This course will be an opportunity to explore how various aspects of mathematics can be visualized by physical and virtual models, often in quite beautiful ways, and conversely how mathematics can be used as a tool in designing beautiful physical and virtual models.

Here are some examples that we may look at, but some choice of topics will be guided by the interests of the class members.

- Symmetry: How many different kinds of wallpaper patterns are there? How can we recognize them?
- Polyhedra: What are they, and what role do they play in art, chemistry, etc.?
- Proofs without words: How can we "see" such formulas as the sum of the first n odd integers is n squared?
- The fourth dimension: How can we visualize it?
- The Mandelbrot set: Some of us have seen it many times. What is it?
- Fractals: What are they, and how are some fractal images generated?
- Animations: What is some mathematics underlying animated films such as those produced by Pixar?

The prerequisite for the course is facility with algebra and geometry, and a willingness to learn more as needed. Calculus is not a prerequisite, but if you know it, you will find use for it! Knowledge of a particular computer programming language is not a prerequisite, but we will be learning how to use some computer programs that require some attention to logic and detail, so patience in this regard is likely to be needed.

At the end of the course it would be nice to host an exhibition!

- Assignment #1
- Assignment #2
- Assignment #3
- Assignment #4
- Assignment #5
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- Assignment #10
- Assignment #11

- Abbott: Flatland
- Banchoff: Beyond the Third Dimension: Geometry, Computer Graphics, and Higher Dimensions
- Holden: Shapes, Space, and Symmetry
- Steinhaus: Mathematical Snapshots