The first Nordic mathematics competition for university students was arranged in the beginning of 2007. The participants in this team-based competition should be Bachelor's or Master's level students in Nordic universities. Faculty in these universities are asked to encourage and support the participation of able students. There is no fee for participation, but teams are required to pre-register. Details can be found in the competition rules.
Participating teams will solve a set of mathematical problems at their own institutions during one week's time and submit the solutions by e-mail. The level of the problems will be chosen so as to provide even the most able of students with sufficient challenge. For an appreciation of the kind of problems possible we recommend you to have a look at the problems from the International Mathematics Competition for University Students.
Problem 1: x and y are distinct points in X. "Midpoint normal" means the normal, which goes through the midpoint.
Problem 2: non-degenerate means that the side-lengths are greater than 0 and that angles at the vertices are not 0 or pi.
Problem 3: You can assume that xy > 0 to avoid the problem with the definition of the function 0/0.
Problem 10: The dot in \beta_i \cdot \beta_j is just multiplication.