Welcome! For many of you, this course will be unlike any of your previous courses because it uses a different educational paradigm. Under this paradigm the emphasis is placed on continuous learning and improvement, rather than teaching and testing; on the process used in getting to a goal, not merely the goal, and on cooperation, rather than competition. In this course it is not sufficient merely to answer a question: How clearly you communicate your reasoning and the assumptions you use are just as important as the conclusions you reach.

There are two major sections to this text---the course readings and the in-class activities. All in-class work is done in small groups in a lab-style format. The lab format increases the opportunities for you to discover for yourself many of the fundamental ideas of modern mathematics. The readings are designed to give you the background and context necessary for you to construct your own conceptual framework to organize the information to which you are exposed. For information to become knowledge, it must be organized by the learner. The implications of new concepts and their relation to existing knowledge must be thought through.

Educational research gives compelling evidence that students learn mathematics well only when they construct their own mathematical understanding. Quoting from the national report, Everybody Counts, " All students engage in a great deal of invention as they learn mathematics; they impose their own interpretation on what is presented to create a theory that makes sense to them. Students do not learn simply a subset of what they have been shown. Instead, they use new information to modify their prior beliefs. As a consequence, each student's knowledge of mathematics is uniquely personal."¹

These materials are intended to aid you in this process of constructing meaning and to help you become a more efficient learner. Your abilities to interpret and communicate information, to reason critically and quantitatively, to work with others, and to solve problems, like any other skills, are improved through practice and self-reflection. To enhance your learning and humanize the text, whenever possible we have included the historical development of a topic. By examining the historical development of a concept and contrasting historical with current practices, we gain valuable perspective and thus deepen our understanding of the concept.

This is an applied course, mathematics is viewed as a language and a set of tools that help us to formulate, solve, and communicate real-world problems. Technology is an integral part of this process. It removes the need for contrived problems, opens the door for realistic and interesting applications, and allows the focus of the course to be on problem solving and exploration. In today's information age, the computer is an invaluable tool, allowing us to quickly acquire, analyze, and communicate information.

Why Require Mathematics?
Historically, a study of the "liberal arts" (or "studies befitting a free citizen") has always included a study of basic mathematics. From the time of the first schools in ancient Sumer over 4000 years ago, mathematics has been an integral part of the curriculum. Seven branches of learning were studied in the Middle Ages: arithmetic, geometry, logic, grammar, rhetoric, astronomy, and music---more than half the curriculum involved mathematics.

Mathematics plays an even larger role in our modern technological society. The ability to understand quantitative issues that involve mathematics, science and technology is a critical skill for all citizens today---on and off the job. Environmental and fiscal policy issues facing today's electorate will profoundly affect our future quality of life. The world's population will likely double in the next 40 years, yet we are already expending energy at rates far beyond sustainable levels. Appropriate policies in response to such critical issues as an exponentially growing population, and the allocation of dwindling natural resources, emissions of greenhouse gases, ozone depletion, and the "disposal" of nuclear waste must be established. Responsible choices in these policy areas cannot be made by those without a basic mathematical literacy.

In recent years, numerous national reports have highlighted the importance that everyone have some significant proficiency in mathematical thinking and technique. This proficiency is often referred to as quantitative literacy and is prerequisite for science literacy, which encompasses basic proficiencies with mathematics and technology as well as the natural and social sciences. To help you develop a basic level of mathematical literacy and thus to set your feet firmly on the path to science literacy is the primary goal of this course. In this it differs significantly from traditional entry-level mathematics courses, in which mathematics is too often understood by students to consist solely of symbol manipulation skills, according to set rules and procedures. This is not the kind of mathematical literacy that society requires. Rote and passive learning of mathematical facts and procedures is not sufficient. Understanding, explanation, and prediction are the real destinations. In this course you will learn to use the computer to quickly acquire, organize, analyze, model, and communicate information. You will be asked to draw inferences, interpret models, estimate results, suggest alternatives, and make reasonable testable guesses, as you apply mathematical methods to the solution of real-world problems.

