The Spectre of Math

December 7, 2009

Picard’s theorem

Filed under: Mathematics — jlebl @ 7:59 pm

Just finished the proof of Picard’s theorem on existence and uniqueness of solutions to ODEs in my real analysis class:

Theorem (Picard). Let I,J \subset {\mathbb{R}} be closed bounded intervals and let I_0 and J_0 be their interiors. Suppose F \colon I \times J \to {\mathbb{R}} is continuous and Lipschitz in the second variable, that is, there exists a number L such that

\lvert F(x,y) - F(x,z) \rvert \leq L \lvert y-z \rvert for all y,z \in J, x \in I.

Let (x_0,y_0) \in I_0 \times J_0. Then there exists an h > 0 and a unique differentiable f \colon [x_0 - h, x_0 + h] \to {\mathbb{R}}, such that

f'(x) = F(x,f(x)) and f(x_0) = y_0.

That was the last lecture for the semester, yay! The proof is essentially the standard one, but of course I don’t use the fixed point theorem on metric spaces since I don’t have that. Convergence and uniqueness is shown purely by methods taught in the class. The only thing which I had to define to state and prove the theorem was continuity in two variables. I think it’s the longest proof in the book, being 2.5 pages long (it’s 12pt font, plus it’s given in a lot of detail).

See the last section in my real analysis notes/book.

I was thinking of using something else such as implicit function theorem or some such, but Picard’s theorem is just cool. Plus the proof uses everything we’ve learned: continuity, derivatives, Riemann integral, uniform convergence, swapping of limits, etc… Plus the proof is a bunch of estimates. It doesn’t get any more “analysis” than that.

“run fsck manually” … really? WTF ubuntu moment.

Filed under: Technology — jlebl @ 6:26 pm

This was rather disappointing. Marketa’s computer got somehow hosed by flash. The whole thing froze. It wasn’t trashing, so I don’t think it was a mem leak. I think the display driver hit some bug. In any case, the machine froze completely after a few minutes of me trying to kill firefox. So I let the thing go for a moment, in case the kernel was still syncing to disk. Then I hit the power button.

Ubuntu came up, and the disk checking text started flickering down on the splash screen (not particularly pretty, but … ok I can live with that). What happened next is inexcusable. It dropped to root shell and told me to run fsck manually. One part of me said “WTF!” and the other part of me felt nostalgic. I mean this was something that I would expect from slackware 10 years ago. For a desktop OS, this is inexcusable! Basically, the machine would be dead to marketa, including all the data on it. She doesn’t know what fsck is and she doesn’t know how to run it. Once it would be running, I suppose it would be sort of OK. She’d answer yes to all the questions “foo bar is b0rk, should I try to fix it.” OF COURSE YOU SHOULD YOU STUPID MACHINE, I HAVE NO CLUE WHAT YOU ARE TALKING ABOUT. But she would never get to this point.

What should happen in this case should be some warning (can be done in text) dialog that says: “things seem seriously hosed should I try to fix it? If not I’ll assume you know what to do in a root shell.” (not exactly those words, but something like it. Then it should ruin fsck FOR YOU. It should warn you to check that all your data is fine and check backups and all that, but it should try to get you a working machine. A root shell is a dead machine to a non-geek.

Damnit, even I don’t know what all those things fsck is asking me are. Why would I NOT let fsck try to fix whatever it is trying to do. I know what inodes are, but I am not an expert on ext3, just like 99.9% of the population (including 99.8% of the geekdom). So I’ll let fsck do whatever it tells me to.

It turns out that because I was able to run fsck manually, all her data seems fine. But it sucks that she had to ask someone with unix experience. I would have hoped this was fixed a LONG time ago. It is really not that hard to fix. If the people responsible for this part of the boot process tell you “but you need to be knowledgeable to run fsck”, then they are morons. They are working on a server OS not a desktop one. And an obnoxious server OS. The whole point of ubuntu being easy to use is that it should work for people who are not knowledgeable. And it should try its best to recover from being b0rk. Ubuntu doesn’t do its best. It does its worst it seems.

