Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with mathematics-education
Search options answers only
not deleted
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/
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 …
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 …
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".
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 …
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 …
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
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