Off to a good start

Mathematics is an easy subject to study anywhere. My brain, somewhere to write my thoughts, something to write them with, and maybe a math text or two are pretty much all I need (well, those and coffee). This and a shortage of keys to my office [1] for the first half of the summer meant that I got into a routine of working either at home or at a nearby coffee shop. By the time I finally did get my key, the routine was set. Even though I had the key, I continued to work in the same old pre-key locations.

Mathematics is not an easy subject to teach anywhere, however. You need to be in a classroom, and in multi-section courses, you need to coordinate with other profs. Today, I had a meeting with the two professors who will be teaching the other sections of one of my courses. It was the first time I had been back in almost two weeks, and the first time I actually needed the office key. After the meeting, I walked toward my office, along with one of the other professors from the meeting. I reached into my pocket for my keys, then turned to the prof beside me, and said, "It wouldn't be a start of a new school year if I didn't lock myself out of my office on my first day back." Fortunately for me, the head of the department has a master key.

Sometimes the fact that I have a PhD still seems unbelievable to me. My teachers always saw the potential in me, if their report card comments can be believed, even though my grades didn't usually reflect it. I'm now finally beginning to see what they saw. Already in grade school, I was misplacing keys at the PhD level.

[1] For security reasons (which no longer seem all that relevant), RMC recently upgraded its locks to a more secure type of lock. Among its features is the difficulty of making copies. Unless you "know a guy", it can only be done by the company who installed the locks in the first place, not at the local key shop and not at any on-site facilities, and apparently it can only be done at a snails pace.

And there was much rejoicing

When I took my undergraduate math courses, almost everything was done on the blackboard. When I took my graduate math courses, almost everything was done on the blackboard. Almost every seminar presentation I've seen has been done on the blackboard.

Sometimes overheads were used in my lectures, but their purpose was used to illustrate the main subject matter, and not to present it. There was one exception to this in a second year calculus course. It was a one term course created by merging two other one term courses, so there was a lot of material to be covered. Even then, it wasn't until the end of the course that the professor made use of overheads to present the main subject matter. In that case, though, we were being taught something that was a straightforward generalization of a concept that we had learned in first year, so even though it was impossible follow the details of the argument, it was possible to understand, if not to predict, the overall structure of the argument.

At some point in my undergrad, professors started wheeling laptops with projectors into classrooms, and by the time I was done, most of the larger classrooms had been equipped with their own permanent projectors. There were a number of courses that I took in my first year or second year whose classroom technology consisted entirely of pen, paper, and the human voice. In my third year, a number of my first or second year friends were taking many of these same courses. Every lecture was now accompanied by a set of downloadable PowerPoint slides summarizing the main topics of the day's lecture. These were not math courses, however. The portable projectors did make an appearance every once in a while, but just like for overheads, they were only used to illustrate the concept of the day, and thus were only used for a small portion of the small number of classes they appeared in.

I was sceptical that the PowerPoint slides were of any significant value in any class. I was even more sceptical that they would ever be worth using at all in math class. I never experienced it personally, and being finally finished with school, I likely never will. I have, however, been to a fair number of math seminar talks that used PowerPoint (or some variant thereof). Not many of them have used the technology effectively. After one seminar talk at RMC, one of their math profs was talking about pressure they were getting to use slides in their lectures. Everyone who said anything thought it was a bad idea. I agreed. In fact, most mathers that I talk to feel more or less the same way.

I taught one course in the Winter term of 2007. There were a few instances where I could've used the projector to demonstrate how to use computer software to solve certain problems, but never once did I feel that using slides instead of the blackboard would've been preferable.

This past fall, I started teaching another course. The only thing I inherited from the previous instructor was the topic schedule for the year, which I've tried to stick to as closely as possible. At first, I was using the blackboard exclusively. But according to schedule, before the end of the first chapter, I was already at least a week behind. I knew that the professor who designed the course did all of his lectures using an overhead projector. I don't know exactly how he did this. I assume he had some overheads with stuff already printed on them, and then wrote more on them in class. I didn't consider this an option for me, since my handwriting isn't that great to begin with (occasionally, though, it has garnered compliments, which mystifies me). It would be worse with my arm positioned awkwardly over the projector, while simultaneously trying to maintain visibility to the students. Not only that, but my fine motor skills seem to disappear when faced~ with the not-so-relaxing task of speaking in front 100 or so people.

