Lecture material for my courses
Player zero and player nonzero play the following game: starting from an empty square matrix A of size n ≥ 2, the players take turns in choosing any element of A, and assign it any real value. When all elements of A are chosen, det(A) is computed. If det(A) = 0, player zero wins. Otherwise, player nonzero wins.Each first year class of students that takes my Linear Algebra 1 course can compete against classes of previous years and establish a legacy for future classes. The competition works as follows. Each class can earn up to 12 points; one for each of the 12 version of the determinant game. The 12 versions are distinguished by n = 2, 3, 4, 5, even or odd, and by the choice of starting player (zero or nonzero). Any student can earn a point for the whole class by beating me in any of the 12 version. The student can choose whether he takes the role of player zero or player nonzero. The following rules apply:1. Each student can challenge me at most 3 times for each of the 12 versions2. The class can obtain at most 1 point per version3. The time frame in which points can be earned is limited (specified in the lecture).Advice: before challenging me, practice a lot with your fellow classmates. For most of the 12 versions I know a winning strategy for one of the two players (zero or nonzero). However, there are still a few versions left where I do not know such a strategy. I hope to be surpassed by a smart student some day :-)