Is anyone here applying abstract algebra to technology projects which might interest us HN readers?
I studied it as an undergraduate; when I think about applications I've found in technology work and computer science, the following spring to mind:
* Linear algebra -- obviously very useful, although not everyone would consider it abstract enough to lump under abstract algebra.
* The structural side (category theory, universal algebra etc) very useful for grokking theoretical computer science
* Lattices, order theory, boolean algebras etc -- also very useful for computer science, but perhaps tending a bit away from algebra and towards logic.
I'm not sure I've really wielded in anger any non-trivial theorems from the theory of groups and rings though. Maybe a little bit of basic group theory. But perhaps I've lead a boring life. Interested to hear what people are doing with it in the tech / comp sci field :)
(Crypto, I guess, is one important area. And the 'patch algebra' of the darcs VCS was another interesting application I spotted)
It's an interesting question. I discovered in high-school that an avid interest in science expressed through reading back issues of national geographic, popular science, and other similar magazines can give you a significant leg up (giving me a lot of advantages in biology, chemistry, physics, mathematics, and computer science).
In some ways a lot of what's available online for free is better (wikipedia is generally better than most physical encyclopedias, not least because it's so fast to search), but in some cases there's still a gap. There are plenty of bite-sized nibbles, but there aren't as many cohesive, well put-together larger bites of knowledge such as you'd find with popularized science books and magazine articles.
I tried and quickly stumbled learning abstract algebra from this book. I liked "A Book of Abstract Algebra" by Pinter better because it was lighter on the presentation. But maybe I'm just a wimp. This text by Judson seems to be geared towards graduate studens. From what I can tell it's very thorough, though.
I haven't tried learning from it, but it doesn't seem to be higher level than Fraleigh's classic book on Abstract Algebra, which I use and is intended for undergraduates.
I studied it as an undergraduate; when I think about applications I've found in technology work and computer science, the following spring to mind:
* Linear algebra -- obviously very useful, although not everyone would consider it abstract enough to lump under abstract algebra. * The structural side (category theory, universal algebra etc) very useful for grokking theoretical computer science * Lattices, order theory, boolean algebras etc -- also very useful for computer science, but perhaps tending a bit away from algebra and towards logic.
I'm not sure I've really wielded in anger any non-trivial theorems from the theory of groups and rings though. Maybe a little bit of basic group theory. But perhaps I've lead a boring life. Interested to hear what people are doing with it in the tech / comp sci field :)
(Crypto, I guess, is one important area. And the 'patch algebra' of the darcs VCS was another interesting application I spotted)