Applied Euclidean Geometry
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(Tentative)
logistics: MAT 5932-003, CRN 12902 MWF 10:45 – 11:35 in PHY 108 Instructor: Greg McColm, http://www.math.usf.edu/~mccolm Primary text & materials: Crystal Nets by Michael O'Keeffe
& Bruce Hyde, available on-line at http://www.public.asu.edu/~rosebudx/okeeffe.htm Students will also need to get Maple 12
(available from the bookstore), and art supplies (!) TBA. Audience: Mathematically proficient
graduate (or precocious undergraduate) students in the natural sciences,
engineering, or mathematics education. |
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One
of the revolutions of the 21st Century will require the return of Old-Fashioned
Geometry, the 2- and 3-dimensional kind.
If you want to build something simple, a nano-rod or a glass, then preliminary
planning may not require much architectural design of the structure you wind up
with. But if you want to build something complicated, with many kinds of
parts, like a crystal or even a mesoscopic device – like a tiny robot or a tiny
3D computer chip – then you need to work out the design in advance. And
that requires mathematical tools.
Including tools from geometry.
This is a course on geometry for people who plan to work on the architecture of
matter, of virtual matter (as displayed in computer consoles), or other tiny objects.
It is intended for natural science and engineering
graduate students, although it may be useful to mathematics education students.
Our primary text is O'Keeffe &
Hyde's Crystal Nets, but we will look
at additional material as well. We will cover geometry from a graph theoretic
point of view, starting with polygons and polyhedra, making complicated things
out of simpler things (including tiles, tilings, and crystals), and
non-crystalline nets, geometric symmetries, a little topology and other topics
as time permits. We will learn a little
about using computer programs (we will use Maple in this class), but no prior
experience is required.
Prerequisites: I assume no specific
background in science or engineering (as backgrounds of different students may
vary), and while I will assume that students have taken undergraduate Linear
Algebra (MAS 3105 or equivalent), I will not assume that people remember it all
that well, so I will remind people of what they need to know as we go along.
For more information, you may contact me at 974-9550 or mccolm@cas.usf.edu.