Questions tagged [topology]

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5
votes
2answers
152 views

How to intuitively convince the students that a strip with two full twists is homeomorphic to the standard annulus?

Intuitively speaking, one space is homemorphic to another if one can be deformed continuously to another without tearing and gluing. It is more or less easy to convince the students that a square is ...
4
votes
1answer
138 views

Reference request: undergraduate combinatorial topology

I teach at an American research 1 university. I am planning a course on combinatorial topology for undergraduates whose background is: multivariable calculus linear algebra at least one proof course ...
2
votes
0answers
100 views

Which book to use concurrently with each of these mathematics texts?

I'm in search of a good book that I can read --- and recommend to my proteges to read --- along with each one of the following books. Topology by James R. Munkres, 2nd edition Introductory ...
7
votes
3answers
162 views

Topology presentation for middle school

My 12-year-old got interested on topology puzzles and thought it would make a great presentation for his school assignment. I myself am not familiar with topology so am of little help. Basically, he ...
14
votes
2answers
386 views

Colored chalk recommendations

Background: I am a fourth year math graduate student in the US. Perhaps you will think this question silly, but I intend for it to be a serious question. In teaching courses such as calculus and ...
30
votes
5answers
5k views

What is a good method for drawing a Möbius band on the blackboard?

This week I'm going to give a talk on fiber bundles, and I found myself with an unexpected problem. Since I'm not using slides, I'll need to draw a Möbius band on the blackboard. Usually what I do is ...
20
votes
8answers
1k views

Introduction to Topology for 11 year olds

I am planning a 1-hour lesson for a group of 20 11 year olds. I would like to expose them to topology, as an area of research-level mathematics that could be accessible to them. I want to convince ...
6
votes
0answers
153 views

Teaching an alternate definition for a compactness via the induction principle

In this post on Reddit, a user proposes an alternate definition of compactness, as an "induction principle": A topological space $X$ is compact iff given a statement $P$ whose truth or falsity ...
16
votes
6answers
4k views

Explanation for cutting a Möbius strip at one-third its width

Can anyone offer a concise, convincing explanation for why cutting a Möbius strip along a line, not midway but rather one-third of the width of the strip, and eventually joining back to itself, ...
5
votes
1answer
155 views

Solidifying Bubble Surfaces

Dip a wire frame into a bubble mix and you have a bubble forming a minimal surface spanning the wire frame. These bubble surfaces have been used to demonstrate math and physics concepts like ...
3
votes
5answers
291 views

How can I demonstrate triangulations of surfaces with real hands-on objects?

For a math circle activity on Euler Characteristic, I'd like the students to be able to triangulate some surfaces and count the number of vertices, edges, and faces of the result. There are a lot of ...
18
votes
3answers
4k views

Pedagogical challenge: Homeomorphic vs. Homotopy equivalent vs. Homologous?

I believe it is the case that, between spaces, homeomorphism is stronger than homotopy equivalence which is stronger than having isomorphic homology groups. For example, the annulus and the circle ...