Final Options

There are three options: (1) Take the final (20%), (2) Complete a third project using Maple to be turned in by final time (20%), or (3) do both (1) and (2) (40%). If you do both, I will drop the lowest of the first two exam scores.

The final exam will given on Thursday of final week 3-5 in the Lab, CB 313. It will consist of a blend of 8 to 10 problems over topics covered on the first two exams: polynomials, binomial theorem and extensions, commuting polynomials, semigroups, selfmaps, counting principles, basic counting problems, generating functions, series, advanced counting problems, complex numbers and the geometry of their operations (this covers several subtopics), the fundamental theorem of algebra, moebius maps, orientation preserving maps, angle preserving maps, the poincare disk model for the hyperbolic plane, and using complex numbers to solve geometry problems.

The final project. Here are the possibilities.

1. Do the project on extended Mobius maps (the one that no one chose amongst the alternatives for project 2).

2. Prepare a worksheet in which an at least two moderately hard geometry problems are solved using complex numbers. I suggest this for one:

Given a convex quadrilateral, erect a square on each side exterior to the quadrilateral. The two segments obtained by joining the center of each square with the center of the opposite square are perpendicular and of the same length.

The worksheet should contain a word drawit which takes the vertices of a quadrilateral and draws the quadrilateral, the squares on the four sides, and the two segments in question.

The other can problem can be an open ended question which you use complex numbers to investigate. I suggest the question: What if the word `square` is replaced with `equilateral triangle` in the above problem?

3. Revise and extend the worksheet hyperb.mws which I posted Tuesday. By that I mean 1) work the problems that are listed in the worksheet, 2) add two words to the vocabulary 3) Use the vocabulary to experiment with finding the analogue in hyperbolic plane of a theorem in the euclidean plane: I suggest here you investigate how to tile the hyperbolic plane with a triangle.