Office 1D MLH |
Office Phone (319) 335-0768
FAX (319) 335-0627
Email jonathan-simon (at) uiowa.edu
Also affiliated with the interdisciplinary Ph.D. program in Applied Mathematical and Computational Sciences
A brief professional resume (several years old - need to update)
Materials from some courses. [NOTE: Materials for courses since Fall 2009
are/were distributed via ICON and are not posted here.]
The documents for
each of the courses below include Course Descriptions.
For high school students -
"Which College is Right For You?
Special Opportunities for our Current Undergraduate Math Majors: Research Assistantships and Other Positions
Department of Mathematics: Undergraduate Program website
Undergraduate Handbook: Requirements and other program details and guidance
BA/BS requirements for Program A in Mathematics
BA/BS in Program C, Mathematics + Computer Science
BA/BS in Program C, Mathematics + Statistics or Actuarial Science
See the work by Jenelle McAtee (current Ph.D. student) on knots of constant curvature.
See the program "MING" (graphic version "min"), a computer program implementing a gradient descent type algorithm by Ying-Qing Wu to minimize
MD-energy of knots.
Amit Ganatra has adapted Wu's program MING to run on more platforms.
Visit the knots page of Kenny Hunt who implemented a random perturbation algorithm for minimizing the MD energy and developed an interactive knot editor for visualizing and manipulating polygonal knots. Prof. Hunt and I have worked together to develop a simulation of knots moving through an obstruction field .
Visit the home page of Eric Rawdon who is my former (8/97) Ph.D. student, and subsequent co-author, working on thickness of knots. (Link to his thickness page.)
Here are some results and pictures on
|ILLUMINATING PICTURES OF KNOTS|
Why do different types of knots travel at different speeds in DNA gel electrophoresis?
Knots Moving Through an Obstruction FieldHere is a series of screenshots of a knot "moving through an obstruction field" (joint project with K. Hunt), a very preliminary graphic simulation of gel electrophoresis of a knotted DNA loop. See K. Hunt's web page for mpeg's. (Note the mpegs are large files, on the order of 20-30 mb, so they will take a long time to load.) This series of pictures is taken from his "Simulation 2" mpeg.
The knot is being driven
towards the left. (To keep the knot in view, the pictures have the
illusion that the obstructions are moving towards the right.) The
obstructions are rods, so that the knot can get 'hung up', as well
as directly blocked. Here the knot is temporarily caught on a pair of
crossed rods, and then wiggles off.
Here are three principal axis views of a Five(sub)2 knot. The knot has 50 segments, began as an irregular conformation and was evolved to minimize our "MD energy" using the program "min" cited above. After evolving, the knot was rotated in 3-space to have the x,y,z axes the principal axes (i.e. to have the second mixed moments of the vertex set be zero). This rotation makes it easier to discover apparent symmetries. The fourth "bonus" view was observed during freehand rotation and is a 90/90/45 degree view relative to the principal axes.
Here is an illustration of theorems on "Thickness of Knots" from paper by R. Litherland, JS, O. Durumeric, and E. Rawdon
Here is an illustration of projections of knots.
This is a 10 foot courtyard sculpture, Oribasius (c. 1970) by Martin Goldman.
You can see a Campus map showing our building, MLH=MacLean Hall.
to the Department of Mathematics
Research ideas and results described here have been developed with suport from the National Science Foundation. The contents of this web page are the views of the author (J. Simon) and do not represent views or opinions of the Department of Mathematics or the NSF.
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