sagetex: graphics with Sage

We've seen that you can use Sage and sagetex to produce graphics with Tikz and pgfplots plots in LaTeX. We've also seen you can tap into Python graphics using sagetex and matplotlib. If that's not enough reasons, here's another. You can also use sagetex with Sage to create graphics. Try doing this with Tikz.

You can find the example above, along with others, here. You can download the code shown above on the Plotting with Sagetex page.

TCEC Superfinal

There's a clash of chess giants going on but I'm not talking about Carlsen or Anand.  It's even better (or, more accurately, higher rated): the TCEC Superfinal between Stockfish and Komodo. The TCEC Superfinal is an unofficial world computer championship and this time the final is between Stockfish, rated 3164 and Komodo, rated 3155. Stockfish, a freely available open source program has come out above the closed source, proprietary programs. Clearly you don't always get what you pay for. Here's a moment from round 9. Note in the picture below that Stockfish is calculating 41 ply(!) [21.5 moves ahead]. Chess has been killed by computers, much like checkers and, with a little more time, Go.

You can follow the action on Chess Bomb or why not just go to the site itself. Stockfish has a 12-8 lead and with no losses it's poised to win but the games have been entertaining. Check it out for yourself.

Two "easy" problems

Another year is almost over and of all the memorable events 2 problems (which aren't particularly difficult) caused tremendous difficulties for far too many students. It's especially surprising because I have a class of (mostly) good students: some are highly gifted and others compete for (and win) various math contests.

Problem 1: Solve for $latex x$:  $latex \pi^{1-x}=e^x$

Problem 2: Find the domain of $latex f(x)=\sqrt{4x-x^2}$

Problem 1 is from a Thai entrance exam; the Thai version of an SAT test. I put it on a regular test expecting to challenge the bottom 25% of the class. Instead, it took down the "bottom" 75-80% of the class and some good students blanked on it. If you work it out, you'll see there are multiple ways to do it and none of them are particularly difficult. The exponent $latex 1-x$ (as opposed to, say, $latex x-1$) combined with $latex x$ on both side poses problems, even for "good" students. The second problem was actually part of a problem on finding the minima and maxima of the function. It was causing difficulties during the problem session in class so I tried to break the problem into pieces and have them get the domain. You could count the students who could get the correct answer on a mutilated right hand. And I even told them that inside the square root was a parabola....

As a result, I've added these two problems to the Problems page. Try them on your students!

LaTeX Templates

Chances are, if you use LaTeX, you were probably drawn to it by some of the many beautiful examples that have been created. Everything looks better with LaTeX.  Lately I've been looking at various templates  to make my work look a little more polished; whether it's a book template (such as LeGrand Orange shown above), CV, article, Beamer presentation, or thesis it's good to have some templates on hand. I've added information on the LaTeX page to get you started. In addition to several sites with a good variety of templates to look at, I've listed some of my personal favorites as well.

Graphics: Hyperbolas

I've added several hyperbolas to the Graphics page: two with asymptotes, foci, etc, and one without. Strangely enough, using sagetex with tikz is generating an extra page (a 2 page PDF with the second page blank). I don't know why that's happening. I used PDF-Shuffler to delete the second page.

Understanding "The Prediction"

Math Awareness Month is over and if you haven't kept up with the website, you can check out the different videos that they posted throughout April here. My favorite video was posted on the April 5th: "The Prediction" by Richard Wiseman. In case there's a problem with the mathaware website being taken down, here's the link to the video on Wiseman's Quirkology site. I enjoyed the video enough that I've put together an explanation of the math behind it; it uses the fact that the graph of the moves is bipartite. You can read the details in the PDF (screenshot above). It's posted on the Other page.