Traditionally, literacy refers to the ability to read and write. Webster's New World Dictionary, suggests that "literate" is synonymous with "well educated." In any given society, at any given time, the level of proficiencies that one must possess to be called literate reflect social, economic, and educational conditions. In the late 19^th century, the U.S. government considered a person literate if they could read and write their own name. Today, the United Nations Educational, Scientific, and Cultural Organization (UNESCO), classifies literacy as understanding and producing a simple statement on everyday life. To succeed in our modern technological society requires much more sophisticated communication and problem-solving skills. If, by literate, we mean "able to participate and contribute to society," then we must include proficiencies in mathematics and science.

Most of us would be shocked if, at a social event, we overheard a prominent social figure admit that he or she could not red or write, yet few of us would be surprised to hear this same individual admit to being unable to do algebra. Many educated people exhibit or even flaunt great deficiencies in basic mathematical knowledge and skills. As a society, we can ill afford this attitude. The level of mathematical literacy needed to participate in the world, its jobs, its economic and social orders, and its democratic institutions has risen dramatically in the last decades. The following quotes from recent national reports highlight the need to expand our definition of literacy to include mathematical and science literacy:

To function in today's society, mathematical literacy---what the British call "numeracy"---is as essential as verbal literacy ... Numeracy requires more than just familiarity with numbers. To cope confidently with the demands of today's society, one must be able to grasp the implications of many mathematical concepts---for example, change, logic, and graphs---that permeate daily news and routine decisions---mathematical, scientific, and cultural---provide a common fabric of communication indispensable for modern civilized society. Mathematical literacy is especially crucial because mathematics is the language of science and technology.²

To participate rationally in a world where discussions about everything from finance to the environment, from personal health to politics, are increasingly informed by mathematics, one must understand mathematical methods and concepts, their assumptions and implications.³

The impact of science and technology has become so significant in our daily life that the well-educated citizen requires a background in the liberal sciences as well as the liberal arts. It has long been recognized that mathematical literacy is an important goal of all liberal education.⁴

Other things being equal, a person who has studied mathematics should be able to live more intelligently than one who has not. And, up to a point at least, the more mathematics studied, the more intelligent the life should be⁵.

...More and more jobs---especially those involving the use of computers---require the capability to employ sophisticated quantitative skills. Although a working knowledge of arithmetic may have sufficed for jobs of the past, it is clearly not enough for today, for the next decade, or for the next century.⁶

Many adults, and especially college graduates, are very likely to assume positions in their communities and in professional organizations where quantitative literacy (e.g., the ability to deal intelligently with statistics) will come into play and may even be essential for effectiveness. A quantitative literacy requirement can thus be expected to enhance the quality of citizens.⁷

These materials are still very much under development; and there are rough spots and most likely both errors and omissions. For these we ask your patience. Your input, constructively given, is welcomed. It will help us to refine these materials, thereby improving the course for future students.

1. NRC, Everybody Counts: A Report to the Nation on the Future of Mathematics Education. Washington, DC: National Academy Press, 1989.
2. Ibid.
3. Cheney, Lynn V., 50 hours: A Core Curriculum for College Students. Washing ton, DC: National Endowment for the Humanities, (1989), p. 35.
4. Committee on Support of Research in the Mathematical Sciences (COSRIMS) of the NRC, The Mathematics Sciences: A Report. Washington, DC: National Academy of Sciences, (1968)., p.56.
5. NCTM, A Source book of Applications of School. Reston, VA: NCTM, (1980), Preface.
6. NRC, Moving Beyond Myths: Revitalizing Undergraduate Mathematics. Washington, DC: National Academy Press, (1991), p. 11.
7. Quantitative Reasoning for College graduates: A Complement to the Standards, MAA/AMS (1995).