Looking at Roman's beautiful blog, I really couldn't take it no more. I finally removed that scourge of a tiny font size from the blag, now it is actually possible to read everything on a commonly shaped screen. At this point I wished this had been done in LESS, because then I would probably only have to change two variables in order to achieve, what now took me, approximately one hour.
Let $K\subseteq L$ be a field extension, and let $V$ be a $K$-vector space. The extension of $V$ by scalars in $L$ is the tensor product $E=V\otimes_KL$. I will prove that every $L$-vector spaced is obtained as some extension in this way and that $\dim_L(E)=\dim_K(V)$.
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I learned three new Windows shortcuts today:
* Win + Pause: System Properties
* Alt + Space, n: Minimize window
* Alt + Space, x: Maximize window
Especially the latter two are very useful for me.
On Android Smartphones you can use GoogleMaps app for Navigation — unfortunately, it requires an internet connection and this can be very expensive if you use this outside your home country. Therefore, I was looking for a free app which supports downloading the entire maps for certain regions. I think Navfree does the job.
Most people probably know about the stacks project, but fewer might have heard about the CRing project. Now, there might be certain disadvantages to having a large number of contributors to a single document, but I would like to put some emphasis on the one, big advantage: You actually end up with a very complete reference, not just the narrower standpoint of one or two authors. If done correctly, group efforts of this sort are the perfect way to cover all basic (whatever that means) knowledge in some field. I really hope to see more areas pick up on the idea.
I was doing some math with Lars and during our session, we came up with the following inequality. Let $a_1,\ldots,a_r\in\mathbb N$ be integer numbers with $a_i\ge k$. Then,
\[ \frac{\sum_{i=1}^r a_i}{\prod_{i=1}^r a_i} = \sum_{i=1}^r \frac{1}{\prod_{j\ne i} a_j} \le \frac{r}{k^{r-1}}= \frac{rk}{k^r} \]
The inequality is completely obvious, but I found it useful and didn't want to forget about it.
# Why TaskWarrior?
After I've heard of the software TaskWarrior in summer of 2012, I started using it instantly. My main reasons are:
* Since I'm a big fan of self quantification, I wanted the data to be accessible and independent of the existence of any software company. The TaskWarrior stores its data in text, which is imho the most future proof format.
* Everything from the system described in David Alan's book "Getting things done" (short GTD) can be implemented with TaskWarrior.
* It is cool and geeky to use (via command line!). This has a real advantage too: you have the full power of your shell at hand and the programm itself also has powerfull batch processing capabilities.
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On the second day of 29c3, we talked about the group law on an elliptic curve based on our old script (in German) called "Das Gruppengesetz auf Elliptischen Kurven". Today, we explained to some people how elliptic curves can be used to factorize the product of two primes, i.e. attack weak RSA keys. When we were done, we let the flipchart paper taped to the wall and sat down. Few minutes passed before two people in passing showed an unusual interest in our notes. A few words into the conversation, I bluntly asked them about their mathematical background, which was met with an amused
> I'm a math professor, does that suffice?
These people turned out to be Tanja Lange and Daniel Bernstein, two scientists who are rather big shots in mathematical cryptography. I am ashamed to say that I did not even know that, but I certainly understood that they knew a lot more about elliptic curves than me and they were willing to share. To be precise, they were really friendly, and good at explaining it. That's rare. Of course, I eagerly listened as they began elaborating on the advantages of Edwards coordinates on elliptic curves. The two of them had attended the talk by Edwards introducing the concept in 2007 and observed the cryptographic potential:
Basically (and leaving out some details), it's all about the fact that
\[ x^2+y^2 = 1+dx^2y^2 \]
defines an elliptic curve, with all relevant points visible in the affine plane; check out the picture. Choosing $(0,1)$ as your neutral element, a group law on this curve is given by
\[ (x_1,y_1) \oplus (x_2,y_2) := \left( \frac{x_1y_2+x_2y_1}{1+dx_1x_2y_1y_2}, \frac{y_1y_2+x_1x_2}{1+dx_1x_2y_1y_2}\right). \]
With this shape, you never have to mention projective coordinates, the group law can be explained in a very elementary kind of way — and then it turns out that this shape also yields faster algorithms for point multiplication. In short: If you're into curves, cryptography or both, I thoroughly encourage you to check out their summary page about Edwards coordinates.
We have arrived at the 29C3 and set up shop. We will talk a bit about elliptic curves and stuff, but whenever you find us hanging out in 1C, you can stick around and talk to us about anything.
It seems that you can't ((Force Windows 8 Metro Apps to run lower resolutions below 1024x768)) ((Windows 8 Metro style apps running on low screen resolution netbooks)) ((How to enable Windows 8 Metro style apps on an older netbook)) ((Google-Suche)). If you are ok with a squeezed look, set all registry values of
Display1_DownScalingSupported to 1 and change the screen resolution to at least 1024x768.
I was asked today if one could make LaTeX skip all occurances of the value 13, in all counters, as some buildings do. Well, of course you can:
\let\stepc\stepcounter\renewcommand{\stepcounter}[1]{%
\ifthenelse{\equal{\value{#1}}{12}}{\stepc{#1}}{}\stepc{#1}}
\stepcounter macro in \stepc, then we renew its definition by stepping the counter twice if its current value equals 12, therefore effectively omitting the 13th occurance. Also, you should watch the thirteenth floor, it's a nice movie if you're into scifi.
Because apparently, some people our age still do not know about the Pilot Frixion Pen ((At the time of writing, this ebay shop is Germany's cheapest option.)), let me just very briefly inform you about this ingenious item. It is a regular ball pen, but the ink it uses turns invisible under a certain amount of heat. Hence, the Frixion has a little rubber nob at the end, which effectively works as an eraser, because rubbing it against a sheet of paper produces enough heat to turn the ink invisible! Good news: Leaving your lecture notes on the heating does not erase them. Seriously though, this pen is just awesome.
Let's say you have a Windows PC on a 64 bit machine. Obviously, you have Cygwin because anything else would just be silly. Then you want to develop C-Applications that you can compile and run on large Linux-based servers, so you turn to an an IDE that can work with Cygwin. Now here comes the twist: For whatever stubborn reason, you want to be able to compile your applications native 64 bit, and you want to do it in Eclipse, and you want to be able to debug them.
Do you want to know how?