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Finding the fun in good math; Shredding bad math and squashing the crackpots who espouse it.
Mark Chu-Carroll (aka MarkCC) is a PhD Computer Scientist, who works for Google as a Software Engineer. My professional interests center on programming languages and tools, and how to improve the languages and tools that are used for building complex software systems.
Category: Chaos
One mathematical topic that I find fascinating, but which I've never had a chance to study formally is chaos. I've been sort of non-motivated about blog-writing lately due to so many demands on my time, which has left me...
Posted by Mark C. Chu-Carroll at 6:37 PM • 78 Comments •
Category: topology
One of my fellow ScienceBloggers, Andrew Bleiman from Zooilogix, sent me an amusing link. If you've done things like study topology, then you'll know about non-euclidean spaces. Non-euclidean spaces are often very strange, and with the exception of a...
Posted by Mark C. Chu-Carroll at 11:56 AM • 13 Comments •
Category: topology
As I alluded to yesterday, there's an analogue of L-systems for things more complicated than curves. In fact, there are a variety of them. I'm going to show you one simple example, called a geometric L-system, which is useful...
Posted by Mark C. Chu-Carroll at 10:15 PM • 7 Comments •
Category: topology
Via The Art of Problem-Solving, a great video on Mobius transformations. I never really got how the inversion transformation fit in with the others before seeing this!...
Posted by Mark C. Chu-Carroll at 8:43 PM • 15 Comments •
Category: topology
I've been getting tons of mail from people in response to the announcement of the mapping of the E8 Lie group, asking what a Lie group is, what E8 is, and why the mapping of E8 is such a...
Posted by Mark C. Chu-Carroll at 3:03 PM • 38 Comments •
Category: topology
One thing that comes up a lot in homology is the idea of simplices and simplicial complexes. They're interesting in their own right, and they're one more thing that we can talk about that will help make understanding the...
Posted by Mark C. Chu-Carroll at 11:03 AM • 7 Comments •
Category: topology
I've been working on a couple of articles talking about homology, which is an interesting (but difficult) topic in algebraic topology. While I was writing, I used a metaphor with a technique that's used in homotopy, and realized that...
Posted by Mark C. Chu-Carroll at 9:32 PM • 13 Comments •
Category: topology
One of the more advanced topics in topology that I'd like to get to is homology. Homology is a major topic that goes beyond just algebraic topology, and it's really very interesting. But to understand it, it's useful to...
Posted by Mark C. Chu-Carroll at 8:30 AM • 10 Comments •
Category: topology
It's been a while since I've written a topology post. Rest assured - there's plenty more topology to come. For instance, today, I'm going to talk about something called a fiber bundle. I like to say that a fiber...
Posted by Mark C. Chu-Carroll at 10:32 AM • 16 Comments •
Category: topology
There's another classic example of sheaves; this one is restricted to manifolds, rather than general topological spaces. But it provides the key to why we can do calculus on a manifold. For any manifold, there is a sheaf of...
Posted by Mark C. Chu-Carroll at 8:23 PM • 3 Comments •
