website.
My most detailed talk concerning this research. I describe the problem of defining scalar field dynamics in non-globally-hyperbolic spacetimes, and how one can use operator techniques to solve the problem. Linear field quantization is also discussed. I was invited to give this talk in April 2004 at the University of Wisconsin, Milwaukee's Relativity Seminar. This talk is aimed at research in general relativity and is quite technical.
A condensed version of the previous talk, presented at the Seventeenth International Conference and General Relativity and Gravitation (GR17) in Dublin, Ireland. This conference is the tri-annual meeting of International Society for General Relativity and Gravitation. Again, this is a technical talk intended for researchers in the field.
A colloquium presented at the University of Mississippi ("Ole Miss") in May 2005. This talk should be accessible to most graduate students in physics and perhaps advanced undergraduates. I describe the rudiments of general relativity needed to understand the problem, and then describe the solution by analogy to similar techniques in quantum mechanics.
An undergraduate-level talk geared primarily towards mathematics majors. It has been given in a few different places, most recently as a math colloquium at Knox College. This talk should be accessible to anyone who has passed a solid course in linear algebra.
A preliminary report on my research in causal sets, which involves writing a new code to simulate "generalized percolation". Since this is a specialized topic, I do include a fair amount of background material, but this is a talk intended researchers in relativity.
A talk summarizing the results of arxiv:/0809.2258. Again, I provide a fair amount of background, but this is a talk intended for researchers in relativity.
In this talk I describe how topics in quantum mechanics can be used to teach linear algebra techniques. The focus is primarily on the spectral theorem, but other topics are also discussed. The target audience is mathematics with little to know knowledge of physics. Presented at the 2007 Joint Mathematics Meetings in New Orleans.
As the title suggests, this topics presents additional quantum mechanical topics which illustrate linear algebra . Presented at the 2008 Joint Mathematics Meetings in San Diego.
In this talk I present what I call 3-dimensional bifurcation diagrams, and then I argue they are pedagogically superior for introducing bifurcations of ODEs with a single free parameter. Mathematica code for creating these diagrams is included.
Mathematica Notebook PDF Version
In this talk I present a way of implemented differential operators in Mathematica in a way similar to how they are presented in introductory ODEs texts. While I focus on the method of undetermined coefficients, I also discuss variation of paramaters and related topics.
Mathematica Notebook PDF Version
Following up on my 2009 talk I present a package for creating 3-dimensional bifurcation diagrams. This pedagogical package makes creating the diagrams as easy as using Plot3D. The associated package is below; the documentation notebook includes installation instructions and more detailed usage information. The CDF document is viewable and interactive using the free CDF player but editable in Mathematica.
CDF Document of original JMM2012 talk CDF Document of revised ICM 2014 talk Associated package Documentation notebook
In this talk, I argue that on of the reasons that coordinate chnages are so confusing is that two different operations share the same name. By clarifying this difference and using a CAS to do the computations, we can introduce coordinate changes more systematically, and leverage them to help students visualize and explore vector fields. The CDF document is viewable and interactive using the free CDF player but editable in Mathematica.
In this talk I explain how the Frenet-Serret frame (aka, Tangent-Normal- Binormal basis or TNB basis) provides a nice application of the Gram-Schmidt process and therefore fits nicely into a linear algebra course. In this context, the formulae for the curvatures make much more sense. The CDF document is viewable and interactive using the free CDF player but editable in Mathematica.
Due to horrible rerouting, I flew around the world: Dallas-London-Seoul-Dallas. Trying to console myself, I did a quick estimate of the frequent flyer miles I'd rack up by computing the length of the middle parallel in this journey. This, however, turned out to be a significant overestimate. Why was this such a bad estimate? How could I do better, using either naive estimates or some differential geometry? These questions are explored in this talk. The CDF document is viewable and interactive using the free CDF player but editable in Mathematica.
This version includes a bonus slide not present in the original talk, based on a suggestion from Sarah G. Raynor. My thanks to her.
CDF DocumentIn the past decade, symbolic ordinary differential equation solvers have moved beyond their traditional focus on solving classical equations in terms of special functions. Solvers for piecewise or "engineering function" driving terms, hybrid or event-driven equations, differential-algebraic equations, and even delay-differential equations are now available. These new solvers greatly expand the range of models for which symbolic solutions are possible, and which students can therefore explore from a varienty of perspectives. In this talk I will survey these topics and how you can explore them using Mathematica. The CDF document is viewable and interactive using the free CDF player but editable in Mathematica.
All documents on this page are copyrighted © by Itai Seggev (see each document for the exact copyright years). They may be freely distributed w/o modification for non-commercial use under the conditions of the Create Commons Attribution-Noncommercial-No Derivative Works 3.0. I have chosen to use this rather restrictive license primarily to prevent my research from being misused. If you are a teacher or researcher and would like to reuse a portion of a document, please contact me to ask for permission. I will be glad to provide the modifiable source version of the document (either LaTeX Beamer or Apple Keynote, depending on the talk.)
Although every effort has been made to ensure that there are no errors in any of these documents, and at the present time the author believes that there are no major errors in them, these documents are provided "as-is". The author provides no warranty of any kind as to their correctness, merchantability for a particular purpose, or any other defect.
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