Open Standards, Web-based Mathlets: Making Interactive Tutorials Using the HTML5 canvas Element

Cite as:

Shane Steinert-Threlkeld and J Tilak Ratnanather. Open Standards, Web-Based Mathlets: Making Interactive Tutorials Using the HTML5 canvas Element. Loci: Developers. Mathematical Association of America. September 2009. http://mathdl.maa.org/mathDL/55/?pa=contentsa=viewDocumentnodeId=3340

Abstract: Interactive math tutorials, often called mathlets, are designed to provide a more visceral learning experience than traditional textbook methods and to enhance intuitive understanding of complex ideas by allowing users to alter parameters that influence visual scenes. We describe methods for creating such tutorials using the HTML5 canvas element. First, we discuss some motivations for writing such mathlets, then walk-through the process of creating a mathlet with canvas. Then, we compare canvas to alternatives, explaining our decision to use it, and provide links to other demonstrations and resources.

Read the paper.

Platonism, Structuralism, and Mathematical Applicability

Talk given in April 2009 at George Washington University Undergraduate Philosophy Conference based on a paper submitted.  Selection for the conference was conducted by the faculty of the GWU Philosophy department.

NOTE: I wrote this paper at a time when I was much less familiar with the literature surrounding the topics discussed. When reading this paper or viewing the slides, please keep in mind that these were created at a much earlier stage in my intellectual development.

Here you can find copies of the slides presented at the conference and the paper on which the slides are based.

Limiting Idealizations in the Inferential Conception of the Applicability of Mathematics

Presented at the 2010 Johns Hopkins University Undergraduate Philosophy Conference on May 1, 2010.

Abstract: Why are mathematical explanations so useful in the natural sciences? This talk will begin by motivating this question generally.  I will then jump into a specific dialogue between Robert Batterman, Chris Pincock, Otavio Bueno, Mark Colyvan and Steven French (among others) in the current literature on the applicability of mathematics and offer a few potential improvements. At the end, more general comments are made and a few questions raised.

Click here for slides of this talk.

Injective Resolutions in Abelian Categories

As part of a student seminar series in Abstract Algebra II, I delivered a 20-minute lecture with the following abstract:

In this talk, I will begin by introducing abelian categories and the notion of having enough injectives. This former step will require a brief introduction of initial, terminal and zero objects, pullbacks and pushouts, and normal morphisms. (If time permits, I will explain how pullbacks and pushouts are examples of the more general phenomenon of limits.) I will proceed to show how having enough injectives allows one to create a long exact sequence of the form for any object B in the category and where are injective objects and then define derived functor. Next, I will show that for any ring R, the category of left (or right) R-modules is an abelian category with enough injectives. I will conclude by mentioning that in this context, are derived functors and that this setting gives rise to homological algebra generally.

Click here for slides of this talk.