After spending four years studying math at University, what will you know? what will you be able to do? and who will pay you to do it?

Have you ever wondered just what sort of job you could get if you studied math at University?

The first thing to realize is that there are a lot of different fields that use applied mathematics and you will probably focus primarily on one or two areas. There's chaos theory, optimization, operations research, biological modelling, game theory, fluid dynamics, numerical analysis, mathematical physics, statistics, teaching and many more.

Chaos
You have already seen that chaos is an important part of our models of the weather. Engineers want to avoid chaos because it is unpredictable and can lead to catastrophic failure. An example is a chemical factory in India that exploded because the engineer in charge did not understand the chaotic nature of the chemical processes.

Optimization/Operations Research

Every day at least once, the mail vans collect mail from all the mailboxes in Boulder. That's a lot of gas and a lot of time. You could be the person to decide the route.

Large ships carry cargo around the world. There could be a lot of different types of cargo all different sizes, all different weights and all on the same ship. It could be your job to decide how that ship is loaded. It could be your job to decide the schedule for a fleet of ships, which ports they visit and when.

Think about all the airplanes carrying passengers and cargo all over the world everyday. Who do you think designs their schedules?

Biological modeling
How and why do animal and plant populations fluctuate? How do species interact within an ecosystem? How many mountain lions can a wildlife sanctuary support? How many deer?

Game theory
How do we make perfect decisions when we have complete information? How do we make best guesses when we have incomplete information? What trajectory should we tell the computer that controls the missiles?

Fluid Dynamics
Fluid dynamics is essential to understanding the atmosphere and the ocean.

Ever thought about designing an airplane? How should the wings be shaped so that the plane can fly faster, use less fuel and maneuver more safely?

Ever thought about how dolphins and sharks glide through the ocean? How should ships be designed?

What should the nose of the space shuttle look like? Will it heat up too much when it re-enters the earth's atmosphere?

Lots of people would be very grateful if you could predict hurricanes and their movements.

Are you interested in global warming issues? People who study the climate and how it changes use fluid dynamics and lots of mathematics.

Scientific Computing
How can we design approximate solutions to hard problems, so that we can use computers to get valuable answers? Can we give doctors new information about how blood flows through a vein, so they can design and improve techniques to help more people?

Mathematical Physics
Do you like spying? Ever sent a secret message? New results in quantum modeling form the basis of a secret code that the ultra-secret, spook-filled, National Security Agency is very interested in.

Actuarial Science
Insurance companies are sitting on millions of dollars in insurance premiums. Lots of new policies get written every year, and millions of dollars get paid out on existing policies. They really need to know just how likely you are to have an accident and even when you're likely to die.

Statistics
Before drug companies spend millions of dollars distributing and marketing new cancer drugs, they need to know exactly how effective those drugs are. And before they get the green light from government, they have to prove to the government that they know. They can get both these things after statistical analysis of the results of clinical trials on many humans. Statistical analysis is worth a lot of money to the drug companies.

Teaching
One of the most important jobs in our society is teaching.  With a degree in Math you could teach Math in high school. There is currently a national shortage of Math teachers. With a Ph.D., you could teach Math at a University.
 

Andrea Codd and Cristina Perez
Graduate Students
Department of Applied Math
University of Colorado at Boulder