This document discusses several key aspects of mathematics and algorithms used in internet information retrieval and search engines: 1. It explains how search engines like Google can rapidly rank billions of web pages using algorithms based on the topology and link structure of the web graph, such as PageRank. 2. It describes two main types of page ranking algorithms - static importance ranking based on link analysis, and dynamic relevance ranking based on statistical learning models to match pages to queries. 3. It proposes a new ranking algorithm called BrowseRank that models user browsing behavior using Markov chains and takes into account visit duration to better reflect true page importance.