ACCESS-UGS 1430
For week 1 schedule, go
here.
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 College of Science Math Department Nick Korevaar's home page |
Send e-mail to :
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JULY 7-11, 2008
Welcome back to Math! Our themes for this week are scaling laws in nature, and fractal geometry. Our tentative schedule is shown below. It may change as the week progresses. A current version of this schedule lives at http://www.math.utah.edu/~korevaar/ACCESS2008.
As part of your project work this week, you will be testing the "Body Mass Index" hypothesis, that human body weights should scale like the square of their heights, for people of proportional size. To run this experiment we need lots of height-weight data, which you shall collect from family and friends. I'll need this data from you by this Thursday July 5, at the latest. Please record weight in pounds and height in inches, (or feet and inches). We will especially need data from babies and children.
Monday July 7
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8:30 a.m.-noon JTB 120 |
Geometric scaling: how to rescale space and gingerBob with affine transformations. How do lengths, areas and volumes change when you rescale? Introduction to classical fractals and fractional scaling dimension. |
Tuesday July 8
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JTB 120 8:30-10:15 |
What are fractals, how can they have a fractional dimension, and how can you turn Bob into one using iterated function systems? |
| 10:30-11:20 | Women in Mathematics Panel: Emina Alibegovic, Kelly MacArthur and Angie Gardiner (ACCESS 1992) will talk about their math careers, what they do in our Math Deparment, and answer questions from you. If they were in town, Alla Borisyuk and Elena Cherkaev would also have come. |
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11:30-noon |
Math class advising with Angie Gardiner...along with lunch from skoollunch. |
Wednesday July 9
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8:30-10:45 a.m. PC-Lab 1735 |
Fractals in the computer age and making your own fractals with Maple. This will be part of your group project for this week. Use the files in the directory fractals. |
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11:00-noon JTB 120 |
ACCESS panel: Katie Kormanik, Yasmeen Hussain, and Megan Morris, current and recent ACCESS math majors, will tell you about their undergraduate experiences and answer your questions. |
Thursday July 10:
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8:30-10:15 a.m. PC-Lab 1735 |
Continuing your project work on fractals. Then, Erin will explain the math behind the "least-squares" method for fitting lines to collections of data points, along with the log-log method for trying to fit power laws to data points. This will help you on your project, when you try to find a power law relating human heights and weights. The Maple file which showed how to automate this process is located from links at erin's home page; precisely, it's the file http://www.math.utah.edu/~erin/Access/LeastSquares.mws. |
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10:30-noon JTB 120 |
"What if Animals were Fractals?", a presentation by Nessy. An original reference for Nessy's talk is "A General Model for the Origin of Allometric Scaling Laws in Biology", G.B. West, J.H. Brown, and B.J. Enquist, "Science Magazine" 276 4/7/97 p. 122-125, www.sciencemag.org/cgi/content/full/276/5309/122. There are subsequent papers which both support and attack this model, which does not represent settled science. |
Friday July 11:
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8:30-noon PC-Lab 1735 |
Project work: Making fractals, and testing the body mass index hypothesis with the data you have collected. You'll also do some research on the history of BMI, and present your results in a paper. Here is your precise assignment: assignment2. Here, bmi.mws, is a Maple document with some national height-weight data, and the power law it implies. Are you curious to see if the results from our own data points, htwts.mws are close to the ones from national data? |