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Markov Chains, Random Walks, and Card Shuffling
(East Carolina University, 2016)
A common question in the study of random processes pertains to card shuffling. Whether or not a deck of cards is random can have huge implications on any game being played with those particular cards. This thesis explores ...
The Spectral Theorem for Self-Adjoint Operators
(East Carolina University, 2016-04-25)
The Spectral Theorem for Self-Adjoint Operators allows one to define what it means to evaluate a function on the operator for a large class of functions defined on the spectrum of the operator. This is done by developing ...