On the first day of class, I made an attempt to use presentation slides to cover some administrative details of the class, such as office hours, tutorials, test and assignment dates, etc. It didn't work. My computer didn't appear to recognize the projector. So later in the term, when it was becoming clear that using using blackboard was taking too long, I decided put some of the material on overheads, which were nothing but printed out slides. Using overheads made some things worse, and other things better. I still relied heavily on the blackboard, which meant a lot of running back and forth between the overhead projector and the blackboard (the front of the classroom is 6 blackboards wide). There was also no way to adjust the lights (that I could figure out) so that both the blackboard and the screen were clearly visible to the students. On the other hand, since I intended to post my overheads to the course website, they didn't need to write as much down and could focus on what I was saying rather than just trying to write it down. Not only that, but having most computations completed on the overheads meant that I wasn't going to make copy errors. Aside from one student's request to post the completed overheads on the course website before I finish making them, I didn't get any feedback from my students. So perhaps I hadn't made things better, but at least I hadn't made things appreciably worse.

Near the end of the term, the instructor for the class that took place right before mine in the same classroom showed me how to get my laptop to work with the projector. It turns out I had taken a more complicated route than I needed to (which is necessary if I want to use a tv as the display) I decided to make use of my newfound abilities and delivered the last two lectures of the term with slides.

When the winter term started, I tried using the blackboard, but by the third week (Jan 21), I got to a point where I needed to project something onto a screen by some means. I decided I would use slides, and not wanting to deal with the hassles of transitioning between blackboard and projector, I decided to carry out the whole lecture that way. From my perspective, things seemed to go more smoothly. From the students, I heard one positive comment and one negative comment which included another request that I post the completed slides before I've completed them.

One of the most obvious mistakes in using slides is that the presenter tends to plough through the material too quickly. I'm reluctant to say that math is hard to understand (though I'm sure many in my audience don't share that reluctance). But it's certainly hard to understand a slide containing math in the brief amount of time that a careless presenter leaves the slide up. Writing on the blackboard, on the other hand, forces the presenter to pace himself. Leaving the slides up longer would mean talking longer than I need to, or else standing there silently (and feeling awkward) trying to guess the point at which a sufficient number of students have comprehended what I'm going on about.

To guard against the tendency go too fast, I tried to structure the slides, as much as it was possible, to resemble how I would write the same material on the blackboard. For example, if there was a calculation with many steps, each step would get its own line, and the lines would be displayed one at a time (with spoken explanations of how I got from one line to the next, as each line was being displayed). There were times, however, where I was forced to split something up into two slides when it would have been better if all it could have been put on one. This, I think, gets at to one of the other primary disadvantages of using them in math. In almost all classrooms there are at least two blackboards (or whiteboards in some newer classrooms). One could see how the material on the blackboard I'm writing on would relate to blackboard I've just written on. Being able to display only one screen at a time is analogous to having only one blackboard to write on. Since they would be able to download the slides later, though, they could go back and see for themselves how the different slides relate to each other (whether or not they would is an entirely different story). I weighed these and other factors, and decided to stick with slides.

I continued to deliver my lectures using slides for about a month, until I got to a point where I couldn't come up with a sensible way to make slides for a certain topic. I decided, at least for the time being, that I would go back to the blackboard. When the day came (Feb. 27) to present that material, there were still some slides that I didn't get through in the last class, so obviously I presented those first. When I finished with the slides I announced that I would be going back to the blackboard. At this point there was much rejoicing. Well, it wasn't quite rejoicing. It was more like a handful some scattered murmurs, though with a definite tone of approval. This is a math class, though. Aside from cancelling a class altogether, how much rejoicing do you expect?

Astounding

For years, one of the standard references in graph theory was "Graph Theory with Applications" by J.A. Bondy and U.S.R Murty, first published in 1976. More recently other texts have played that role. On November 30, 2007 a follow up to this book, entitled simply "Graph Theory", was published. When I told my supervisor, he was astounded. Apparently word isn't out yet. So I'm letting you know. My supervisor went to the bookstore this morning to get himself a copy, and they had already exhausted their supply [1], so it seems to be a hot item. Hurry on down to your local campus bookstore and get one for yourself before it sells out.

So far, I haven't been able to find any reviews of this long awaited book. If you see one, let me know.

[1] Their supply consisted of one copy.

Facetiousness immitates the academy...

...sort of.

A few weeks ago, I wrote a rather lengthy post on an alternative voting system, based on Google's algorithm for ranking websites. It was more of a thought experiment than a serious proposal.

