Independent Projects
for
Colorado State University, Pueblo
Math 330 — Introduction to Higher Geometry
Spring 2008
The independent project componenet for this course is a chance
to do a bit of work outside of class, from sources other than
(only) the course textbook, on an area of geometry which particularly
interests you. You will then explain, in your own words, (some of) the
big ideas and (some) specific technical details in this area, both in
a written and oral form.
The first step will be to pick a topic. Here are some possibilities:
- spherical geometry
- projective geometry
- finite geometries
- differential geometry
- geometry and physics
- ruler and compass constructions
- origami constructions
- elements of topology (e.g., the classification of surfaces)
- graph theory (e.g., the bridges of Königsberg)
- the four-color theorem
- abstract algebraic aspects of symmetry
- Escher's non-Euclidean art
- tilings (regular, aperiodic, etc.), wallpaper groups
- Godel's Incompleteness Theorem
- the Platonic solids
Please discuss your idea(s) for a project with me, ASAP. If nothing
above appeals at all, and you have another idea (or, even more, if you
do not have another idea) talk to me and we can find something better
suited for you.
The product you should produce for this project will have two parts, as
mentioned above:
The written part will consist of a paper that has at least the
following components:
- An introduction, setting your topic into
(mathematical/historical/social/artistic/political) context.
- A preliminary techical section, giving precise definitions
of some mathematical objects you will explore
- A main technical result, giving a statement and proof of at
least one significant techinical result in your chosen area, explained
clearly and completely
Please keep in touch with me as you get started working, so that we can
agree upon what is sufficient background to include in the preliminary
technical section, what is a sufficiently important result to be your
main statement, and how you will prove it.
The oral part will be a presentation you will give to you classmates
(and perhaps other invited guests) of some (most) of all sections of the
above-described written part; mostly, the part to skimp on is the full
details of a complex proof — although a broad outline of a proof is
necessary.
Jonathan Poritz
(jonathan.poritz@gmail.com)