This article begins with an exploration of the origins of the Gregorian Calendar. Next it describes the function of school inspector Christian Zeller (1822-1899) used to determine the number of the elapsed days of a year up to and including a specified date and how Zeller's function can be used to determine the number of days that have elapsed in any given common year (a non-leap year). This is followed by a discussion of Charles Dodgson's (also known as Lewis Carroll) (1832-1898) method for determining the day of the week given any date in the Gregorian calendar. The article concludes with thoughts from John Conway, Professor of Mathematics at Princeton University, on the day of the week and a discussion on the origins of the sequence of day names in the modern calendar. The algorithms presented in this article could easily be adapted for the classroom. Students could develop computer programs around the Zeller congruencies and junior students in particular could strengthen basic arithmetic concepts by learning the Lewis Carroll technique as well as getting the chance to see mathematics as a powerful and practical pursuit.