December 1, 2009

Real analysis notes functionally complete

Filed under: Mathematics — jlebl @ 8:48 pm

I have removed the last “FIXME” from the notes, meaning that they now include all that I want them to include. I even ran a spellchecker on the thing. I will wait another week or two and read through a bit before I sprinkle holy pee on them and call them finished. I figure I should at least teach through to the end of the course before I call them really finished (I always find typos when refreshing myself on the notes before class). I might also think up an extra exercise or two while writing the final exam.

November 30, 2009

Real Analysis

Filed under: Mathematics — jlebl @ 3:38 am

So the colleague of mine who was teaching my real analysis course for me went a bit faster than I expected and therefore he went straight through to the end of my prepared material. The bad part of this is that I had to prepare new material, the good part is that I really am going to get through Picard’s theorem (existence and uniqueness of ODE) as I wanted (that’s just a cool theorem, and it uses all the things learned in the course). So I spent today writing that section and polishing up the notes overall.
I am getting very close to being “functionally complete” with the notes. I now even made a webpage for them. They still lack the Taylor theorem section (which I did not cover in class) and some extra exercises in places. Just another few hours worth of work should be good for a first draft kind of quality.

November 22, 2009

MSIE vs. Firefox

Filed under: Technology — jlebl @ 4:19 pm

Yesterday I saw the diffqs page for the first time in IE at my dad’s place. Of course the whole thing was jumbled. Apparently writing to standards is not enough. When the DOCTYPE line is not just right IE will start ignoring certain parts of your CSS. So it happens that in IE, the ads that were supposed to be on the right, out of the way, were unstyled and at the top taking up a whole page. So you had to scroll down to see the content. I guess that could have reduced the number of downloads. So I tested a few days worth of logs to see what the percentage of IE vs. Firefox users are among people looking at the diffyqs page, to see how it could affect the numbers. So in 829 real users with identified browsers, there were 665 various Firefox uesrs (more than 450 of those were version 3.5), there were 122 IE users, 39 Safari users, and 3 Opera users. I guess majority of the users are students and those are more likely to use Firefox. There were 38 Linux users and 125 mac users and the rest were windows users.

Anyway, IE is fairly braindead.

November 18, 2009

advancecomp

Filed under: Technology — jlebl @ 10:11 am

poking around I just found advancecomp which uses the 7zip compression deflate algorithm which seems to get often better results than running optipng with the full 1000 trials. Though I guess running first optipng and then advpng is probably best. optipng optimizes for the correct filter and advpng then might (not always) get better compression. It would be good if optipng also tried the 7-zip algorithm. The plot2-nq8.png didn’t decrease anymore, but plot2.png went down by 2k and is now 51k.

adsense, diffyqs, pngnq, optipng, zareason

Filed under: Mathematics, Technology — jlebl @ 9:21 am

Firstly, I have so far made about $3.50 on adsense over past 3 weeks or so. I’m soooo rich. Strangely this correlates with a drop in diffyqs downloads. However, it can’t possibly be from the ads (that is, my first theory was that with the ads less people hit the download link). But the hit rate dropped as well (though I don’t have very good statistics of that before I installed adsense). The first, and I think the main, reason that the hit rate dropped is that geocities went offline. One of the main sites for free textbooks was on geocities. Though the site has a mirror somewhere else, the majority of hits seemed to have come from the geocities site. I assume it will take some time before things get realigned. Just as a side note, there have been over 3200 unique IPs downloading the notes so far.

I think the other reason the hit rate dropped is that we are well inside the semester, so most people taking university courses that were looking for online notes have already found them. I wonder if there will be a “before finals” spike, and if the traffic will pick up in the beginning of the spring semester as it did in the beginning of the fall semester.

One thing that threw me off last time is that the site appeared on stumbleupon. So the hit rate I saw the few days after installing adsense was actually overinflated. Most people that hit the site with stumbleupon never download the pdf. I suppose that’s understandable. When a random person is presented with the possibility of looking at differential equations, they will quickly run away. The hits that come from either google or some of the textbook listing sites frequently result in downloads. Obviously, people searching for “differential equations” are likely to download a textbook on said topic. The normal day hit rate is nowdays more like 100-200 hits with about 10-20 downloads.

