an undergraduate and faculty member in the Department of Applied and Computational Mathematics and Statistics

Mathematics is one of the great achievements of the human mind. The mathematical way of thinking empowers the human intellect, enhances critical thinking, and facilitates rational decision-making. This has been recognized since classical times, and for this reason mathematics has become part of a great intellectual tradition, which includes the philosophical writing of Plato and Descartes and the four subjects of the medieval quadrivium. Representing ideas in a symbolic manner and analyzing arguments with the help of logic are, first and foremost, mathematical exercises.

Applications of mathematics pervade today’s culture. Policy makers and ordinary citizens increasingly confront issues in science and technology which are formulated in mathematical language. However, mathematics far exceeds this historical scope. For example, mathematics is used to analyze personal finances, formulate government fiscal policy, justify data-based decisions, encode and protect information, provide a unified understanding of the forces of nature, and manage the treatment of disease. Understanding the scope and power of mathematics enables graduates to better make informed decisions as citizens and as potential leaders of the country and of the world.

Goals and Perspectives

Following are specific learning goals for courses which satisfy the University mathematics requirement, and a few comments about these courses.

1. The main goal is to provide students with experience in the mathematical way of thinking, especially insofar as this way of thinking fosters the development of disciplined habits of mind and enhances the power of the intellect. Students will learn deductive reasoning in problem solving and the inductive process in drawing conclusions from mathematical analysis.

2. Students will learn to read and understand mathematical symbols and formulas, and to be able to express their thoughts by using symbols and equations. They will demonstrate the ability to use mathematical formulas to express clear and precise relationships between the variables involved. It is sometimes said that the best way to clarify a thought is to write it as an equation. Students will work as active learners to understand the language of mathematics.

3. The courses will stress conceptual learning along with technique. Students will learn that there is a commonality in the world of mathematics by seeing fundamental concepts in different settings. For instance, in calculus they will learn that notions like velocity, acceleration, and marginal profit are all particular manifestations of the general concept of derivative. Students will learn how mathematics can be used to abstract key features of our world and reason about these features in a general context.

4. Students will learn mathematical techniques and methods by using algebraic or analytic manipulations to produce explicit solutions to computational problems. Students will learn mathematics by doing mathematics.

5. Students will develop modeling skills. These skills include describing the situation under consideration clearly, translating appropriate aspects into equations using suitable variables, symbols, and mathematical concepts, and interpreting possible mathematical solutions in terms of the original process. Students will come to appreciate that since mathematical models only approximate real world situations, they sometimes require adjustment or improvement.

6. Students will learn that mathematics informs solutions to a wide variety of problems in modern society. Problem areas include but are not limited to the environment, the economy, health care, and politics.

While it is important that there be a variety of mathematics offerings which satisfy the mathematics requirement, we expect that these will include a few specific subjects. We mention three in particular: calculus for its central place in the western intellectual tradition and its importance in modeling the physical world; statistics, because it has become an essential tool for engaging the vast amounts of data that accompany many problems in business, engineering, science, and social science; logic, since it is the foundation of rational discourse.

Approved April 20, 2005, by Academic Council