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Results tagged with mathematics-education
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user 4362
For questions in Mathematics Education as a scientific discipline. For more hands-on questions on teaching Mathematics, please use the tag teaching. There is also a Stack Exchange community http://matheducators.stackexchange.com/
54
votes
What is your favorite isomorphism?
Here is an example that Mel Hochster used to explain the notion of isomorphism to a group of talented high school students. I was one of the course assistants rather than one of the students, but I'm …
36
votes
Accepted
Analysis from a categorical perspective
I hesitate to let this out, but there's always this cute little note that I learned from another MO answer (I don't know which one): https://www.maths.ed.ac.uk/~tl/glasgowpssl/banach.pdf. Maybe this …
- 29.2k
23
votes
Is Euclid dead?
Euclidean geometry is still taught in American high schools, but I am strongly against it. I think it should be replaced with linear algebra.
Arguments against Euclidean geometry:
Most of what y …
21
votes
Is there a database for tracking the dependencies of mathematical theorems?
The Stacks Project provides an example of what you're looking for. Every definition, lemma, theorem, etc. is given a tag, and the tags are used as references in proofs. They even provide an API for …
- 29.2k
11
votes
Elementary + short + useful
The isoperimetric inequality.
Ubiquitous in geometry.
Among the easier examples of variational problems.
Can be used to illustrate why we need rigorous proofs of things that are "obvious".
6
votes
Examples of undergraduate mathematics separation from what mathematicians should know
1)
-The Sylow theorems are a great example. I think they are taught so ubiquitously because they provide perhaps the most elementary example of the broad pattern in mathematics of determining the st …
5
votes
Elementary + short + useful
Heisenberg's uncertainty principle.
Everyone should be exposed to quantum mechanics.
Appears frequently in analysis and probability (not to mention physics).
Showcases some of the highlights of Fo …
1
vote
Elementary + short + useful
The Gelfand-Naimark theorem: every commutative C* algebra is $C_0(X)$ for some locally compact Hausdorff space $X$.
The spectral theorem is a corollary.
The theorem introduces students to the idea …
0
votes
Elementary + short + useful
Maybe a stretch, but...
Finiteness of the class number via Minkowski's theorem.
Everyone should at least have a rough idea what the class number is.
Minkowski's theorem has other amusing and useful …