Exam I will be in the usual classroom on Thursday, October 16, 2008. It will cover the material that we have studied from Chapter 1 of the text.

Calculators or other mechanical assistance are not needed and are not to be used. Blank paper will be provided on which to write your solutions, so all you will need is something to write with.

Some of the exam problems will be similar to homework problems, while others will draw upon the material presented in the lectures. As on any exam, it is wise to start with the problems that you feel confident that you know how to do, before moving on to others. If asked for a definition, give the definition that we have used in this course.

There are 63 points possible. I expect few if any students to be able to do all of the problems. In fact, 32 out of 63 points (i. e. a 32-31 victory) might be a C-level "win." No doubt you will give up some fumbles and interceptions, so just relax, do your best, and move on.

The following topics are very likely to appear, although the exam is not limited to these topics:

1. Lines, their description as P + [v], direction of a line, unit normals, description as an equation ⟨X−P,N⟩=0,
2. Orthonormal bases and the Orthonormal Basis Theorem.
3. Isometries, their definition and basic properties.
4. Calculations using the formula for a reflection.
5. The translation and reflection groups TR(L) and REF(L) for a line L.
6. Isometries of R2: reflections, translations, rotations, and glide-reflections, their definitions and basic descriptions.
7. Homomorphisms, isomorphisms, cosets of subgroups, index.

The following topics do not appear, at least not explicitly: Cauchy-Schwarz inequality, Triangle inequality, general distance functions, distance between parallel lines, formulas from the Existence of Perpendicular Lines theorem, finding intersection point of two lines, dilations, the matrices ref(θ) and rot(θ), representation theorems, orders of elements in groups.

There is no need to memorize long proofs of theorems. You should be able to do computations involving the formula for a reflection Ω_L, and have some facility with the basic ideas we have used in the many proofs we have examined in the lectures. Certainly one should know how to find perpendicular vectors, unit vectors, and so on. One should know the definitions, of course, but if you have been keeping up with the course and studying your notes from the lectures, you should be quite familiar with them by now.

If you want to see some exams I have written in other courses, many of them are available at the links that appear on my course pages page. Some were 50-minute classes, but most were 75-minute classes.