This is a course covering a number of concepts and techniques of discrete mathematics. Topics covered: Counting: selections; inclusion-exclusion; generating functions; recurrence relations.

Let T denote a subset of the possible transitions between the states of a finite Markov chain and let Yk denote the time of the kth occurrence of a T-transition. Formulae are derived for the ...

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We characterize the maximal class of functions that generates such a metric. Further, we show how some interesting properties of these probability metrics arise directly from conditions on the ...