New post at Not About Apples.
Another digression from Galois theory based on something that happened in my geometry class. This time, what happens when two sets of numbers collide.
Permalink: Borderlines
NAA: Borderlines
7 November 2009 by Cap KhouryNAA: Field day
5 November 2009 by Cap KhouryNew post at Not About Apples.
We’ve said a lot about what symmetries are by now. Galois theory is about symmetries, but not symmetries of geometric objects. Galois theory is about symmetries of number systems, specifically of a kind of number system called a field.
Permalink: Number systems
Another Halloween come and gone…
5 November 2009 by Cap KhouryI like Halloween. I like the idea of getting to wear costumes without social sanction (really, shouldn’t that be more than once a year? I’m thinking quarterly), I like the look and feel of fall, and I like the season of family-time holidays it ushers in (Thanksgiving and Christmas). I don’t particularly like candy, true, but that’s why I have children, to dispose of any candy which might accidentally come into my possession.
NAA: bigger and bigger
4 November 2009 by Cap KhouryNew post at Not About Apples.
A digression from Galois theory to address a common misconception.
Permalink: Increasing vs. Unbounded
Where are the Cows?
3 November 2009 by Cap KhouryI have been a great fan of Robert Abbott for some time through his outstanding site http://www.logicmazes.com, but I am a relative latecomer to his 1997 book SuperMazes, which I found here on his site. One of the mazes from the book is included, but more intriguing is the reference to the hardest maze in the book, Where are the Cows?
This puzzle originally appeared in Scientific American 1966, and it has been called the hardest logic maze of all time. And you’ve gotta love a puzzle with a name like “Where are the Cows?”
Well, if you’re anything like me, you can’t resist an implicit challenge like that. So if you’re bored on a Tuesday, follow the links below. Good luck!
If you want to see it as it appeared in print, go here.
If you’d prefer a version you can play online, go here.
And if you solve it (or have solved it in the past), post boastful comments!
NAA: G is for Group
3 November 2009 by Cap KhouryNew post at Not About Apples.
Building on the symmetry post, we introduce the formal definition of group, my nominee for the most important math concept you’ve never heard of.
Permalink: G is for Group
NAA: S is for Symmetry
29 October 2009 by Cap KhouryNew post at Not About Apples.
It’s been a long time already since A was for Abstraction. Today another contribution to the mathematician’s alphabet, S is for Symmetry. I claim that, just as the mathematical language of numbers fulfills a human need for the abstraction-act of counting and quantifying, the appreciation of symmetry, both geometric and not, is a thing we all do instinctively but which longs for the right language.
Permalink: S is for Symmetry
NAA: More Math with Aliens
22 October 2009 by Cap KhouryNew post at Not About Apples.
Last time, the aliens’ notion of number was a lot like ours. In particular we could find a shared metaphor of a “real number line”. What if we couldn’t? What if the aliens have much “different-er” ways of thinking about numbers? Turns out what happens is we find the starting point for a very deep and beautiful theory.
NAA: Math with Aliens
20 October 2009 by Cap KhouryNew post at Not About Apples.
Suppose you were responsible for establishing communications with an intelligent but very different alien race. Starting from scratch, how might you establish common vocabulary for basic math concepts?
Permalink: Thought Experiment: Talking to the Alien
Matroids
20 October 2009 by Cap KhouryOne thing that consistently brings me joy is when a funny story or thought from long ago dislodges from the rest of the gumballs in the gumball machine of my mind and rolls to the front of my mind
After my shower this morning, I found myself recalling an incident from grad school.
I was taking a course in combinatorics, and one day the professor decided that we should learn about matroids, a somewhat exotic combinatorial structure which combines and generalizes some aspects of vector spaces and graphs. (Don’t worry if you’ve never heard of them, neither had I–and anyway the only thing that matters is the word anyway.)
The most common pronunciation among Americans is MAY-troid, but the professor this day had a subtle accent, which distorted some vowels a bit, so it was pretty hard for people of my generation who’ve spent any time playing video games not to be thinking of a different word.
So there was sporadic stifled chuckling and exchanged glances as the lecture went on. The basic gist of the lecture was that even though relatively few people know what a matroid is, they actually show up in problems more than you’d expect, and now we would know to be looking for them, and have some basic techniques for analyzing them.
So when the professor said to be alert, since you never know when there might be a matroid lurking under the surface of a problem and asked if, now, we would know what to do with a matroid when we saw it, several of us answered as one.
Freeze it! And shoot it with missiles!
