Counting problems are rich in opportunities for students to make meaningful mathematical connections and develop non-algorithmic thinking; their accessible nature and applications to computer science make counting problems a valuable part of mathematics curricula. However, students struggle in various ways with counting, and while previous studies have indicated that listing...
Pardoxes in voting has been an interest of voting theorists since the 1800's when Condorcet demonstrated the key example of a voting paradox: voters with individually transitive rankings produce an election outcome which is not transitive. With Arrow's Impossibility Theorem, the hope of finding a fair voting method which accurately...
We consider the problem of wireless spectrum management in cognitive wireless networks that maximizes the revenue for a spectrum operator. Specifically, we study the problem on how a wireless spectrum operator can optimally allocate its limited spectrum to various classes users/devices who pay differently for their spectrum per unit time....
For a certain class of Z²-actions, we provide a proof of a conjecture that the ratio of the Perron eigenvalues of the transfer matrices of the free boundary restrictions converge to the entropy of that action. Also, a novel method for computing the entropy of Z²-actions is conjectured.
This thesis examines the mixing times for one-dimensional interacting particle systems. We use the coupling method to study the mixing rates for particle systems on the circle which move according to specific permutations e.g., transpositions and 3-cycles.