The Math Explorer’s Club is an NSF supported project aiming at
developing materials and activites to give middle school and high
school students an experience of more advanced topics in mathematics.
In this activity, we introduce and develop the notion of Markov chains,
consolidating the student’s grasp of (simple) probability theory
introducing two important discrete
relationship between graphs
and recurrence relations
material developed here is not difficult and with graphing calculators,
the computations are not hard. A basic understanding of probability
theory is assumed though. The reader might want to consider having a
look at the Probability math explorer’s
write-up, for example.
introduce the example of a mouse in a maze and develop the idea of a
. After playing with this toy model, the next
section introduces the framework of Markov chains and their matrices
showing how it makes it easier to deal with problems like that of the
mouse in great generality. We then investigate the model and then
provide a few applications to practice the learned skills.