Before entering ÃÛÌÒÓ°Ïñ, most students' mathematical experience has been with applications in which mathematics is seen primarily as a problem-solving tool. Courses in algebra, geometry and perhaps calculus usually stress this aspect of mathematics. These courses concentrate on the skills of formulating a problem in precise terms and then solving it by applying a series of manipulations or formulas, some of which are thousands of years old. There is, however, another aspect of mathematics which beginning students rarely glimpse – so-called pure mathematics. This is the creative side of mathematics in which new systems and formulas are discovered or derived. Here lies the challenge to reach beyond the world as we know it and to speculate, to invent.
In reality, the categories of pure and applied mathematics are not as distinct as they may first appear. Today's applied problem often leads to tomorrow's theory. And, just as often, what was yesterday's esoteric theory provides the practical solution to today's technical challenges. So, for example, modern computer circuitry was developed using the tools of mathematical logic invented in the late 1800's. And the mathematical limitations of computing machinery were derived decades before the physical machines existed. Likewise, the practical problem of errors in transmitting information over telephone lines or satellite channels led to a whole new field of mathematical investigation – "error-correcting codes."
Because of this continuing interplay between pure theory and practical applications, the mathematics curriculum at ÃÛÌÒÓ°Ïñ is designed to open the door to the creative side of mathematics while also providing an atmosphere in which each student's application skills can continue to grow. The curriculum can be tailored to fit an individual's interest. Some students choose to concentrate on subjects with immediate applications such as probability, statistics and differential equations. Others choose to pursue more abstract topics such as modern algebra, topology or logic. Others are interested in preparing to teach mathematics at the primary or secondary level. In any case the curriculum is designed to provide the technical skills for growth in the discipline.
