Today I made a few changes to the way I intend to interact with phones, and I thought I'd see if any folks out there had any advice for me about these changes.

I switched to a pay-per-minute plan for my mobile phone today, and also signed up for Google Voice (thanks to an invite from a twitter follower), with a new Google number. My mobile plan is now 1 dollar every day I make or receive (actually answer) a call, plus 10 cents for each minute of those calls.

So here's what I'm planning on doing: I'll tell people my Google number. They'll call that, and it'll call my phone, and I'll not (in general) answer it, but I'll notice that somebody called because my phone will ring. Then I can wait for them to leave a voicemail, and check it online (assuming I'm near a computer (which I probably am)). If it's important (and the person isn't online where I can just chat with them) I can then call them back.

Perhaps this is selfish and a hastle for the people that call me. But there simply aren't that many people that call me, and most of them (Mom, e.g.) probably won't mind or even notice the slight hastle. And if I know somebody will be calling (a friend arriving somewhere, say), I don't have to let the call go to voicemail. And I can tell folks that if they'd really like to reach me, now and on the phone, they can just call twice or something.

I thought I'd see if anybody out there does, or has done, or has had a friend do, something similar. If you've got any comments of feedback about my new scheme for being a cheap-ass hermit, please leave one below. Don't bother calling me :)

That's basically the end of this post. But my original version of the post started with the story behind making these changes, and it's all written out, so I thought I'd include it anyway. If you don't care, then go find something else to do, I won't be offended (I won't even notice, but even if I did, I wouldn't be offended). If you're bored... here's the story:

I think I've never really been a fan of talking to people on the phone. Certainly not recently. I'd almost invariably rather talk to somebody via email or instant message. But I've got a phone, because apparently you've gotta have one. And, I'll concede, they have their uses.

When I started grad school, I got my own mobile phone (look at me all grown up), and an individual phone plan. I've been on the cheapest mobile phone plan since then (5+ years now). I have never gotten particularly close to using anything like my allotted minutes. My most recent bill claims I used 6 minutes total. Not exactly something I was happy paying 50 dollars a month for, but I was too lazy to look into many other options.

The other day I accidentally left my phone in my pants pocket when I put those pants through a cycle in the laundry machine. It was an old phone that I'd gotten for free for signing up for whatever plan anyway, so I can't say I was too upset when it came out of the laundry and wouldn't turn on. I was mostly amused, and glad it didn't do any damage to the laundry machine (water and electronics being what they are... I figured).

After letting it sit for a few days on the hope it might sort itself out, with no luck, I decided it was time for something new. What I probably most wanted to do was get a Droid. This would mean paying more for my phone service, but it'd be paying for something I'd almost certainly use. Not the voice service, so much, but certainly data. However, I listened to the voice of reason (for now :)) and decided instead to switch to a pay-per-minute plan with AT&T (my current provider, inertia being what it is). I went and got a new phone (the cheapest), and am now (after some slight hastle with the SIM card, and having lost all of my contacts) on a plan where I pay 1 dollar every day that I make or receive a call plus 10 cents per minute that those calls take. While I certainly can see that some months will be more expensive than others (due to travel or getting stuck on hold doing something stupid), I have a hard time believing any will be more than the 50 dollars a month I was paying. That's something like 6 minutes of calls every day, or a couple of hour long calls scattered through the month. I'm not sure there's anybody I want to spend an hour on the phone with.

None of that is particularly interesting or exciting, I suppose. It's new for me, so a little exciting, but I can't see why you'd care. What's more exciting is Google Voice. Thanks to an invite from a twitter follower, I now have a Google number. In fact, it's HAM-BLET (in an area code that isn't where I am), which is a little fun (ANIDIOT wasn't available). And I guess the idea is I have the number... indefinitely. And then I can add any of my usual phone numbers (the one I've had for a while now, e.g.) to my Voice account, and whenever somebody calls my Google number, I see the call on my normal phone. And if I decide to not answer, Google will record the voicemail for me and send me an email (or text message, but I turned that off) with a transcript, or I can even listen to it online. That's probably the most exciting thing I've seen in... rather a while. Pressing some buttons online and having my phone ring is pretty magical.

I started doing daily homework assignments for my calculus class when we got to series convergence tests. The idea is that they will read the section in the book and work some problems to turn in, before we talk about it in class. It isn't going well.

Mostly students are "getting the right answer," but the write-ups are fairly bad (mostly making me feel like understanding is pretty low). I spent about 20-30 minutes in class Monday telling them about the things they were doing that are driving me crazy.

