Mathematics of Voting----------------While many people tend to take voting for granted, mathematicians should not. The reason is that it requires the muscle power of mathematics to appreciate and understand what is required to ensure that election outcomes more accurately reflect the views of the voters. In this expository talk, I will outline the kind of mathematics that is needed to understand voting. As for Arrow's Theorem, forget it; after it is introduced, we will show why it does not mean what everyone has thought it meant for the last half century. Also, be prepared to leave the lecture worrying about the legitimacy of the outcome of the last election that was of importance to you.