences may be needed. Sample problems
Math Around Us (MAU/Lobster)
Like MATS, this is an individual olympiad for two hours with problem sets depending on the league. The problems are essentially mathematical, but their scenarios, as a rule, are borrowed from real-world situations and don’t require any special knowledge from physics or other sciences.
Both in MATS and MAU, problems have well-defined answers, possibly approximate with a given precision.
Optimization Contest (OC/Goat)
Each task of this contest is an optimization problem represented by a computer model supplied with tools that allow us to create manually various solutions to the problem. Each solution is characterized by a certain number and the goal is to make this number as small (or as large) as possible. Submitted solutions are ranked according to these numbers, but usually, the absolute optimum is either practically unreachable or even unknown. Sample problems