Homology Theory — A Primer

Resource | v2 | updated by janarez |
Type Web
Created 2013-04-04
Identifier unavailable


This series on topology has been long and hard, but we’re are quickly approaching the topics where we can actually write programs. For this and the next post on homology, the most important background we will need is a solid foundation in linear algebra, specifically in row-reducing matrices (and the interpretation of row-reduction as a change of basis of a linear operator). Last time we engaged in a whirlwind tour of the fundamental group and homotopy theory. And we mean “whirlwind” as it sounds; it was all over the place in terms of organization. The most important fact that one should take away from that discussion is the idea that we can compute, algebraically, some qualitative features about a topological space related to “n-dimensional holes.”


about Homology

In mathematics, homology is a general way of associating a sequence of algebraic objects, such as abe...

created by Jeremy Kun

My name is Jeremy Kun. I’m currently an engineer at Google. I earned a PhD in mathematics from the Un...

follows The Fundamental Group — A Primer

Our eventual goal is to get comfortable with the notion of the “homology group” of a topological spac...

precedes Computing Homology

In our last post in this series on topology, we defined the homology group. Specifically, we built up...

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10 rating 6 level 9 clarity 4 user's background

Awesome article. Very approachable and great explanation.