Recently, while researching something on a different, though related, topic, I found out that the main idea behind Google's algorithm is a variation on something called the Kendall-Wei method. Wanting to know more about it, I decided to google Kendall-Wei. To my surprise, the fourth page that came up is a paper titled "An Introduction to Vote-Counting Schemes" [1]. So I'm not the first person to make a connection between Google's ranking of websites and the ranking of political candidates. Although, the use of the Kendall-Wei method described in this paper is quite different from my suggestion (thus the "...sort of" at the beginning of this post). Nevertheless, the fact that someone else besides me has connected elections with the use of the Kendall-Wei method, suggests that perhaps I ought to be taking my ideas more seriously. Expect me to announce the publication of my paper on the subject soon.

[1] You probably won't be able to download the paper, unless you happen to be on a university campus with a subscription to JSTOR.

Thesis Pieces

About 5 years ago, when I had to decide whether or not I wanted to do a PhD, I had a number of reservations. One of them was the fact that, in order to actually finish the program, I was required to do an oral exam. The longest that it could have taken was three hours. It's a very small amount of time when you consider that it took 4-5 years to get to the point where I could do the defence, but up to the time that I had to make the decision, and for quite some time after that, I was terrified by the idea of public speaking of any kind, even if it was just in front of a small number of people. The fact that every member of my audience would be evaluating my performance to determine whether or not I actually deserved the degree that I had been working on for more than four years didn't make the idea any more appealing.

Now, here I am, and I've done it.

So how was it?

You already know that I passed.

The defence consisted of two parts. The first is a twenty minute presentation, which is public. The second is a question period, which is not.

I've only been to one other defence presentation other than my own, and in both mine and his it felt like far too much material was covered in those 20 minutes. I feel like nobody who didn't already know what was going on would be able to understand the material [1]. Not so much because it's hard to understand, but because it is spoken about so quickly and in such sparse detail that it would be hard to absorb what little could be said long enough to appreciate it.

I wasn't sure what to expect from the question period in terms of the character of the examiners and in the types of questions that would be asked. I'd heard a few stories from people who had already done their PhD's. At least one person said that the examiners question you until you feel stupid. Not that this is their goal. They are trying to determine the limits of your knowledge, and that limit is reached when you can't answer a question that they ask, at which point you feel stupid. Or so went the reasoning. More recently, a friend told me that his friend's father was a professor, and he would actually try to make the candidates that he examined cry. Other than the external, I knew all of the examiners on my committee beforehand, and of those I knew, none seemed like the type to do that. The only unknown was the external. My experience did not reflect either of the above scenarios. On the contrary, when one of the examiners sensed that I was feeling uncomfortable he assured me that it was natural to feel that way, given the setting. My performance wasn't flawless, and so I felt a bit silly here and there when I my answers didn't come out quite as well as they should have, but I never felt stupid because of the content of my answer. There was a point where I knew that I knew the answer to a question, but I couldn't remember it right away. It was something that I felt I should have been able to answer immediately, but it took a few leading questions before I gave the examiner the answer he was looking for. The most difficult questions to answer, though, were not the ones about things that we knew were true, but about the open questions. Do I think that the answer to this question is yes or no? If it is no, do I think that the answer is almost always yes. Some of the questions required me to talk about things that I'm only vaguely familiar with, leaving me to fumble around awkwardly trying to find the right words. Most of these negatives, though, I feel are minor.

I don't think that I could have done much to prepare for the questions in the five weeks between submission and defence. Some of them I was able to anticipate, but most of them I wasn't. I did spend some time reading through the thesis trying to make sure that the material that I thought was important was actually committed to memory. However, I would have been able to answer almost all of the questions without this extra effort. It wasn't that I had committed every important detail to memory. It was more that the questions could mostly be answered without having memorized them.

Overall, the defence didn't feel too different from a presentation that I might have given in a seminar. The main difference between the two is that the presentation is shorter and the question period is much longer. It was hard to forget that I was being evaluated, but I don't think that my answers would have been very different if I wasn't. Certainly it wasn't nearly as horrible as I had expected it would be when I started the program.

[1] This was confirmed by the chair of the committee. During the defence, his role is to maintain order (could things really get that out of hand?), so he didn't say anything to me or ask me any questions. After the defence, however, when he was no longer required to maintain order, and all chaos broke loose, he told me that he was lost after the first slide.

I thought you might like to know.

I passed my defence.

