Western science relies on mathematics as a powerful language for expressing the character of the observed world. Mathematical models allow predictions (more or less) of complex natural systems, and modern computing has magnified the power of those models and helped shape new models that increasingly influence 21st century decisions. Computer science also relies on mathematics for its culture and language of problem solving, and also enables the construction of mathematical models. In fact, computer science is the constructive branch of mathematics. In addition to science and computer science, activities in many other disciplines rely (somewhat surprisingly) on mathematics – witness pattern in art, architecture and statistics in the social sciences, to name a few.

Lamentably, however, in spite of the centrality of mathematics, and its inherent beauty, many in our culture have, sometime in their schooling or careers experienced real or perceived barriers to learning or appreciating or using mathematics.

Though this program focuses on connections between mathematics, computer science and the natural sciences, we seriously examine difficulties in our culture to learning mathematics, and the barriers that represents for individuals. We will develop mathematical abstractions and skills needed to express, analyze and solve problems arising in the sciences and particularly computer science. The program is intended for serious students who want to gain a fundamental understanding of mathematics and computing before leaving college or pursuing further work in the sciences. The emphasis is fluency in mathematical thinking and expression, along with reflections on mathematics and society. We will learn to program visually pleasing geometrical shapes in a surprisingly powerful, albeit fun, programming language (Logo).

Topics include concepts of algebra, functions, algorithms, and programming; and calculus, logic or geometry; all with relevant historical and philosophical readings. We will also address in seminar and the problem solving workshops the psychological, pedagogical and development aspects of mathematics teaching and learning, in particular as we discuss the place where each of us got “stuck” or “stopped” in our earlier involvement with mathematics.