## ACCESS-Math Portion Summer 2001

#### Send e-mail to : Professor Korevaar Links: Nick Korevaar's home page Department of Mathematics College of Science

The schedule for the first week of ACCESS is now located at ACCESS1.html.

The theme for the fourth week, July 2-6, is scaling laws. Here's my current plan for what we'll be doing. It could change as the week progresses.

Monday July 2:
 8:30-10:15 a.m. JTB 120 We will discuss how classical geometric objects rescale when the underlying space is deformed, and how this relates to their "dimension". Strange objects called fractals also have rescaling laws, and resulting dimensions which are most likely NOT natural numbers, i.e. you can get "fractional" dimensions. We will discuss some of the history and construction of fractals.
 10:30-noon Physics 205 (Math Lab) Play with fractals in MAPLE. Unfortunately the site license problem has come back to bite us, and we must work in the Math Computer Lab rather than the Marriott lab. This means you'll get to work in a UNIX environment, which is good for you because UNIX is not uncommon on campus, but which is mildly irritating because it's yet another operating system....Anyway, once we're in Maple it doesn't matter what platform we're on.
tutorial.mws     intro to math lab and maple, worksheet format.
tutorial.pdf     pdf format

firstfracs.mws     Sierpinski & Koch, Maple worksheet
firstfracverb.pdf    pdf format
bush.mws     a bush, made with only two iterating functions! Maple worksheet
bushverb.pdf    pdf format
crystal.mws     like a pattern of window ice, also made with only two iterating functions! Maple worksheet
crystalverb.pdf    pdf format
dragon.mws     dragon with 3-fold symmetry, from class notes. Maple worksheet. pdf file including picture was too big to post.
pracaff.mws     A very useful procedure to test whether you've made the correct affine transformation - it draws the box-with-L pictures like in the notes and in the book, so you can see if you've got things set up right. The procedure is illustrated with the "twig" from yesterday's notes Maple worksheet
pracaffverb.pdf    pdf format

 Barnsely Fern Mandelbrot Set This fern applet is better than anything we'll be able to do in Maple. We won't discuss Julia and Mandelbrot sets in detail, but they're wild.

Tuesday July 3:
 8:30-10:15 a.m. THIS IS A CHANGE!!! Physics 205 Play with fractals in MAPLE. We must work in the Math Computer Lab rather than the Marriott lab, see above. Since we had so much fun on Monday talking about fractals, we only get to play with them today......We will have to talk about human height-weight scaling on Friday ... I need your data by Thursday!!!
 10:30-noon JTB 120 "What if Animals were Fractals?", a lecture by Fred Adler who is fractional himself, being 1/2 Math Professor and 1/2 Biology Professor.

Wednesday July 4:
FOURTH OF JULY HOLIDAY!!!!

Thursday July 5:
 8:30-10:15 a.m. JTB 120 Advising Session for Math Courses, with our Director of Undergraduate Services Angie Gardiner.

 10:30-noon JWB 335 "Percolation, polycrystals, polymers and penguins: the mathematics and physics of Antarctic sea ice and hi-tech composite materials" lecture by Math Professor Ken Golden.
bmia.mws     Notes on the body mass index, with national data example worked out. Maple worksheet
bmiverb.pdf    pdf format

Friday July 6:
 8:30-10:00 JTB 120 Discussion of the height-weight project
htwt.mws     The heights and weights you gave me - Maple worksheet
htwt.pdf    pdf format
 10:00-12:00 South Physics 205 Project work on fractals, and on how human heights and weights are related.
assign2.pdf    Week 4 project assignment