Math – Bave Blog

Prelude to Math

Since I now seem to be the sole author posting on this blog, I feel liberated to take this in my own direction. I have a part-time academic life outside of my fairly-demanding full time job, and it’s hard to find time to devote to really developing an intuition for some of this esoteric academic stuff. I am trying to involve myself in research in theoretical computer science, which of course is just applied mathematics. I have the best intentions each time I commit to reading some paper or watching some video on some topic I’m trying to learn, but more often than not I just can’t (won’t?) make the time.

Drawing Graphs Using LaTeX

There are a few ways one can plot graphs within LaTeX documents. I think the most intuitive option is to use pgfplots, which is specifically designed to draw function plots with a (relatively) straightforward user interface. Some illustrative examples are available on the pgfplots website.

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LaTeX – Boxes Around Text

Have you ever wanted to enclose text in a LaTeX document in a box? Sure, there are a million ways to do this, but I have a way that will allow you to break the contents across pages while still adding a line at the bottom of the box on each page. You can also specify the internal padding between the lines of the box and the text. Wow!

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Weekly Riddle Number FIVE

Remember how depressing the song “Do They Know it’s Christmas?” (by Band Aid) is? Here are some of the lyrics:

And there won’t be snow in Africa this Christmas time. The only gift they’ll get this year is life. Where nothing ever grows, no rain or rivers flow, do they know it’s Christmas time at all?

Still, it’s pretty catchy. There should be radio stations that play it 24/7 from Halloween until Christmas, like some cable stations play “A Christmas Story” for six months straight each year.

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Weekly Riddle Number FOUR

So the Putnam has come and gone, thank god, and I can get back to my regular life. For those who care about that sort of thing, I got 5/12, or 50 points, but I’d like to put an asterisk next to it. One of the concepts in one of the questions was particularly up my alley, and rather than continue with the test, I spent about an hour exploring the ramifications of one clever concept. So I probably should’ve gotten a 60/120 (I was able to answer another question later that night), but I still would’ve been disappointed with myself. My goal was to get higher than a 60, and that wasn’t happening even with the extra ten points. Ah well, there’s always next year.

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Weekly RIDDLE Number Three

pudzian

Hi there. I spent the entire day sitting in the student lounge of the college in which I teach, administering the Putnam examination to the latest batch of Math luminaries. I say that without irony, because these are some of my best students, and the Putnam test is no joke!

What is the Putnam Exam? It’s Mathletes on a Mariusz Pudzianowski heaping of steroids, a grueling six hour gauntlet designed to humble the orneriest math student. What’s Mathletes? Well if you don’t know, then you either accidentally clicked on the wrong link, or, Hi Mom, thanks for visiting my site! The Putnam is pretty much the most difficult Mathematics Exam out there, requiring both extensive book learnin’ and extreme outside-the-box thinking ability. Lest you think that you have an aptitude for math and could walk in cold and score some points on the Putnam, let me dispel that illusion immediately by informing you that the average score on the test is a 0. A test taken by only the very best college undergraduates across the country, and on average, zero points are earned. Still don’t believe me? Here’s question 1 on the Putnam this year:

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The FIRST and SECOND Weekly Riddles

peterson I love recreational math. I’m sorry to have to say it, but there it is. It’s practically what I do for a living. I’m a math teacher by trade (in that I’ve been all around this great blue and green marble and ply my trade wherever math teachers are needed), and rather than teach what the curriculum states I should, I warp the curriculum to satisfy my desire to do recreational math.

That isn’t really as intimidating or boring as it sounds. A lot of people enjoy the mathematics of games, and spend a lot of time pondering riddles. Most people, however, don’t know that when they are contemplating a brain teaser, they are actually performing a subtle form of mathematics. Take this guy for example:

pencil-lift Remember him? He’s that guy you used to doodle into your notebook back in grade school. Or maybe junior high school or high school, or all of the above. The goal is to sketch the drawing of this barn-type thing without lifting your pencil off the paper, and without crossing over any lines that you have already drawn.

No doubt at some point in your life you attempted this little game, and no doubt after a bit of work, you figured out a way to accomplish the feat stated above. How did you do it? Did you use logic and reasoning, or did you just draw it a bunch of times until trial and error revealed the solution? No offense, but probably the latter- at least that’s how I used to do it.

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