Martin’s Blog

Courses I could do next semester:

MATH536B – Algebraic Geometry
MATH518 – Integral Lattices, Linear Codes, and Finite Groups
MATH636 – Information Theory (this course is actually an electrical engineering course and assumes some probability theory but I could probably cope).
MATH599 – Independent Study

Each course is 3 units so I need to take three of them (for other possible wacky choices see the schedule of classes or the topics courses offered). I probably should take the algebraic geometry course because I eventually need to complete two full year sequences outside the compulsory first year.

My latest theory on what I could do instead of number theory is some kind of coding theory/information theory/data compression/other discrete computational stuff. This seems like it would at least give me some useful skills in computer programming and possibly some job opportunities outside academia. The electrical engineering department at the UofA has a research group in this kind of stuff.

The other person at the UofA who does something like this is Marek Rychlik in the math department. He’s spent the last three years working as chief scientist at a company that did data compression. I talked to him today about various things I could do in an independent study course and he had a lot of different ideas. First I could learn some stuff out of Mackay’s “Information Theory, Inference and Learning Algorithms”. Then I could do research on one of (among other things):
- entropy of genetic code: if you know some biological fact about the structure of the genome how much does it drop the entropy of the code?
- RAID6 and similar things
- Learning/grouping data using fuzzy K-means
- optical character recognition
- stochastic grammars

The other thing he was quite excited about was FPGAs (Field programmable gate arrays). These are special purpose computer chips that you program with a language like VHDL. The theory is that we use this to do some computations using fancy math stuff (elliptic curves and the like) and the fact that nobody in math departments knows about FPGAs (and nobody that works in engineering know this kind of math) means that it’s new research.

Other things he mentioned:
- Quantum computing
- Groebner bases.

Since I’ve been teaching college algebra/precalculus I’ve forgotten some calculus but I know lots of random tricks for doing without it. A question that came up in the tutoring room today:

Maximise without using calculus or any technology.