Abstract Algebra: Theory and Applications (A Free Textbook)(abstract.ups.edu)
abstract.ups.edu
Abstract Algebra: Theory and Applications (A Free Textbook)
http://abstract.ups.edu/
12 comments
Not me of course, but Armstrong began Erlang by writing an algebra for telephony exchanges.
Codd wrote an algebra for relations.
Thompson implemented Kleene's regular expressions (notated with an algebra).
Codd wrote an algebra for relations.
Thompson implemented Kleene's regular expressions (notated with an algebra).
This blog post (and stuff linked in the comments) talks about ways to use properties of semirings to parallelize algorithms for free: http://blog.sigfpe.com/2008/11/approach-to-algorithm-paralle...
Sometimes, I wish I was 20 years younger so that I could have been reading stuff like this all through my childhood.
I wonder how long before we see child prodigies who read all these free textbooks, Khan academy stuff, and online MIT courses coming out in droves?
I wonder how long before we see child prodigies who read all these free textbooks, Khan academy stuff, and online MIT courses coming out in droves?
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.
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.
Another nice Math textbook - really solid presentation.
I also recommend Algebra by Michael Artin--but it isn't free, unfortunately.
It's used in the course "Abstract Algebra" (Harvard). Lecture videos are available: http://www.extension.harvard.edu/openlearning/math222/ Benedict Gross is a great lecturer and I recommend watching them.
I just gave this a cursory glance, and I have to say I'm impressed.
Anyone studying CS could benefit from this book.
Anyone studying CS could benefit from this book.
It's on bitbucket too: http://bitbucket.org/judson/aata
Nobody's commenting on the fact that this book is open source, GFDL.
Nobody's commenting on the fact that this book is open source, GFDL.
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)