Mathematics has served science and commerce for thousands of years. Yet the attraction of mathematics to mathematicians has frequently been the pure beauty of the subject without regard for its applications. Hence, for many teachers who first found mathematics magnetic for its own sake, the acts of teaching and having to justify the service function of their courses is often a challenge. Even now, many American graduate students in mathematics are exposed only to the relationship of mathematics to physics. Their graduate training does not require even a nodding acquaintance with statistics, operations (operational) research, model building, numerical analysis or simulation techniques. Since those students who are trained in the most abstract mathematics are the most likely to be teaching in the nation's colleges and universities, American undergraduates face a ridiculous irrelevancy in the mathematics classroom.

In most American colleges and universities today incoming students can choose a first mathematics course from

• remedial mathematics – intermediate algebra

• finite mathematics – usually for business students

• liberal arts mathematics – “math for poets”

• precalculus – functions (algebraic and transcendental)

• technical mathematics – for the trades (two year colleges)

• statistics – for social science, business, economics and health sciences

• short calculus – for non math and science majors

• calculus for mathematics, science and engineering three or four semester sequence in which advanced placement is possible

• discrete mathematics – for computer science and mathematics students