Jonathan Simon


Department of Mathematics
University of Iowa
Iowa-City, Iowa 52242





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
and some Publications and Preprints available online.

(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.

M10 Notes on Least Squared fitting a line to data
22M:013 Math for Business (Spring 09)
[NOTE: IMPORTANT...read the two messages that are posted. Then please read the Course Description and note the various special dates in the Schedule.]


22M:201 Intro to Algebraic Topology (Fall 08)

22M:013 Math for Business (Spring 08)

22M:132 General Topology (Fall 07)
22M:028 Calculus III [multivariable calc] (Spring07)
22M:201 Intro to Algebraic Topology (Fall 06)
22M:033 Engineering Math III: Matrix Algebra (Sum 06)
22M:201 Intro to Algebraic Topology (Fall 05)
22M:016 Calculus for the Biological Sciences (Fall 05)
22M:028 Calculus III [multivariable calc.] (Spring 05)

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



Research Interests include:

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 Harmonic Knots which are knots represented as finite trigonometric parametrizations. This is from the Ph.D. work of Aaron Trautwein, my former Ph.D. (5/95) student; link to his homepage.


ILLUMINATING PICTURES OF KNOTS

Why do different types of knots travel at different speeds in DNA gel electrophoresis?


Knots Moving Through an Obstruction Field
Here 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.


square knot figure from page of R. Scharein


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.


Back 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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