All Questions
Tagged with teaching at.algebraic-topology
8 questions
14
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1
answer
3k
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An elementary proof that the degree of a map of spheres determines its homotopy type
I'm helping to teach an undergraduate algebraic topology course (out of Hatcher's textbook). We have recently defined the degree of a map of spheres using homology, and the professor and I thought it ...
86
votes
16
answers
9k
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Teaching homology via everyday examples
What stories, puzzles, games, paradoxes, toys, etc from everyday life are better understood after learning homology theory?
To be more precise, I am teaching a short course on homology, from ...
40
votes
16
answers
11k
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"Homotopy-first" courses in algebraic topology
A first course in algebraic topology, at least the ones I'm familiar with, generally gets students to a point where they can calculate homology right away. Building the theory behind it is generally ...
15
votes
1
answer
757
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Teaching cohomology via everyday examples
This question is a "sequel" to my similar questions about the fundamental group and homology. All of these questions were inspired by seeing a talk, by Tadashi Tokieda, about the interesting physics ...
16
votes
2
answers
1k
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Teaching Steenrod Operations
I am teaching a class on topology and want to introduce Steenrod Operations. I have talked about simplicial sets and classifying spaces of groups but have not talked about Eilenberg–MacLane spaces. ...
27
votes
2
answers
3k
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Teaching the fundamental group via everyday examples
This question is a "prequel" to a similar question about homology. Both questions were inspired by seeing a talk, by Tadashi Tokieda, about the interesting physics that appears in toys.
What ...
7
votes
3
answers
3k
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The etale fundamental group of a field
Background and motivation:
I am teaching the "covering space" section in an introductory algebraic topology course. I thought that, in the last five minutes of my last lecture, I might briefly sketch ...
4
votes
2
answers
869
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Terminology question on covering spaces
I'm teaching an elementary class about fundamental groups and covering spaces. It was very useful to use "fool's covering spaces" of a space $X$, defined as
functors $\Pi_1(X)\to Sets$, where $\Pi_1(X)...