1. Mathematics at Google

2. Brief history Started in 1996 as the research project ‘Backrub’ by the then PhD student Larry Page Sergey Brin joined in Became incorporated in 1998 Began selling advertisement in 2000 Became public in 2004 – Initial raise $2,718,281,828 (e * 10 ^ 9) – Implied value of 23 billion

3. The 25,000,000,000 vector Represent the web as a huge directed graph Constantly traversed by a “random web surfer” Forward and backlinks The importance of each page is based on importance of the pages linking to it

4. Importance of a page Transition matrix

5. Stohastic matrix – All entries are non negative – The sum of all entries in a column is 1 (unless the node corresponding to that column has no links)

7. Dangling nodes Nodes with no forward links

8. Dangling nodes (continued) If A is the matrix whose entries are all zero except for the columns corresponding to dangling nodes, in which each entry is 1/n, then S = H + A.

9. Final Matrix Google Matrix α – damping factor, usually 0.85

10. Other examples Google maps – graph of all cities. -Selected route is the shortest path between the nodes -YouTube rankings -Ad serving -Selection algorithm -Various areas of research

11. Forecasting Simulation of the ad server Sampling of data Ad selection based on satisfaction index of the ad

12. Machine Learning Marriage between statistics and computer science Adaptive models for predicting and classifying data regression analysis, neural networks, support vector machines

13. Math in management Chief Economist of Google is Hal Varian -professor in University of Berkeley specializing in microeconomics and information technology -Employee ratings -Resource allocations