We cannot teach people anything; we can only help them discover it within themselves.
Galileo Galilei

Another talk about the Futurama Theorem

On December 7, 2011, I gave my second talk about the Futurama Theorem during the Plymouth State University Mathematics Seminar.  The Futurama Theorem is a theorem about the symmetric group that was developed for and proved in the episode “The Prisoner of Benda” for the TV show Futurama. The theorem was proved by show writer Ken Keeler, who has a PhD in applied mathematics from Harvard.  

Image taken from http://theinfosphere.org/

The first time I gave a talk about this theorem was during the Mathematics Forum at Gordon College just few weeks earlier.  You can find my blog post about my first talk by going here.

During the episode, Professor Farnsworth and Amy invent a mind swapping machine and after they swap minds, they realize that the machine cannot be used on the same pair of bodies again. After several characters swap minds, they are confronted with the problem of putting everyone’s mind back where it belongs. The Futurama Theorem proves that regardless of how many mind swaps have been made, all minds can be restored to their original bodies using only two extra people. If you want to know more, check out the slides.

The slides for the second talk are very similar to the first set, but there are a few differences:

  • The second talk is shorter.  I trimmed a few things from the first talk that were not completely necessary.
  • I’ve improved the wording in a few spots.
  • In the second talk, multiplication of permutations is right to left.

As with the first talk, I used deck.js to create the slides.  This allows you to view the slides directly in your web browser. To advance the slides, just use your arrow keys. Also, note that I used MathJax to typeset all of mathematical notation.

Combinatorics and graph theory are cool

This semester I am teaching a course for freshman mathematics majors.  The course is called Introduction to Formal Mathematics.  One purpose of the course is to develop a tight-knit cohort of mathematics majors and another purpose is show them that mathematics is about more than “solve for $x$.” We do some problem solving, a little proof writing, and introduce them to a few topics they may or may not see in future courses.  The course is a lot of fun. Feel free to check out the course webpage.  

The last couple weeks we have been doing a little combinatorics and some graph theory. Today one of the students remarked something to the effect, “I liked math before, but this stuff is just so cool.”  I agree.  There is no reason why we couldn’t teach these topics to high school students or even middle school students.  Unfortunately, we’re too obsessed with trying to make sure students pass standardized tests and can take calculus in high school.

The obstacle is the path.
Zen saying, author unknown.

Alfred and Evernote

I’m a big fan of using the Mac productivity tool Alfred and I use Evernote to store all sorts of snippets of information. Alfred is free, but if you purchase the power pack, you gain the ability to add custom scripts via Alfred extensions. While browsing the extension gallery, I stumbled on the Evernote extension by Kristian Hellquist that allows you to use Alfred to create a note in Evernote with the subject and tags that you specify. However, using the default script, you cannot add content to your note via Alfred and Evernote does not come to the front.

Typically, when I want to create a new note in Evernote, I have something specific that I want to make a note about, and it seemed that having to then click on the note you just created in Evernote to add content defeated the purpose of using Alfred. Within a few hours of asking about this, Kristian was kind enough to create a new script that brings the note you just created to the front for you to add content to. To use this alternate script, copy Kristian’s gist found here and then update the original Evernote script by going to the Extensions tab of Alfred’s preferences.

Talk about the Futurama Theorem

On November 3, 2011, I gave a talk in the Mathematics Forum at Gordon College about the Futurama Theorem. The Futurama Theorem is a theorem about the symmetric group that was developed for and proved in the episode “The Prisoner of Benda” for the TV show Futurama. The theorem was proved by show writer Ken Keeler, who has a PhD in applied mathematics from Harvard.

During the episode, Professor Farnsworth and Amy invent a mind swapping machine and after they swap minds, they realize that the machine cannot be used on the same pair of bodies again. After several characters swap minds, they are confronted with the problem of putting everyone’s mind back where it belongs. The Futurama Theorem proves that regardless of how many mind swaps have been made, all minds can be restored to their original bodies using only two extra people. If you want to know more, check out the slides.

As a side note, this is the first talk that I have given using deck.js, which allows you to view the slides directly in your web browser. To advance the slides, just use your arrow keys. Also, note that I used MathJax to typeset all of mathematical notation and I was able to embed a single cell instance of Sage to do some live computations.

I really enjoy this short video introduction to group theory by James Grime (aka Singing Banana), especially since it mentions Coxeter groups (one of my research areas).

Mathematics, rightly viewed, possesses not only truth, but supreme beauty — a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry.
Bertrand Russell, Mysticism and logic

Using Mendeley with BibTeX

Note: This post overlaps significantly with Mendeley’s blog post found here.

My current reference manager of choice is Mendeley, which is a free desktop and web solution designed for storing, annotating, and sharing research papers, discovering research data and collaborating online. It combines Mendeley Desktop, a PDF and reference management application (available for Mac, Linux, and Windows) with Mendeley Web, an online research paper management tool and social network for researchers. You can find a short YouTube video that describes what Mendeley is here.

For nearly all of my academic writing, I use LaTeX together with BibTeX. One of the many benefits of Mendeley is that it will automatically generate BibTeX files. However, at least with version 1.1.2 and earlier, integration with BibTeX is lacking in a few ways. In order for things to go smoothly, I suggest the following set up in Mendeley Desktop.

You want to uncheck the “Escape LaTeX special characters” box so that braces, backslashes, dollar signs, etc. don’t get clobbered by Mendeley when it generates the corresponding .bib files. You should choose “Create one BibTeX file per collection”. This generates one .bib file for each subcollection (folder or group) you create in Mendeley Desktop. If you don’t do this, Mendeley will create a duplicate entry in your synced .bib file for each entry appearing in a subcollection, which will in turn prevent LaTeX/BibTeX from compiling properly if you happen to cite one of the duplicate entries. I create a new subcollection for every document that I am writing that might require a bibliography.

Once you’ve got everything set up, it is really easy to incorporate Mendeley into your LaTeX writing workflow. If you want to cite a particular item, just click on it in Mendeley Desktop, hit “command/control-K” to copy the BibTeX citation key, then paste it into the appropriate location in your .tex file.

Why use inquiry-based learning (IBL)?

Amélie G. Schinck from Cal Poly San Luis Obispo has written a great piece titled “Why use IBL?”, which is posted over on The Academy of Inquiry-Based Learning.