Discrete math challenges calculus as cornerstone of college mathematics
Standing before a blackboard with chalk in hand and wearing plaid shorts to beat the late summer heat, Donald Small could just as easily be a football coach positioning X's and O's as a math professor explaining the revolution taking place in college mathematics departments.
''Just about every math department in the country is looking at ways in which discrete math can be incorporated into their curriculum in the next few years,'' says the Colby College professor.
Discrete math - sometimes called ''the language of computers'' - is challenging calculus as the cornerstone of mathematics study at the collegiate level. Its growing prominence springs from the tie to computers, and thus to a growing number of fields that rely on computers in research.
The new-style math focuses largely on the solving of quantitative problems. For instance: How much oil will an offshore well produce each year if it is producing 1,000 barrels a day at a declining rate of 1 percent per week? Such calculations are known as discontinuous math, in contrast with calculus (calculating the speed of a particle in physics, for example), which is known as continuous math.
Interest in discrete mathematics intensified this past summer when the Alfred P. Sloan Foundation announced grants to six colleges and universities to develop a new curriculum with discrete mathematics as its core.
Grants totaling $240,000 went in equal shares to Colby College, the University of Delaware, the University of Denver, Florida State University, Montclair State College, and St. Olaf College.
The importance of discrete math lies in its application to the challenges inherent in an information-based economy. ''Discrete math is a better system for problem-solving than what we have now - and industry wants problem solvers,'' says Dr. Small. ''There's no question the economy - and society in general - will be highly dependent on discrete math. Whether it will depend on the discrete mathematician, though, is another question.''
That dependence, as well as the upsurge in interest in discrete math, can be linked to computers. Computers function like discrete mathematicians - in terms of quantities and symbols. Social scientists, engineers, and physical scientists all use computers, and thus could benefit by training in discrete math.
''With the advent of computers we are much, much more concerned with efficiency and that's what discrete math is all about,'' says Small. ''It is also algorithms. And when you are writing a computer program you are writing an algorithm.''
The problem with discrete math is this: there is at present no univerally accepted definition of what should constitute a discrete math course. Unlike calculus, discrete math has no fundamental theorems.
The major obstacles that confront the schools awarded grants are condensing the traditional 11/2-year calculus program into one year and developing a full one-year discrete math course. Currently there are few if any textbooks focusing on discrete math.