Applied Mathematics John Gilbert Google and the Random Surfer How does Google figure out which web pages are most important? An important page is one that lots of important pages point to. Start at any web page and follow links at random. Forever. Youll see important pages more often than unimportant ones. Analyzing the Web with graphs and matrices 1
1 2 2 3 4 5 6 7 1 2 Graph
4 7 5 Matrix 3 4 5 3 6 6 7
Graph nodes are web pages Arrows between nodes are links between web pages Matrix entries are links from column pages to row pages The Page Rank comes from algebra on the matrix The matrix has 8,058,044,651 rows & columns (as of yesterday) Applied mathematicians use mathematics to solve problems in physics, biology, medicine,
economics, engineering, technology, and more. Sometimes they also call themselves Computer scientists Numerical analysts Computational biologists / physicists / engineers / Just mathematicians What kind of problems do they solve? How does an enzyme fold up into a particular shape? How can you predict the spread of a forest fire depending on weather, ground cover, and type of trees?
How can you get more data through the Internet faster? How would disease spread after a bioterrorism attack? How can you make an animated movie more realistic? How much would global warming be reduced if all cars used fuel cells instead of gasoline? How could you design a more fuel-efficient airplane?
The difference: Better math, better computing F-117A Stealth Fighter 1981 B-2 Stealth Bomber 1993 Where do applied mathematicians work? Universities Government laboratories Big companies
Startup companies Wall Street and lots of others So, what do they get paid? There is a very wide range! University salaries in Computer Science (2003 Taulbee Survey):
figures are for 9 months/year, not counting summer. Assistant professor lowest: $48,269; median: $76,392; highest: $124,542. Full professor lowest: $52,200; median: $107,670; highest: $280,786. Industry and government labs tend to pay a little bit more. How do you get into this field anyway? Middle school and high school:
Math, science, English (!!!) College Learn about everything! Especially math, science, computing. Graduate school Masters degree Ph.D. Tell me again why you think this is fun? Applied mathematicians usually work in teams, with all kinds of scientists and engineers and other interesting people.
Mathematics helps to solve a lot of their problems! You never know what kind of things youll get to learn about and work on . . . PolyBot: A Modular, Reconfigurable Robot Instead of one complicated robot, why not make hundreds of simple ones? Pointers to applied mathematics for students April is Math Awareness Month!
Mathematics and the Cosmos: http://www.mathaware.org Society for Industrial and Applied Math info on careers: http://www.siam.org/careers/career1.htm MAA Math career profiles: email me: [email protected] http://www.maa.org/careers John Gilbert, http://www.cs.ucsb.edu/~gilbert
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