Week in Review: April 30-May 4

First week was pretty good. Getting used to this whole 9-5 stuff, and even though I imagine this stuff will ultimately make me immune to ibuprofen from the headaches it's causing, I'm actually enjoying it. I've learned a nice bit about differential geometry, and my programs are starting to look bug-free and does the right job within reasonable error. So what's in store for next week? Stay tuned and find out!

Numerical Techniques: Part Three

Okay, so not a whole lot new accomplished today. Merged all the programs into three simpler programs, which makes it a lot easier to test new calculations. Though honestly, I have no idea whether these are coming out right or not :P. But, they do work out perfect for a sphere, and the only changes I make for any other surface are the formulas used to calculate the surfaces, so I'm supposing they work out right.

Numerical Techniques: Part Two

So today I expanded on the programs I made yesterday. Now it can handle a sphere, an ellipsoid, or torus, and ultimately finds what is called the "intrinsic curvature" of the object in terms of a particular distortion (currently involving just increasing the radius, essentially, but can be modified for any kind of distorting). I have no idea what this curvature actually represents, but apparently my programs calculate it right! That's always good.

Numerical Techniques

Today I began implementing some simple numerical differentiation and integration routines, applying them to some techniques found in differential geometry.

In the span of nearly three hours, I wrote a series of five programs. These programs must be run sequentially, as each uses the data of the previous program (except, of course, for the first which generates the data).

Five programs and three hours and I can successfully calculate the area of a sphere with radius 1.

Okay, so maybe I'm demeaning this process a little. My initial application was a unit sphere. But the first program can be modified to generate data for any kind of surface, and the remaining programs can find the area of said surface with little-to-no modification.

Differential Geometry

So today I read up on this titular subject, and came to the conclusion that it is the possibly cannibis-induced lovechild of set theory and vector calculus. For those unfamiliar with the subjects, they are two very core fields in mathematics. I know many people who are good at one and only one (myself included); I know of none adept at both.

The following words have defined mathematical meanings that I was completely unaware of before today:

• Patch
• Umbilical
• Monkey saddle
• Maximal
• Compact
• Pullback
• Pushout
• Categorical dual
  
• Bundle
• Fibre product
• Functor

And no, I am not exaggerating in any way. Each and every one of these terms is related in some manner to differential geometry, I have discovered them all in my reading.

Update: I reworded things a little, as previously this entry sounded far more harshly than I intended.

Welcome

My name is Miike Barriault. I am a math student at Memorial University of Newfoundland. Starting April 30, 2007, I began working for one of my profs under a research grant. It is my intention to, every day, post on this blog whatever interesting thing happened to me that day or, if nothing is worth saying, just rant about something that's bugging me (or that I enjoy) about my job.