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Results tagged with big-list
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user 4281
Questions designed to generate a "big list" of certain results, examples, conjectures, etc. via many individual answers, each contributing one or a few instances. Such a question should typically be in Community Wiki mode (CW); after asking, please, flag for moderators attention requesting the question to be made CW.
6
votes
Ingenuity in mathematics
Mathematicians are used to seeing these sorts of problems and are generally more intrigued by their solutions, but I came across this recently:
Colour every point in the plane either black or white.
…
2
votes
Proving theorems by using functions with fixed points.
I am familiar with a good example from the theory of 2nd order elliptic PDE. Technicalities omitted...
A special case of the Leray-Schauder Theorem says the following:
Let $T$ be a compact mapping o …
138
votes
Most harmful heuristic?
Along the same lines as Qiaochu's and Zach's responses, the commonly taught heuristics pertaining to functions, differentiability and integration are a pet hate of mine.
I certainly left school think …
8
votes
What is the definition of "canonical"?
I would say that "canonical" ought to be used to describe when no choices have been made.
A nice example of a non-canonical identification: A principal bundle is made up of principal homogeneous spac …
6
votes
Which book would you like to see "texified"?
Leon Simon - Lectures on Geometric Measure Theory
0
votes
Applications of connectedness
You can get the maximum principle for subharmonic functions: Write $F$ for the supremum of $f$ in $\Omega$, write $A$ for the set where $f = F$ and $B$ for the set where $f < F$. Then
$\Omega = A \cu …
34
votes
Accepted
Introductory text on Riemannian geometry
Personally, for the basics, I can't recommend John M. Lee's "Riemannian Manifolds: An Introduction to Curvature" highly enough. If you already know a lot though, then it might be too basic, because it …
11
votes
5
answers
4k
views
Brownian motion, martingales, Markov Chains - Rosetta Stone
What are the most
fundamental/useful/interesting ways in
which the concepts of Brownian motion,
martingales and markov chains are
related?
I'm a graduate student doing a crash course in p …
55
votes
17
answers
16k
views
Computer science for mathematicians
This is a big-list community question, so I'm sorry in advance if it is deemed too soft but I haven't seen anything similar yet.
I've seen computer scientists post questions looking to learn things …