Questions answered, unanswered

I was discussing publishing papers with my supervisor today. There are at least two papers, though he has reservations about both. This prompted a question from me. Part of my reluctance to commit to the world of academics is the worry that I won't be able to come up with anything publication worthy. I know that I'm not alone in this. How will I know when something I've done is ready for publication? How will I even know whether my questions are interesting enough that they would even be worth trying to answer them? On this second question, I feel somewhat validated that papers on ideas and questions that I've come up with on my own have already appeared in the literature. The first question I am less certain about, and this is what I ask my supervisor. It's subjective, he responded.

After his response, I added that it depends on whether my goal is just to get a certain number of papers in print, or whether I could actually be proud to associate myself with the papers that bear my name. This reminded me of a former graduate student from Queen's who had published a large number of papers, about 10 times as many as I have had published or accepted. He gave a presentation on some of the material from these papers at a seminar once. The results weren't very interesting. I said as much to my supervisor, and this was enough for him to be able to identify the student that I was talking about. His opinion was about the same as mine.

He then told me that this student tried to insist that the department hire him for a faculty position straight out of the Ph.D. program. He didn't get hired. In fact, no Queen's Ph.D. graduate, no matter how well qualified, would ever get hired by the department for a full time faculty position without having gone somewhere else first for. It sounds like even a post-doc somewhere else is not enough. This answers another question that a number of people have asked me. Do you think Queen's would hire you? Maybe 10 or 20 years down the road, they would, but the question is clearly being asked about the present. In that case the answer is no (though a number of students have done short post-docs, or limited term teaching positions, but in most cases I don't think this is what the questioners have in mind either).

Out of the frying pan...

It's been a while. I'm sorry.

Conference preparations and teaching got in the way of regular blogging for most of this past term. It also got in the way of the more important (to me at least) activity of thesis editing. Once I got back from the conference, I took a few days to catch my breath. I didn't do much of anything important, aside from tying up the last loose end with my course, between the time that I got back to the time I posted about the conference. The next day, I started getting ready to move and working on the thesis.

Everything aside from a few odds and ends was moved out on 29th of April. I picked up the the odds and ends the next day when I went back to help (now former) housemate number 1 clean up the old place--(now former) housemate number 2 had packed and left a few days earlier--and deliver a carload of her stuff to their new place that the movers, who were already behind schedule when they arrived, didn't have time to deliver. By the time that was done, I barely had enough strength left to lift my fingers to type.

The boxes were mostly left unmoved during the first week in my new place, except to find this or that item that I happened to need, since most of that week was spent working on the thesis, either making corrections or discussing them with my supervisor. Needless to say, after spending that much time thinking about corrections and typing them into the computer, the ideal break-time activity was not sitting at my computer thinking about and typing up blog posts. Besides that, blogging is usually a spontaneous activity, writing posts when things come to mind. There isn't much room for that to happen when my thoughts are focused on my thesis.

On top of moving and editing, I was asked a few weeks ago to give a talk. I couldn't think of an excuse on the spot, so I had to give a talk in the Queen's/RMC discrete math seminar on Thursday. Most of the talk was spent discussing known results, so preparing the talk wasn't difficult, but it was still quite time consuming, and it was yet another thing to do amidst being quite busy already. My supervisor said that it went well, which I take to mean that it went well.

Instead of handwriting the corrections onto a paper copy of Chapters 4, as my supervisor has done so far for Chapters 0-3, he made a nonpaper copy of the file and typed his own corrections to that file. So today the roles were reversed, and I spent the evening reading his corrected version of my file and making my own corrections to his work. It's the first day in about two weeks where a substantial part of the day was not spent typing, so here I am blogging... about why I haven't been blogging.

Hopefully soon I can get back to blogging about things other what I've been up to lately.

99 Red Balloons

This past weekend, I went to the conference in Tucson that I had anounced a while ago.

My biggest worry about the whole thing, once I had secured my passport, was getting there. This turned out to be not much of an issue. That is not to say that it wasn't. It just turns out that it was no worse than the most common triggers of the dreaded effect. There was a moment in the ascent where the plane seemed to suddenly but briefly drop in altitude, which caused some discomfort, and things were fine until the plane began to descend in Phoenix four hours later. Here, it was definitely worse than at the beginning, but still not as unbearable as I had been expecting. The worst case seemed to be on the return trip from Tucson to Phoenix. Aside from this, the whole travelling portion trip went off without a hitch. I would have preferred not to leave at 2:00 am from Kingston, but no luggage was lost, there were no problems with tickets or customs, and all flights left on time. I was warned about problems with the ears popping, or not popping. I can't remember what exactly was supposed to cause the problems that never happened. As we changed altitude, I could certainly feel that there was a pressure difference building up, but it was nowhere close to uncomfortable. On may way out of the airport, I was also lucky enough to run into a friend who was waiting for his dad at the airport. Or rather, he was lucky enough for me to run into him. It was around 8:00 pm when I met him, and his dad's flight was supposed to arrive around 5:00 pm. I talked to him for at least a half an hour before he saw his dad.

