It's Not Easy Being Green

Hi all, not much to report really. My days are spent wistfully preparing for my oral exam and putting off the corrections of my second paper. One thing of note though, my good friend R defended his dissertation yesterday and it was wonderful. I love final defenses, they're so exciting, especially when you're friends with the person defending. For those of you not in the know, to get your PhD you spend years writing your dissertation, then when it's all over you get up in front of your committee and whoever else wants to come and show off your work. It's not really a hurdle, unless of course your adviser did all your research for you. Most defenses I haven't understood one bit, R's however was really easy to follow, at the least the motivation. He works in biomath (with applications to amphibian populations), which is a very hot area in mathematics right now. I'm not very interested in it, but what they're trying to do is really easy to follow. They have the advantage of being able to explain their research to the layman, which is a luxury I don't have (unless you've taken calculus or, even better, DE). Anyway, congratulations R, or should I say Dr. R.

P.S. The above picture was actually on one of R's slides, for the section on Dispersion and Migration, get it? What a day.

I Don't Do Sympathy

 

What's the deal with fractions? Say it like Seinfeld and it's kind of funny. Say it exasperated while shaking your head, as I usually do after class, and it's not really funny at all. Really? What's the deal with fractions? It's one of the things I'll never understand as a teacher. Let me explain, I've broken down things students do into two categories: things I understand and things I'll never understand. As you can probably expect, that first category grows ever smaller while the second increases without bound. Don't misunderstand me though, I'm not completely unreasonable, there's plenty in that first column. For example, I can totally understand why a student would have trouble with logarithms the first time they see them; after all they require a complete backwards thinking that we haven't quite felt since learning that division was the opposite of multiplication (which by the time you hit logs was a long long time before). There are plenty more, keeping integration rules straight, dealing with Z mod 2 the first time and learning that 1+1=0 there and so on. Though as time goes on I start to wonder if I'll ever be able to stop adding things to this second category. Things I'll never understand include: How can a student solve an equation with xs but give them the same equation with zs then they're lost? Why does a student, who made it all the way to calculus, need their calculator to find 5-0? And of course, fractions, fractions blow minds, and I'll never understand why.

Sometimes I Feel Like ...

My wonderful girlfriend has some very sweet things to say about me and this little blog over at her own blog-a-majig. These words wouldn't even be here without her constant prodding, which I mean in the nicest way possible of course, so go on and give her stuff a read and see what kind of crazy person falls for a mathematician. Spoiler alert: it's not another mathematician, surprise! In fact, she might just be inspiration for anyone out there that wanted to bag a mathematician but thought you had to be good at math first. Turns out it's not a necessary condition (nor a sufficient one har har). Anyway I better quit before I say anything else that I'll regret.

Say What?

So, I mentioned before about a problem dealing with Buffy and Batman, and yes it's quite epic. The math itself isn't all that involved really ... well for me anyway. It's just the write up will be tedious, as well as the figures required, and not to mention the animations. Did I just say animations? You're damn straight, I'm pulling out all the stops ... eventually. For right now though I'm a bit too busy with other stuff to devote the time required for such a feat, and I'll probably stay this busy for a good long while. No worries though, I have plenty of things to fill the void until then. Like, for instance, explaining all my freaking steps from my last post. Those of you who are great at math and have enough background probably followed what I did ok. Those of you who are new to sigma notation and infinite series might benefit from a little explanation. There's a lot of little tricks in there that may be really useful to you. I recommend the following to those of you in Calculus 2 or a higher level probability class, ODE, PDE or any higher level class that requires nasty sigma notation funkiness (Ring Theory when you talk about polynomials for instance). Anyone else? Eh, just hope my next post has something more geared toward your level. Sorry, that just comes with the territory. Anyway, here we go:

And Beyond?

You know nothing about infinity. You probably think you can add it to your argument in order to win, or add one to it to win even more. Nope, nothing about infinity, but I know everything about it (ha!) so allow me to enlighten you. There's this statement you might have heard before, that if an infinite number of monkeys on an infinite number of typewriters type for an infinite amount of time, then at some point they will produce the complete works of Shakespeare. This is an idea that comes from probability theory, and what infinity does to it. Because when you let the time line approach infinity then the probability that anything will happen approaches 1 (i.e. 100%). Therefore we could actually reduce the goofiness down to one monkey on one typewriter. Thus if Bubbles (yes I'm naming it Bubbles) types for an infinite amount of time then at some point it'll produce Hamlet. So on a long enough time line any damn thing can happen, anything.

Even a ... Nevermind

 

You don't know anything about algebra. Nothing, nada, zilch, absolutely none is what you know. Ok, now that I got that obligatory math teacher berating out of my system, let me backtrack a bit and let you in on one of my big pet peeves. Like the boring goofball I am, I like to peruse the various math related internets. Most of what I find is enlightening, fun (to me at least), or at the very least correct. Every once in a while I'll stumble on a page or facebook group (*massive groan*) that touts something about paradoxes and the weak foundations of mathematics. "Oh really?" I think, sounding interesting I continue reading, thinking they must be referring to all the problems and paradoxes found in set theory (the actual foundations of math). And here I read something like: "Oh math is so crazy, through logical foundations crazy paradoxes result. Here follows a list of paradoxes proving that the foundations of math are shaky at best." Then they list some paradoxes like they promised (they're not jerks after all, just dumb), and most of them are your typical logical paradoxes, you know the ones like: "All bandits are liars," said the bandit. So on and so forth, which are all fine and dandy until they insist on adding this one:

A Beginning Is a Very Delicate Thing

So said Princess Irulan at the beginning of (or somewhere in the middle of) Frank Herbert's "Dune", and I suppose they are. How to start this blog has been the only real thing keeping me from writing it, that and my PhD work, but we'll get to that later. I could start with my motivation for starting such a thing, how I got burned out on uninteresting personal musing blogs in my college years (I'm looking at you xanga), how I wanted to write about something with weight but had no idea where to focus my energies, how I wanted to have something to fight off boredom when my brain was all melty goo from my PhD work. I could start by telling you the story of when my brother one day said "Why not write a math blog? That's your expertise after all," or how my girlfriend has been prodding me to start a blog of some sort, but something with a theme of course. I tried this once already you know? Something based on my music hobby, which is just a hobby and not something I consider bread making if you catch my drift. But again, research got in the way and I had to forget all about the poor little music blog with exactly one (unique heh) entry.