Determining Day of Given Date Mathematically

Computation of day of a week from given date belonging to any century has been a great quest among astronomers and mathematicians for long time. In recent centuries, thanks to efforts of some great mathematicians we now know methods of accomplishing this task. In doing so, people have developed various methods, some of which are very concise and compact but not much accessible explanation is provided. The chief purpose of this paper is to address this issue. Also, almost all known calculations involve either usage of tables or some pre-determined codes usually assigned for months, years or centuries. In this paper, I had established the mathematical proof of determining the day of any given date which is applicable for any number of years even to the time of BCE. I had provided the detailed mathematical derivation of month codes which were key factors in determining the day of any given date. Though the procedures for determining the day of given date are quite well known, the way in which they arrived is not so well known. This paper will throw great detail in that aspect. To be precise, I had explained the formula obtained by German Mathematician Zeller in detail and tried to simplify it further which will reduce its complexity and at the same time, would be as effective as the original formula. The explanations for Leap Years and other astronomical facts were clearly presented in this paper to aid the derivation of the compact form of Zeller’s Formula. Some special cases and illustrations are provided wherever necessary to clarify the computations for better understanding of the concepts.