We've got three more of these daily assignments due over the next week. I'm thinking about doing the following: During class, have the students gather themselves up in pairs and have each student write their name on their partner's paper. The students will spend time looking for mistakes on their partner's paper. And I'll tell them that whatever points I take off of a paper will also be taken off of the partner's paper.

Surely somebody out there has done something like this before. How does it go? Does it help? What do I need to watch out for? I'm a little worried that "correcting" won't happen as much as "copy down what is hopefully a better answer, without understanding it".

If you are still following this blog, after two months with no posts followed by a rambling personal post, then I owe you something. The best I have is the following...

A few weeks ago in a seminar, I was sitting behind a professor and noticed that his t-shirt had a pretty cool picture of a solid shape on it. I drew the picture, and decided I would love to have a 3-d version. My original (and, now, long-term) goal was to make the solid represented in the picture by a piece of wood. Wandering around the craft store, I decided foam was a bit more feasible for me right now. So anyway... I'll just give you a link to the album I put all of the pictures in (click the picture for the album):


I also made a little video of me spinning the thing, to give an idea what it looks like from more angles.
[埋込みオブジェクト:http://www.youtube.com/v/Rynlkh4rIu4&hl=en&fs=1&]

This was my first attempt at this project, and my first attempt carving something out of foam. I'm honestly fairly pleased with the result. Certainly I see room for improvement though, and plan on trying again soonish. I've got two more blocks of foam still...

This post was inspired by my lack of having posted anything else here in a while (2 months, to the day, apparently). Of course, if you've got nothing to say, which I don't, then not posting isn't a bad thing. Another inspiration for this post is that when I sat down to do "real work" (research, toward my Ph.D.) today, I found that I was on the last page of yet another notebook. Seems like a good time for reflection. I wish I could say that I felt like this last notebook had useful ideas. Or that I felt that way about any of the previous notebooks. I guess if it were true I might be out of here by now, or on my way out in the spring.

This post is fairly personal. The only thing you'll learn about, from reading it, is me. And I'm not a particularly interesting subject, I promise. Go find something else to do, there's plenty out there.

For some reason this academic year has been a huge source of confusion and frustration for me. I'm now in my 6th year of graduate school (for math, in case you forgot that part). For the past 5 years, I knew why I was here: I wanted to be a math professor. Maybe I still do, but I'm not so sure any more. My thesis advisor says he thinks I'd make a good prof at some small school, which was always the goal. And yet, I have a hard time convincing myself that this is still what I want. It's sort of an odd feeling to have your main plan in life for... a decade?... not really matter to you any more. Or, to maybe not matter.

I only have some vague idea(s) why I don't care as much about being a professor as I used to. I'll see what I can put into words, as much (more) for my benefit as yours (hopefully you stopped reading around the end of the second paragraph).

• Research sucks. Or I suck at research. Or... something like that. I've been reading math books for fun since high school (after I read all the books on sharks at the local library, and then decided I wasn't one for the water). I still do. And I love reading about math. But perhaps "doing math" is not something I care much for. I know, I know... math isn't a spectator sport, and... if you aren't reading with a pencil and paper and trying to guess what comes next, you're doing it wrong. But F that. I love reading math, the way I read math. If the way I read math means I'm not a "real mathematician", then maybe I shouldn't be here anyway, or shouldn't be teaching the next batch of math students.
  
• How am I supposed to be a professor, and tell my students how to learn math, if I don't do it myself? How can I tell my students to go home and work more problems (a habit I never had), and bang their heads against problems for a while (when, every time I sit down to do research I find something else to do as quickly as possible)?
• Sure, I can tell my students about math. I can tell them definitions and theorems and how to work problems, and maybe even tie it all together in some meaningful way. But lots of people have already done that, and their work exists in textbooks and, increasingly, online.
• Speaking of online, I feel like (and I know I'm not the only one) higher ed. (and probably other ed., and plenty more) is going to be going through a bit of an upheaval in the near future. I'm not sure I see how small, private, liberal arts colleges (like the one I went to, and always envisioned myself teaching at) are in a sustainable position currently. They are too expensive, and for what? I believe that many people are going to start recognizing that the diploma you get from such an institution isn't as valuable as, say, an impressive online resume, which is now something anybody can create with little effort (besides the "doing things that go on the resume" part). People can show everything they are capable of online, for everybody to see. What good is another diploma in relation to that? (I know that a diploma is still good... I'm not going to argue any of the things I say here)
  
