ChapterZero

Since I’m being forced to learn how to program a motorola microcontroller, I figured I might as well put that knowledge to practical use. So yet another vaporware project has misted itself into my head: an arbitrary precision integer and floating point arithmetic system. The thought occurred to me that it would be highly useful in this endeavor to have a memory management system— and I realized that I have no idea of how to go about doing this. So I’d also like to do that. And having messed around with Mathematica so much lately, I’m having the CAS jones again. Luckily, development on Axiom seems to have picked back up— there’s even a portal for it: test.axiom-developer.org. Wouldn’t it be exceedingly sweet if Axiom ever caught up to Mathematica? I hate the fact that I like Mathematica so much, when it is proprietary and closed source.

I wrote my first significant Mathematica code yesterday, a program to solve trusses like the ones in my mechanics class– you enter the positions of the joints, the forces applied and where, the places where reactions occur, the connectivity– all in matrices, and the program determines the reactions, the internal forces, and draws the truss. It can handle three-d trusses. Great! Current location is: http://www2.egr.uh.edu/~aagitten/misc/truss_solver.nb

Once again, I’m starting to get involved in the Putnam competition; there is no other way quite as powerful for securing myself a guaranteed admission to a good school than to score high on the Putnam test— hell, even to score is good. So today, I’m making a trip to the library to check out one Putnam type prep book and return a large load of other books, whose reading I will sacrifice in prep for Putnam.

Time to hit the academic training circuit.

The Xenon project seems to have reached a point where I can start getting excited again. I had been mucking around with the images for weeks, trying to register them so the strong lines caused by mismatching between the bone and skin structure in the images would not affect the FFT— we only want to observe changes in the FFT of the brain tissue. Today, I convinced myself that is impossible— the registration of the raw data set seems to be as good as it’s going to get, because moving an image by even as little as one pixel in any direction causes the number and width of the extraneous lines to increase.

Papadakis suggested that I use an image processing program to remove the bones and skin, and smooth out the remaining edges of the brain tissue, to get rid of the extraneous high frequency content. I started to do that reluctantly, because to do so, I would have to convert the DICOM 0-65536 data to 0-255, and lose information in the process— but then I realized something obvious: I can use GIMP to get a selection mask for the brain tissue in one frame, save that mask as a grayscale image, load it back into MATLAB, and use the mask on all the raw DICOM data in Matlab.

By the time I realized that, my time in lab was up, but I’m definitely going to try that on Monday.

I’ve always dreamed of scanning in notes from several of my more interesting math class, so I could have easier access to them, and share them with others. But I thought it would be too much of a bother to do so. However, last night I discovered that one of the school computer labs has an awesome piece of software (Omnipage Pro), which allows you to scan in as many pages as you like in one go– it prompts you to scan another page or stop– and then saves them all to a single pdf, which it can also automatically upload via ftp. Perfect! On a slightly less legal note, you can also use that feature to scan in books. That’s what I was using it for last night: the library recalled one of the book I’m using for a class, so I started scanning in the relevant chapters. What’s cool is now I can print those pages out and stick them in my class folder; no more carrying the bulky disintegrating book around. I will definitely be using this feature more.

I hate Rudin’s book on mathematical analysis that is supposedly used in all– well, most– undergrad courses in real analysis. It is horrible reading: one theorem after another, with no connective tissue. Some– most– reviewers on Amazon.com say that is laudible conciseness. Personally, I think that it is overly terse… and I would say I have had more exposure to the ideas in Rudin than most people in my class, yet the book manages to bore and confuse me at the same time.

Anyhow, here’s one good problem from Rudin: Given the sequence defined as
, , show that converges, and that it is bounded above by 2.