Welcome to Geometry and the Imagination!
This course aims to convey the richness, diversity, connectedness, depth and pleasure of mathematics. The title is taken from the classic book by Hilbert and Cohn-Vossen, ``Geometry and the Imagination'. Geometry is taken in a broad sense, as used by mathematicians, to include such fields as topology and differential geometry as well as more classical geometry. Imagination, an essential part of mathematics, means not only the facility which is imaginative, but also the facility which calls to mind and manipulates mental images. One aim of the course is to develop the imagination.
While the mathematical content of the course will be high, we will try to make it as independent of prior background as possible. Calculus, for example, is not a prerequisite.
We will emphasize the process of thinking about mathematics. Assignments will involve thinking and writing, not just grinding through formulas. There will be a strong emphasis on projects and discussions rather than lectures. All students are expected to get involved in discussions, within class and without. A Geometry Room on the fifth floor will be reserved for students in the course. The room will accrete mathematical models, materials for building models, references related to geometry, questions, responses and (most important) people. There will be computer workstations in or near the geometry room. You are encouraged to spend your afternoons on the fifth floor.
The spirit of mathematics is not captured by spending 3 hours solving 20 look-alike homework problems. Mathematics is thinking, comparing, analyzing, inventing, and understanding. The main point is not quantity or speed-the main point is quality of thought. The goal is to reach a more complete and a better understanding. We will use materials such as mirrors, Polydrons, scissors and tissue paper not because we think this is easier than solving algebraic equations and differential equations, but because we think that this is the way to bring thinking and reasoning to the course.
We are very enthusiastic about this course, and we have many plans to facilitate your taking charge and learning. While you won't need a heavy formal background for the course, you do need a commitment of time and energy.