• And also, while I'm on the subject of "online"... the experts are out there posting work online. Awesome teachers are posting full lesson plans, and all sorts of incredible resources. And my students could get to it as easily as I can. What extra value do I bring to the table? A convenient face to bounce ideas off of, to ask questions to (before thinking about the problem long enough alone)? Scheduled hours when I'll be around? I think there is a place for web collaboration tools in education, and I'm not sure how I complete with the sorts of individuals that my students have access to online.
• And a final thought: even going in to grad school, I was making a choice between grad school for math, or grad school for computer science. By the time senior year rolled around I was decided on math. I know at least one of my closest friends at the time was surprised. I sort of wish I had talked to my advisor and my CS professors a bit more about my decision, before making it. These days, I feel like I was probably wrong. I can spend all day online reading about computer/tech/programming stuff. I'll work on Project Euler problems, happily, until I solve them - in contrast to research, which I have a very hard time convincing myself to spend even an hour a day "doing". I don't know, maybe this is just a case of "the grass is always greener". Also, Project Euler problems, from what I've seen, aren't meant to be long, whereas math Ph.D. problems are sort of meant to take a little while. But what gets me excited are the projects I want to work on as a programmer, not as a mathematician.
  

Earlier this year I was at a party, and eventually the group I was sitting with decided to play a "tell me about yourself" sort of game. Mine was "I've been thinking about quitting grad school". Somebody asked me why I was still in it. "Inertia". They thought this was a good answer. To stay 5 years in grad school, and leave before getting a Ph.D. sounds like a pretty stupid idea, all around. But I was seriously considering it. A lease that runs until next summer, and no job prospects if I left, though, made it hard to leave. Around the same time as this party I had several talks with my advisor about what I wanted to do, and such. Eventually we decided I'd stick around into my 7th year and finish up, and then I could re-evaluate "be a professor" or "don't be a professor" at that point. That worked for a while. I'm basically back to wishing I'd just quit. I've also re-adopted my anti-social role, skipping most of the parties I've been invited to since. There are simply more interesting things to do. Which is the same problem I have with doing research.

So, anyway. I don't really know where I am. I don't really know where I am going. I'm apparently in not too much of a hurry to find out. I've killed another hour that I should have spent on research.

And, yes, the title of this post is a nod to Tool.

I've been going into my calculus classes to teach with fewer and fewer notes this semester. I've got a few examples in mind, but that's about it. And I really think it is going well. I think it helps that I started this way on the first day. I also seem to have a pretty good class - I've certainly been pleased so far. After today's class, and some others recently, I'm starting to think that posing the same question to my class a few times, either asking for a different solution, or just a differently-stated solution, is a good habit.

Last week we were talking about improper integrals in class. After some introductory discussion, I asked them to tell me which of the integrals, $\int_1^{\infty} \frac{e^{\sqrt{x}}}{\sqrt{x}}\ dx$ or $\int_1^{\infty} \frac{1}{\sqrt{x}e^{\sqrt{x}}\ dx$ could possibly converge, and why. The first answer I got was to actually compute the first integral and notice that it diverges, so that couldn't be it. A good answer, certainly, with an opportunity to talk about $u$-substitution with improper integrals. And then I asked again, for another reason. A student brought up the integral $\int_1^{\infty} \frac{1}{\sqrt{x}}\ dx,ドル which we already knew diverged, and this gave us the chance to talk about the comparison test. I think at this point we about ran out of time, but I know somewhere in there we also had a discussion about functions that approach 0 not necessarily having a convergent improper integral to infinity. We didn't get to L'Hospital's rule (hopefully a reminder, this being calc 2) that day, but did eventually, with this same example.

Today I was talking about parametric curves. I asked them to take a few minutes to try to sketch the parametric curve $(t^2-1,t^3),ドル and then had students come to the board to draw what they had. I was happy to get two different answers - something like a sideways parabola, and then the correct graph, with a cusp. I asked them how we could tell which could possibly be the correct graph, because they both went through the first few easy points, (0,-1), (-1,0), and (0,1). A student pointed out that $y$ was changing faster than $x,ドル so it shouldn't be the sideways parabola. I didn't want to talk about concavity just yet, but we did get to it eventually.

Then I asked basically the same question, drawing three different curves that weren't the sideways parabola. One had a cusp at (-1,0) where the derivative approached 0 from both sides, another had a cusp where the derivative approached +/-1 (or so), and the third had a vertical asymptote at (-1,0), almost like the graph of $e^{-x^2}$ flipped sideways. I asked which of these it could possibly be, several times. I was delighted to get lots of answers, and continue to pressure the students to reformulate their answers to try to be more precise. I like to think that I waited through the quiet moments while students were working on more answers, or reformulating old answers. I like to think that's what they were doing, instead of just waiting for me to tell them the answer.