The other interesting observation is that the extra stumbleupon traffic, which occasionally happens and make the traffic spike up up to 10 fold the usual levels, doesn’t result in more clicks on the adsense ads. I assume this is because the ads are targetted. They are tutoring or textbook selling sites generally, so a random person is also less likely to click them.

Just for kicks I played around with pngnq to quantize the pngs appearing on the site. Quantizing things to 256 colors reduces size substantially, and if the picture is not a photograph, the quality reduction is not bad. For example, see the full version and the quantized version. The size of this png went down from 53k to 22k. Quantizing does not always result in smaller files though, so always check. That picture was originally even bigger. The stupidest way to save a png results in a far larger file, I think this one was over 70k originally. So you always want to run optipng on all pngs. That generally results in substantial savings already losslessly. I ran optipng on all .pngs on the entire website and generally got anywhere from 10-50% reduction. I also ran it some time ago through the pngs appearing in the genius docs, so that should slightly reduce the ondisk footprint on genius when installed.

Finally, I’ve discovered the first harware flaws in zareason alto 2550 laptop. The sound is kind of crappy and very low volume. It is very substandard actually. This includes using headphones, so it is not just crappy speakers. There is a small possibility that this is a software issue, but I think it is more likely to be the hardware is kind of crap. The other fault I found is that the case is not well thought out at certain points. When you pick up the laptop in certain ways the plastic sort of snaps as two pieces of plastic slide under each other and then back. That’s kind of distressing, I hope it doesn’t break and that it is just cosmetic. Overall though I’m still satisfied enough that I would buy it again.

November 12, 2009

New computer (Zareason) and Karmic

Filed under: Personal, Technology — jlebl @ 4:13 pm

So my old dell has reached an old age where I was starting to be afraid the harddisk would go (some of the SMART disk parameters were getting pretty high, I didn’t ever worry in the days before I knew what these were). I suppose I could just replace the HD, but also the screen hinge was slowly going as well, as seems to be a problem with dells (at least for me).

I considered buying a dell with linux, but none of the specs looked good, and the specs that did look good didn’t ship with linux. I wanted a smaller laptop but with a decent resolution. I don’t need a graphics powerhouse I don’t play games. I had the 15 inch monstrocity. The new 15 inch inspirons had even a worse resolution (what’s wrong with these people, I don’t care how wide my screen is, make it high enough so that things fit, especially with the current UI, height is at a premium. I feel like new laptops are the equivalent of driving a tank). And the 15 inch inspirons are heavy. They also have the 13 inch studio, but that sucked for different reasons. And there were no other choices.

So scrap dell. I looked at System76 and Zareason. I was a little bit skeptical as I had before been burned by a bad “linux preinstalled laptop.” I finally decided for Zareason Alto 2550. The machine is very cool and so far no problems with the hardware. Karmic has had several issues already (such as CDs not moounting) that have been fixed by updating to the latest -proposed.

Verdict:

1) Zareson is very cool. They even sent me screwdriver with the laptop so that I could open it and look inside (of course I did just that). The machine is lighter than the inspiron, the screen is the same height but shorter. The keyboard takes a bit getting used to (that is once I’m used to the inspiron location of keys), but it is good. There is a fingerprint reader which apparently doesn’t work without some proprietary nonsense, but who cares, it’s not something I’ll be using anyway. Of course it is a generic barebones laptop that zareason just put together, so they don’t have 100% control of the hardware. The barebones hardware is MSI-made as far as I can tell. The ubuntu key ont he keyboard is cool, even though it is achieved by a sticker. And I finally don’t have to peel off the windows sticker from a new laptop (there is an ubuntu sticker).

