Mathematics behind Google's PageRank algorithm

Google has become a name synonymous with web searching, to the point where Merriam Webster defines google as “verb: to use the Google search engine to obtain information about (someone or something) on the World Wide Web.” Google, Inc. was founded in 1998, and quickly became the leader of Internet search engines. With its use of the algorithm it called PageRank, it retrieved search results that were much more relevant to the interests of its users. The PageRank algorithm works on the basic theory that the more important and useful a page is, the more other pages will link to it. Therefore a page that has many other pages linking to it is more important, and will appear higher in the search results. This proved much more effective than competing search engines at the time, many of which were still searching primarily by keywords, something that was very easily abused. Since the introduction of the PageRank algorithm, there has been many efforts towards the improvement and optimization of the mathematics behind it. There has also been much work to apply the PageRank algorithm to other fields and areas of research. These include determining the relative importance of authors in published in scientific journals, finding potential interactions in proteins, and determining the relative importance of various species in a food web. In this thesis, we will explore the history and mathematics behind the PageRank algorithm, and the optimizations and expanded uses it has found over the years.