I love the feeling that nobody in the class is talking (me especially) because everybody is thinking hard about the same question. I hope that was actually the case with the quiet moments today. I think this process of asking the same question a few ways, or asking for students to answer it a few ways, and me harassing them about their answers, is a good process. We're not just going through "routine" calculations, and I like that. I also hope that I can continue to get lucky with examples that I can do this with.

If you've been following my twitter stream the past few days, you may have noticed that I've been mentioning (and shamefully linking to) a webpage I've been working on to explore parametric curves. Today I decided to make another round of improvements and it was going well, so I thought I'd share here as well. I like to think it is something that calculus teachers might find useful.

Anyway, the page is sort of introduced on my personal website, and the actual "play around with this" page is here. I've only gotten it to work in Firefox 3.5 and Google Chrome. That's enough for me to play with it, so I don't intend to do much more in terms of browser compatibility work on it.

The idea is that your mouse coordinates describe a parametric curve as you move around the screen. The webpage then also graphs the individual curves $x(t)$ and $y(t)$.

There's certainly room for improvement, but I'm happy enough with it as it is to not worry about it for now.

Today was the start of yet another semester at the University of Virginia. The last few days I've been depressed and frustrated and probably a whole host of other negative things, but I think "the routine" starting back up again is helping me out of it. Nice to know that I still love teaching. It also helps that I have friends that treat me far better than I deserve, but that's a story for another day, perhaps.

I had my first class this morning. In fact, I had an 8am class, so I was one of several instructors who taught students their first college class ever. Kinda a fun thought. I hope I didn't screw it up too bad.

I'm teaching Math 132 again, which is Calculus II for math/science folks. I enjoy the course. Which is nice, since this is my fourth time in a row teaching it.

Since I've taught this course several times recently, I'm pretty comfortable with how the material flows, and how I want to make it flow. That, coupled with whatever nonsense I was going through this last weekend, means I hardly prepared for today at all. I had in my mind that I was going to walk in and ask students to tell me about integrals. Just whatever they knew, completely open ended. About 20 minutes before class started I thought maybe it'd be good to review a couple basic derivative rules too - power, e^x, sin, cos. We also talked about some trig identities, since students brought it up.

It's always fun to ask a group of 30-40 students what an integral is. You're bound to get many answers, and I've always been pleased that many of them were ones I had hoped for. It's also interesting to hear ones you weren't expecting. Today we talked through antiderivatives being derivatives "the other way". When asked what antiderivatives were, there was a lovely pause after I fained ignorance about what "the other way" meant ("write it right to left? bottom to top?"). I could feel the class thinking about another way to say this. We got around to it in time. Then we moved on to definite integrals as areas under the curve (but, really, between the curve and the axis, and really the signed version of that). And how they are related to Riemann sums, and how that was different from just a finite sum of rectangles (and did rectangles have to be below the curve? all the time?).

It was a great discussion. I had a wonderful time, and the students seemed to be reasonably content as well. I was shocked to hear what sounded like an entire classroom full of students tell me the derivatives of several functions, basically in unison. At 8:15 in the morning. I hope they can maintain this energy throughout the semester.

I also hope that the course setup can be like this many days, where it's not so much a lecture as a group discussion, with them leading the way. We'll see how that goes. I'm not expecting to try it all of the time. I'm sure that carefully planned examples will be a necessity before too long. I get kinda frustrated thinking about which examples to work. No matter what I do, the problems will always be easier when the students watch me do them, or we work through it together in class. They have to try problems themselves. They have to get stuck. It's the pain about math.

We meet again tomorrow, though, thankfully, not nearly as early. Tomorrow we start techniques of integration, kicking things off with "undoing the chain rule" (u-substitution), and perhaps hinting at "undoing the product rule" (parts), depending on timing. After that, I'm making them learn the other techniques on their own. The other techniques frustrate me. They're not techniques of integration - they are algebraic manipulations to try that come up in lots of integral problems (the problems that show up in calc textbooks anyway). And I would have no idea how to respond if a student asked why they are useful. They're doable by machine (wolframalpha.com, we've been through this before). My hope with making them learn this by themselves, from the textbook (and I encouraged them to find things online, and share what they found with the class), is that the exercise becomes "learn how to learn math by yourself" (well, starting off by yourself, and finding help where you can) instead of "learn these particular tricks". In the long run, that's a more useful thing anyway. In the short run, it might cause some issues, since the midterm will have a hard time testing if they've learned how to learn math by themselves. After they've turned in their first assignment on these techniques, I'll do some review in class, and then give them some more practice problems before the exam.