Looking Into Mathematics: A Visual Invitation to Mathematical Thinking

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Many undergraduates are turned off by mathematics. Their feelings about mathematics veer between negative and hostile, between overwhelmed and dismissive. As a consequence, they are not only missing something in their private lives: as citizens, they are less equipped to evaluate many significant developments in humanity's changing relationship to the physical and social world. Our objective is to engage and sustain students' interest in mathematics by genuinely involving them in mathematical thinking. If some go on in mathematics or science, so much the better. We do not, however, seek so much to recruit mathematicians as to make friends of mathematics. We will develop instructional materials, activities, and software tools in an interactive, visual, experimentally-oriented curriculum that conveys the spirit and flavor of modern mathematics emphasizing a variety of key and central perspectives (such as local/global, intrinsic/extrinsic, dynamic/static, discrete/continuous, and algebraic/geometric). We will enable semi-rigorous interactive experimentation--both manual and virtual--with a rich variety of complex, interesting mathematical objects like curves, surfaces, linkages, knots, and braids. Students will explore these areas using new visual tools that are both powerful and empowering. The audiences targeted by the project include, especially, first-year college students who do not intend to major in mathematics or science, and future mathematics teachers. Pilot sections will be taught at Brandeis Universitiy, Harvard University, Clark University, and the University of Massachusetts, Boston. We will develop materials with a view to their use in a wide variety of colleges and universities, either in introductory mathematics courses or for enhancement of existing courses. Both text and software will be made freely available for adoption and dissemination.