David Seal's Webpage

Provided Courtesy of:

University of Utah
Department of Mathematics
155 S 1400 E
Salt Lake City, UT  84112-0090

Contact Information

General Information

I will be starting graduate school at the University of Wisconsin - Madison starting this upcoming Fall 2006. My current website is located here.

Here is a copy of my resume.

Research

Currently, as of January 2006, I am considering topics in analysis, probability or partial differential equations. I would like to learn more about measure theory in order to gain a theoretical appreciation for probability, so I am currently embarking on a research project on fractals with Professor Davar Koshnevisan. Hopefully this topic will lead to a written senior thesis. We have decided to begin with reading Falconer's book: "Fractal Geometry". One of the essential questions in probability tackles what it means to pick a uniform random variable on some set. In an elementary probability course, one encounters random variables described by density functions. When one chooses to have a uniform random variable, this density function becomes a constant, and the value of this function is defined by the length of the set. However, when the set becomes more complicated, such as the middle-thirds Cantor set, one needs to be able to define a notion of the "length" of a set. This becomes more difficult as the sets become more complicated. My first task is to understand the definition of a Haussdorff Dimension, and from there who knows where we'll go.

Other research I've been involved with included a 2005 Spring REU at the University of Utah with Prof. Nat Smale on Partial Differential Equations. We read problems from Serge Lang's Complex Analysis book as well as studied a few PDE problems from Fritz's book.

I spent the subsequent summer months in Bloomington, at Indiana University where I worked on an accelerator physics project at the Indiana University Cyclotron Facility. This project explored a means of producing beam profiles of particles beams by using ccd images of residual gas flourescence. A non-interceptive means of constructing beam profiles is imperative because in applications such as the LENS project at the IUCF, the proton beam used to produce neutrons would destroy any traditional measuring device placed in the path of beam. Furthermore, a stray beam would melt the accelerator walls if it were to hit the sides of it. A copy of my report and presentation are available online.

Teaching Experience

I have worked at the math department's tutoring center since Fall of 2003. I have also spent two semesters doing supplemental instructing for the math 1010 and 1050 course. My first 'teaching' experience was at the old Hansen Planetarium, now the Clark Planetarium in a different location. I used to give star show talks with my red laser pen, and ran the computers for the star and laser shows.

Links

• My current class schedule.
• Good links for different LaTeX sites. If you'd like to use LaTeX on a windows machine, you'll need to install miktex, as well as a text editor such as TeXnicCenter or WinEdt. Of courses, you could always choose to be old school, and type your files up in notepad, although you don't get the cool little colors that will let you know if you're typing correct syntax.
• Sample LaTeX files and instruction manuals, including a list of 2226 different LaTeX symbols.
• Utah Chess sites.
• Here are a couple of cool sites that simulate the Ising Spin model: (1 2).
• Some pictures.
• Some more pictures.
• A copy of my senior thesis.
• Some problems I solved and wrote up in tex for practice. baby rudin.