The computational mathematics curriculum is a program of study offered by the Department of Mathematics, Statistics and Computer Science that blends the subjects of computer science and applied mathematics. The program is designed to provide a balance between mathematics and computer science that would otherwise require a double major to achieve. It includes those courses in the mathematics curriculum that emphasize applied mathematics as well as those from the computer science curriculum that develop the computing skills required by many of today's applications.
The department seeks to provide each of its majors with a broad understanding of computer science. This broad understanding serves as a coherent framework in which the student can place his or her developing knowledge and technical skill. Moreover, the department seeks to provide each student with a solid foundation in the central ideas and methods of modern computer science. It seeks to produce computer scientists who know, understand and can apply these central ideas and methods to real problems.
Computer science is dynamic. It grows constantly. It evolves continuously. It regularly experiences revolutionary transformation. The Department seeks, therefore, to produce computer scientists who can adapt and grow along with their chosen profession.
The department does not seek to train its majors in any particular hardware device, software product or conceptual methodology. Rather, the goal is to provide its majors with the power to succeed in today's computer environment as well as tomorrow's. Students will, however, acquire ample specific knowledge during their education.
Before entering Marquette University, 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 Marquette University 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.