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Mathematics Overview - Preparation - Day In The Life - Application -
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Day In The Life
Real life as a mathematician bears little resemblance to cliché. Not everyone has a Ph.D. in operations research, nor do they spend days at the computer terminal isolated from human contact. In reality, a mathematician's working experience is a matrix of the type of problems you work on and the relationships among the members of your team. You will find that you need to bring a wide range of skills to bear on your various daily activities.

Typical Problems
At the heart of your work will be the kind of mathematics that you do. There are no typical problems any more than there are typical days, but it is possible to get a general idea of the work that goes on. Most problems in the real world require multiple levels of analysis, planning, detail work, and coordination.


Problem -- A firm wanted to decide statistically with a given confidence level what is the most it can lose over a given time interval. There are several methods to compute this value, the most precise of which tends to be very time-consuming -- requiring on the order of hours or maybe days to run on a computer, which makes it not feasible for a bank. The challenge is to come up with a quick analytical way to estimate this so-called value at risk.
Process -- In order to do this, we drew upon techniques from stochastic processes, differential equations, and also Fourier analysis because we implement a Fast Fourier Transform and we used complex arithmetic in its implementation.
Results -- The analysis resulted in a complete distribution of the firm's future portfolio values. For instance, in one day or five days the full worth of the portfolio could vary by +$50 million to -$7 million or less. We assigned a probability to each of these states. Coming up with such probabilities rigorously involved some fairly interesting mathematics at that level, and it involved other people from the group and collaboration with people overseas. Part of the result of this work was a paper, and it is something that ultimately will get incorporated into our company's product, which is software. In addition, it allowed us to do some interesting research.


Problem -- The goal is to develop a methodology to reduce sonic boom in aircraft design.
Process -- We use computational fluid dynamics and a computational code to study the flow over the geometry of an aircraft. Once the solution is obtained, we use visualization tools to look at the physical flow field over the aircraft. We use a color monitor, called the work station, to bring the solution up visually. For example, if you want to look at the surface pressure of an aircraft we identify a blue color with the lower pressure, and a red color for the higher pressure. So by looking at the gradients of the color changes we understand the pressure on the surface of the aircraft. From this we understand a little bit more about the physics.
Results -- Once we have experience with this problem, we start the design phase using computational fluid dynamics codes and changing the shape of the aircraft. Bit by bit we get to what we want to achieve, a reduction in the sonic boom.


Problem -- Produce a forecast for Department of Defense budgets of how much production of a particular ship will cost in one year (or five years, ten years or 20 years.) We look at what types of factors will drive overhead costs and what kind of relationships exist when estimating future overhead costs versus how they have behaved in the past.
Process -- We use a lot of statistical procedures to build models to project these costs into the future. We look at regression analysis and data collection as well as historical data to figure out whether it will be an accurate indicator for what will happen in the future. We actually build models that will give us some sort of overhead estimate to include in our ship cost.
Results -- Changes occur that make the models nonlinear. Things that happened five years ago are not actually what are happening five years from now and things are just so dynamically changing, that it's very hard to predict what will happen.

Work Environment
Regardless of your job's specifications, it is very likely that you will be part of a team working with people of diverse backgrounds. These colleagues will be a resource for you, as you will be for them. You may be handed assignments directly and given a specific time frame in which to complete them, or your work may derive from a project for which you are generally responsible.

To accomplish your work successfully you will need more than just your mathematical abilities. The capacity to write well and to articulate your ideas to others is imperative no matter what kind of job you have. In addition to communication and interpersonal skills, familiarity with other technical specialties is important. Often the problems you tackle may originate in other disciplines, and knowing the `vocabulary' for that area may speed your work.

Checking email, planning meetings, calling clients, preparing for conferences, creating budgets, researching problems, hiring staff, developing specifications, assigning tasks, training colleagues, running computer applications, writing reports -- the list of activities you perform in any given day will be diverse and long.

Once you are on the job, you may find yourself working on projects that require knowledge in areas new to you. Most employers expect this to happen and give you time to obtain the background you need. When looking for a job, you will want to find out what opportunities and training an employer offers so you can stay abreast of changes in your field.

Note: Some resources in this section are provided by the American Mathematical Society, Mathematical Association of America, Society for Industrial and Applied Mathematics, and the US Department of Labor, Bureau of Labor Statistics.

 Actuarial Science


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