2) Ubuntu should probably make the stabilization period longer. Hold off another 2-3 weeks, make another one or two release candidates with deep freeze. All the geeks will upgrade to release candidates anyway, so it is not an argument (actually geeks will generally update in the alpha stage). I usually update during beta sometime. A final ubuntu release should be more polished. And it seems it always gets polished in another few weeks past release, so waiting a few more weeks would result in far less bad publicity. When reading the buglists, it always seems that many bugs are found just before release, but the fix cannot be pushed through in time. This says to me that the release is too early. And this has always been the case with ubuntu, it’s nothing new with karmic. But as ubuntu is getting more widely adopted, the new userbase will be far less forgiving of problems in a “released” version which should be stable.

November 3, 2009

conservatives using communist terminology

Filed under: Politics — jlebl @ 3:53 pm

So I heard that an anti tax law on the ballot (today I presume) is called TABOR (taxpayer bill of rights). First thing that came up in my head was red flags waving and militaristic communist music. See I assume they used the name because of Mount Tabor in Israel (what does transfiguration of christ have to do with tax limitations is beyond me). However, being a czech that grew up in communism, Tábor means an entirely different thing. The more radical branch of the Hussites (the Taborites) started the town and made a commune there. Suffice it to say the commune did not work actually, but it was used by the communists as an example of the first fairly large scale experiment in communism (they ignored the very religious aspects of course as the town is also named after Mount Tabor because the Hussites were religious fanatics). Anyway, naming something TABOR feels very communist to me. I’m sure they didn’t mean it, but it gave me a laugh anyway. The Taborites were also mostly nutcases and plunged central europe into 200 years of economic and cultural stagnation, culminating with a 30 year war that killed around 90% of central european inhabitants. I’m sure it’s the same kind of result we want from our tax laws.

October 28, 2009

Obsession for … politicians?

Filed under: Politics, Technology — jlebl @ 7:09 pm

What is this obsession with the entertainment industry. In Britian now they will have the “you download three pieces of illegal music and you can’t get on the internet” law. OK, I understand that according to current laws, copying copyrighted material without permission of the copyright owner is illegal. But, to make a law like that? Do you get banned for life from walking on the sidewalk if you have used the sidewalk to walk to 3 shops you robbed? Perhaps it is because your grocery shop doesn’t have the right kind of lobbyist working for them.

Plus it is entertainment industry. It is not like they are curing cancer. Who cares that Metallica only makes half of what they would make if nobody downloaded their songs illegaly. That’s only bad for Metallica, and it ain’t all that bad for them anyway. Why is it crucial for society that Metallica has lots of money (and they seem to be doing fine even with all this evil illegal copying going around). I mean, why is illegal downloading considered such a huge problem? Why isn’t world hunger considered a bigger problem? Why not spend all the energy and money the society spends on protecting the entertainment industry from reality to actually do some good in the world. I bet those kids dying of hunger could care less that some wanker is downloading illegal mp3s. I mean, there’s lots of really bad stuff going on even in the industrialized world. Spend some efforts on that. There are lots of people in a very tough spot in the UK as well (and US and the rest of the world). And they aren’t the entertainment industry.

Is it so important for society to make Metallica rich? You say that there would not be any Metallica. So what! As long as teenage boys want to get laid, they will continue trying to make music and become musicians. I bet far more than 99% of music made in the world is not made for the money. But that less than 1% makes a lot of money. But it is NOT crucial for society if that 1% comes or goes. If music is so unimportant to society that it will go away the moment it is not profitable, then who cares if it is gone.

It will also never get to that. Even if we allow everyone to download music willy nilly, it will still be profitable to make and sell music. It just won’t be so profitable. The people “harmed” are simply not able to make money “in this particular manner.” But there are many ways that I can’t make money. For example, I can’t say that everyone who walks past my house has to pay me $50. I can’t say that I invented blinking twice in a row and then charging everyone doing it. Who cares if I can’t make money that way. Why should there be a law that says that I have to be able to make money like that?

Access to internet will very soon be almost a requirement for life in a modern society. So it will be like banning someone from using the telephone or using the sidewalk or riding the bus.

Actually I stopped listening to Metallica the moment they started pulling this copyright nonsense. They have not gotten a single cent from me in the past decade. And I used to like them. Also, sorry about using Metallica as the single metaphor for the entertainment industry. By Metallica I mean all the successful bands and the whole recording industry and the movie industry, etc…

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