The purpose of this test experience is to help you understand the material and make connections. Research has shown that the effort you expend in studying for tests and clearly explaining your work solidifies your learning. One 8.5*11 sheet with writing on both sides allowed. You can put anything you like on your sheet. One scientific calculator allowed (but no cell phone nor other calculators bundled in combination with additional technologies).

On the test, your grade will be based on the clarity, quality and depth of your responses. Questions will mainly consist of short answer or essay types.

You will be expected to answer questions about activities from class or lab. Review the following:

You might be presented with one of Escher's works, asked to calculate the sum of the angles in a triangle in the space represented, and specify whether the space is then Euclidean, spherical or hyperbolic. If you don't remember how to do this, you should review the relevant worksheet and class notes (or ask me in office hours). Embedded in this analysis is the knowledge that the sum of the angles in a triangle is important since it determines the geometry of a space: 180 degrees for flat Euclidean spaces, greater than 180 degrees for spherical spaces, and less than 180 degrees for hyperbolic spaces.

Review class discussions and arguments for the Simpsons portion of project 1, and problems 1, 3, 5, 6, 10, and 11 of project 2. For example, you should be able to explain in depth the various ways we explored shortest distance paths on a sphere in class (the car, masking tape, string, Chicago-Rome reading in Heart of Mathematics, symmetry...) and the ways we explored the Pythagorean theorem on the sphere (string, algebra, computer program on a transparency, Futurama Greenwaldian theorem), along with more general questions like describing one of the possible finite shapes without edges for our universe.

Instead of thinking about what a 2-D Marge would see if an orange passed through her plane (a sequence of lines/curves that appear, get bigger and disappear), you might be asked what she would see if something more complicated passed through, such as a mug.

You might be given a partially completed torus or Klein bottle tic-tac-toe game and asked to mark a winning move. You may wish to review by playing a few games. In addition, you should understand the tiling view - where identified moves are marked above, below, to the right, and to the left of the board, as on the lab picture or Jeff Week's worksheet.

You might be asked to describe in detail some of the methods being used to attempt to discover the shape of the universe, as well as our classroom discussion of those critiques (Gauss' triangle but light bending with gravity, Rob Kirshner's Supernovae distance/brightness experiments but Supernovae not necessarily exploding at the same brightness, looking for repeated patterns like the quarter-turn space but difficulty recognizing the patterns, WMAP data but difficulty agreeing on the meaning of the data) as in the homework readings and in class.

You might be asked about real-life applications of some of the material we have been studying. A good review for this would be the ASULearn Material Review Quiz.

You might be asked about some of the changes in world view that came with mathematical discoveries, from the videos and homework readings. A good review for this would be the ASULearn Material Review Quiz.

The main web page and class highlights page contain links to homework readings and class activities, which also serve as a good review in addition to this sheet and the ASULearn Material Review Quiz.

I want you to understand the material and I am happy to help n office hours or on the ASULearn bulletin board.