What is optimization?
Optimization problems deal with the point at which a given function is maximized (or
minimized). It is divided into several subfields, depending on the form of the objective
function and the constraints that the maximized point often has to satisfy.What are some applicationsof operations research?
Applications of operations research span a wide variety of fields, especially with regard
to reducing costs or increasing efficiency. The following lists just a few examples: con-
structing a telecommunications network at low cost and top efficiency, especially
when under high demand or after being damaged; determining routes of school buses
so fewer vehicles are needed; and designing a computer chip that will reduce manu-
facturing time.What is information theory?
Information theory is a branch of the mathematical theory of probability and statis-
tics, allowing it to quantify concepts of information. It was formulated primarily by
American scientist Claude E. Shannon (1916–2001; who was also called “the father of
information theory”) to explain the aspects and problems inherent in information and
communication. In particular, it involves efficient and accurate storage, transmission,
270 and representation of information, such as the engineering requirements—and limi-
What is the Monte Carlo method?
T
he Monte Carlo method gives approximate numerical solutions to a number
of problems that are too difficult to solve analytically by performing specific
statistical sampling experiments. Although forms of the method have been
known for a while, it was initially developed for numerical integrations in statisti-
cal physics problems during the early days of electronic computing. It was named
after the city in the Monaco principality, some say, because of the simple random
number generator of roulette played in the Monaco casinos; others say the
method’s creator was honoring a relative who had a propensity toward gambling.
But there is more to the Monte Carlo method than meets the computation.
For one thing, there is more than one Monte Carlo method. For example, one
method, called the Markov chain Monte Carlo method, has played a critical role
in such diverse fields as physics, statistics, computer science, and structural
biology. And the list of applications continues: As recently as the late 1990s,
researchers and statisticians began to realize the usefulness and power of Monte
Carlo methods for prediction.