applied mathematics

Applied MathematicsApplied MathematicsJohn GilbertJohn Gilbert

Google and the Random Surfer

An important page is one that lots of important pages point to.

Start at any web page and follow links at random. Forever.

You’ll see “important” pages more often than unimportant ones.

How does Google figure out which web pages are most important?

Analyzing the Web with graphs and matrices

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)

1 2

3

4 7

6

5

1 52 3 4 6 7

1

5

2

3

4

6

7

GraphMatrix

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?

F-117AStealth Fighter 1981

B-2Stealth Bomber

1993

The difference: Better math, better computing

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

Master’s 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 you’ll 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: http://www.maa.org/careers

email me: gilbert@cs.ucsb.edu

John Gilbert, http://www.cs.ucsb.edu/~gilbert