|
Wednesday, 28 September 2005 |
We combine emerging information technologies with powerful mathematical tools to study a variety of problems that arise in the study of human processes. These problems can be roughly divided into three broad categories:
- Physical: The management of physical resources, including people, natural resources (such as agricultural commodities and oil), equipment (such as aircraft, locomotives, trucks and cars) and products being sold to consumers. Application domains include transportation, logistics and manufacturing, as well as problems drawn from classical areas within engineering such as the design of structures or robots.
- Financial: The pricing of financial instruments, and the allocation of financial resources, with an emphasis on managing risk. Financial managers often face the problem of designing a portfolio of investments that might include stocks or the insurance of houses against earthquakes and hurricanes. The study of financial risk often takes us into the domain of the physical sciences, where we may study weather patterns, earthquakes or the economies of developing nations.
- Informational: The study, analysis and design of effective systems for storing and communicating information. This area spans the fundamentals of representing information mathematically, to the use of the Internet in electronic commerce. Information engineering encompasses the representation of knowledge, and the study of the economics of different types of information and information technologies.
We approach these problem areas using three branches of mathematics:
- Statistics: This is the mathematics of working with data. It allows us to identify what is actually happening in a complex physical process from observations about this process. We might use temperature data to study the likelihood that a ski slope will have a bad winter, or financial data to help determine the volatility of a financial instrument.
- Stochastics: This is the mathematics of uncertainty, and we use these tools to model the possible behavior of a system in the future, where no data is available. For example, we might characterize the behavior of interest rates, and use this to determine the price of a bond. Or we might want to estimate how many books an on-line bookseller should keep in stock.
- Optimization: This is the mathematics of making decisions. One problem class emphasizes making decisions under uncertainty, balancing risks and making decisions that are likely to stand up under different outcomes. A different problem class assumes that all the information is known but where the problem of finding the best decision is very complex. Such problems arise in transportation, the design of distribution networks, or the allocation of assets among competing investments.
|
