Michi’s blog » archive for January, 2006

Introduction to Algebraic Topology and related topics (I)

  • January 1st, 2006

In the spirit of writing some sort of introductory posts to the things related to what I’m about to spend several years thinking and writing about, I thought I’d try to make a (more or less) layman friendly introduction to Homology and Homotopy.

It’s all residing in the realm of Topology. Topology is the field of mathematics, where those aspects of a shape not dependent on distances are studied. Thus rigidity is not interesting, whereas connectivity is. Narrow/thick is not interesting, but what kind of holes the surface has is. The ultimate thing to be said in topology about two objects is that they are homeomorphic, which technically means that there is an isomorphism between the objects in the category of topological spaces; and more comprehensibly means that there are continuous functions between the shapes such that they are each others inverses.

This is a preview of Introduction to Algebraic Topology and related topics (I). Read the full post (1020 words, 1 image)

Some math-y jokes

  • January 1st, 2006

You may have seen some of these before…

\frac{1\cancel{6}}{\cancel{6}4}=\frac{1}{4}

\frac{1\cancel{9}}{\cancel{9}5}=\frac{1}{5}

\frac{\partial}{\partial x}\sin^2(x)=\sin(2x) — just move down the 2.

(15 words, 3 images)

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Michi is a PhD student working in homological algebra. This blog is his outlet for texts with some manner of thought put into them. Over at his LiveJournal intimate details and streams of consciousness might be found.
Not all here is mathematics. All here, though, are my personal thoughts and opinions. Please read the about page (linked above) for more details.
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