Cauchy-Riemann Equations

In chaos theory, we study a bit of complex analsis, necessary for describing the dynamics of complex functions. In doing so, we redefined differentiability for the complex plane (essentially the same limit definition, although it simplifies differently because of the imaginary components). 

We then worked with complex functions and worked at finding whether or not they are differentiable at certain points. In doing this, I noticed a pattern. Through 30 minutes in the math lab with a chalk board, I developed equations that simplify the process of finding the differentiability of a complex function at a point – using partial derivatives, and splitting a complex function into a function on the real part and a function on the imaginary part.

Only just now have I discovered that this is already known, a set of equations in complex analysis! I was just browsing wikibooks and discovered the _very_ same formulas I derived! They’re called the Cauchy-Riemann Equations, and they use partial derivatives to analyze the differentiability of a complex function. 

Do I at least get a cookie or something?

http://en.wikibooks.org/wiki/Complex_Analysis/Complex_Functions/Analytic_Functions

Distinction Update

I’ve finished my Bifurcations program (including the spit-polish, minus one feature). It’s all very nice, I think.

I’ve also finished my Mandelbrot program (again), this time it it’s multithreaded! I really want to bench it against my last iteration. It’s about 10x faster than the old one – instant calculation, unless you zoom to a part with a lot of black (and therefore a lot of iterations). 

The default way to run it uses two threads, but I’ve compiled it with 35 threads and it’ll still run (without as much of a speed boost, of course.) At a certain point extra threads add nothing – in general anything over the number of processor cores, although I haven’t tested explicity (which is why I want to bench everything.)

Mr. Andersen is using my work as I finish it for his chaos class, I’m rather proud of that =). It was, after all, what its itended use was. He showed them the bifurcation program today, I heard, and he’s shown my preview video to the class as well. It’s the video I made (to E-30-something) so that the people overseeing all distinction projects know that I’m doing something. It’s purely a preview, my final (for my presentation) will hopefully go to around E-100. 

Watch it Now!

School Has Begun

It’s been a long while since I’ve posted, and for good reason. School started! 

This means that I have no time, ever, for anything. I’m constantly working. The past few weeks have been kind of ridiculous for me. This past weekend I had to finish my National Merit Semifinalist packet, which required a 500 gloat essay (I hate these. “Tell us how awesome you are, maybe you’ll get some money.”) I also had to complete the preliminary test for the Deutscholympiade (International German Olympics – Dec. 5, Chicago), which was no easy task. Having only had a year of German, my vocabulary is not really amazing yet, so much of my time was spent inferring the meaning of words. I also had to write an essay about myself and my hobbies, which was unfortunate since I didn’t know any of the words for my hobbies (except Differentialrechnung and Integralrechnung – Differential and Integral Calculus).

The LAN Party for the comp sci club is Saturday night – looking forward to it. I’ll probably be lame and do homework – but everyone else should have fun! (I’m president, I’m allowed to not have fun ) Also, SAT is this Saturday – I haven’t studied at all, so we’ll see how that goes. Next weekend is Sadies, and a Math Competition in Baton Rouge. I’ll have to look over lower math…It’s been a while (as conceited as that sounds, it’s true. I can’t do Cal2 anymore)

Somehow I’ve managed to continue working on my distinction project, which will require it’s own post.

I hope this gives at least a little insight into life at lsmsa, I’d eventually like to post some examples of the workload (e.g. “This paper got a D. This paper got an A. Note the difference.”)

-Evan