Blog author here (all of my friends tell me immediately when I get on HN). I appreciate the criticism.
I'm aware of the huge gaps, and I've had low-priority goals to fill them in. The reason is because my blog is not intended to be a replacement for a standard education, but rather a place for me to explore and write about the stuff that I personally find cool. Usually this means I find an interesting application first, and figure out what background information I should present (admittedly tersely) to support it.
Algorithmic techniques are fine and dandy (I do talk about dynamic programming a few times when it invariably comes up in my applications posts), but more often than not I'm simply bored by the standard algorithms lessons and I believe there's a bigger lack of mathematics background in my audience than algorithmic background. Everyone likely knows (at least vaguely) what a hash table is and what it's for, but asking about a group is more likely to receive blank stares, despite the awesome applications to cryptography.
Though I may be wrong about my audience. I have no way of measuring that except to see what sorts of news sites it shows up on; so far no professional mathematicians have seemed to care except to say the equivalent of "that's a cute hobby."
That being said, I do intend to focus more on graph theory in the future. My own research is taking me more into random graphs, randomized algorithm analysis, and related topics. I also want to start a data structure series, where I go through all of the standard examples: red black trees, prefix trees, fibonacci heaps, etc. I would absolutely love to see more applications of these ideas, and I already have quite a few in mind for graph algorithms.
Judging by the article on Bezier curves, I'd say you're doing fine. Very interesting stuff, and a great approach. It even made some linear algebra stuff click for me -- that I should've internalized long ago from my linear algebra class...
I'm aware of the huge gaps, and I've had low-priority goals to fill them in. The reason is because my blog is not intended to be a replacement for a standard education, but rather a place for me to explore and write about the stuff that I personally find cool. Usually this means I find an interesting application first, and figure out what background information I should present (admittedly tersely) to support it.
Algorithmic techniques are fine and dandy (I do talk about dynamic programming a few times when it invariably comes up in my applications posts), but more often than not I'm simply bored by the standard algorithms lessons and I believe there's a bigger lack of mathematics background in my audience than algorithmic background. Everyone likely knows (at least vaguely) what a hash table is and what it's for, but asking about a group is more likely to receive blank stares, despite the awesome applications to cryptography.
Though I may be wrong about my audience. I have no way of measuring that except to see what sorts of news sites it shows up on; so far no professional mathematicians have seemed to care except to say the equivalent of "that's a cute hobby."
That being said, I do intend to focus more on graph theory in the future. My own research is taking me more into random graphs, randomized algorithm analysis, and related topics. I also want to start a data structure series, where I go through all of the standard examples: red black trees, prefix trees, fibonacci heaps, etc. I would absolutely love to see more applications of these ideas, and I already have quite a few in mind for graph algorithms.