The conference was good, but much lower key than I was expecting. All but one of the talks that I went to were those in the Special Session on Graph Theory and Combinatorics. Most of them were well presented and interesting, though they were quick. I'm used to going seeing one hour talks in seminars, whereas these talks were only twenty minutes each [1]. I haven't had much luck with Power Point (or related formats) talks, especially in math, though the ones given here were mostly well done. The one talk that I did go to outside of the special session was the second of three by invited speakers. The talk was not in my research area, and went from zero to incomprehensible in 60 seconds. I left after about 10 minutes, and I wasn't the first. Apparently the first talk by an invited speaker wasn't much better. We all decided not to go to the third. I had a chance to speak with most of the people who came to the session on graph theory and combinatorics, and, based on what I overheard from Saturday night's dinner conversation, I've now met pretty much every graph theorist and combinatorialist in the western United States. Yep. All ten of them.

I wish that I could have stayed in Tucson longer. I don't know how much longer, but longer. Looking out the window of my sixth floor hotel room, I could see mountains (real mountains, not Hamilton mountains) in almost every direction. The same would be true had my room been at the front instead of the back the hotel. If I had more time, I would have like to explore at least one of these mountains. The city seemed rather large in terms of area, though most of that consisted of low density housing, commercial, etc. There were very few highrise towers. I don't know if this has to do with the fact that such things are hard to build in the desert, or if it has do with the fact that sand is not a proctected species, and so sprawl isn't an issue. Most of the houses were, I think, stucco, or something that looks like stucco, or something that looks like what I think stucco looks like. Whatever it is, they looked a lot like stereotypical Mexican houses (the ones you see in TV shows, movies, etc.), which isn't surprising, since Tucson is only 60 miles from Mexico. Besides this, there were quite a lot of red brick houses. Most houses didn't have grass lawns, but rather sandy lots dotted by various sorts of cacti, or else trees that a Canadian would only have in potted form, and kept inside, such as palm trees (I think). The downtown, where most of the few highrise towers are located, was unimpressive, and, like my hometown of Hamilton, the area near the university (of Arizona) was more impressive and looked more like what you would expect (or hope) the downtown of a city to look like. The university campus was attractive. The University of Arizona is as enthusiastic about its red brick as Queen's is of its limestone. Perhaps moreso, since, unlike Queen's, they seem to have escaped the 60's lust for cold and forboding concrete structures. This was about as much of an impression of the city as I could get without use of a car.

Some other things:

• I finally understand the phrase "It's a dry heat." I've heard this phrase many times, but I've never actually experienced one. It was 27 C on the Sunday. I spent about an hour and a half walking around in direct sunlight, I barely broke a sweat, and never once did it feel uncomfortable. None of those things would be true on a 27 C day in Southern Ontario. Being in Toronto for no more than 10 minutes, I could already feel the higher levels of humidity.
• Among the weirdest things that I saw in Tucson was a firefighting supply store, I suppose in case anyone wants to start up their own firefighting company. Of course, fire departments need to get their supplies from somewhere, but I wouldn't expect to find them being sold amidst shops selling hemp and incense.
• Tucson has a brew pub. Partial answer to "How much longer could I have stayed in Tucson?": Long enough to be able to sample each of their potent potables (to borrow a phrase from Kingston's brew pub). The pub had an automatic 18% gratuity for parties of 10 or more, which we were. This was a tad grating to me. My tips almost always fall into the 15-20% range, and this would have been no exception. But when you're forced to pay a gratuity, it's not a gratuity, but rather a fee for having been waited on. I hear this is common in Europe.
  

Finally, to answer everyone's favourite question. I didn't bring you anything. Don't take it personally, though. I didn't even bring myself anything.

[1] I'm told by one of my colleagues at RMC that this was long for a conference talk.

Seeing the Light

Teaching at RMC begins today (at 12:40 EST). I hear it could be time consuming. So blogging may be light for the next few months.

Academic Milestones

I noticed today that one of my publications has been cited in two papers (by the same author). The papers were written in 2003, and the author gets the journal wrong in both cases (or I've got it wrong, but I don't think so).

I was aware of one of these papers, or a paper on the same topic, a while ago, so perhaps I already knew this. But today it came as news to me.

It's a milestone to me regardless.