Linked Questions
10 questions linked to/from Suggestions for good notation
182
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33
answers
32k
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What should be learned in a first serious schemes course?
I've just finished teaching a year-long "foundations of algebraic
geometry" class. It
was my third time teaching it, and my notes are gradually converging.
I've enjoyed it for a number of reasons (...
103
votes
13
answers
37k
views
How misleading is it to regard $\frac{dy}{dx}$ as a fraction?
I am teaching Calc I, for the first time, and I haven't seriously revisited the subject in quite some time. An interesting pedagogy question came up: How misleading is it to regard $\frac{dy}{dx}$ as ...
26
votes
12
answers
2k
views
Examples of improved notation that impacted research?
The intention of this question is to find practical examples of improved mathematical notation that enabled actual progress in someone's research work.
I am aware that there is a related post ...
24
votes
5
answers
31k
views
What is the standard notation for group action
Please let me know what is the standard notation for group action.
I saw the following three notations for group action.
(All the images obtained as G\acts X for ...
16
votes
5
answers
5k
views
When did the abuse of notation $y=y(x)$ start?
It's quite common nowadays to name a function and the application of the function to its input with the same letter. (Possibly more so in applied areas. Certainly many calculus textbooks do this.)
...
20
votes
3
answers
1k
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central extensions of Diff(S^1) and of the semigroup of annuli
$\mathit{Diff}(S^1)$ refers to the group of orientation preserving diffeomorphisms of the circle. The semigroup of annuli $\mathcal A$ is its "complexification": the elements of $\mathcal A$ are ...
9
votes
2
answers
1k
views
Notation for the set of all injections from $A$ into $B$
Is there a common notation for the set of all injections from $A$ into $B$?
Some set-theorists use $B^{(A)}$, e.g., A. Levy in his book Basic Set Theory.
But some combinatorists use $B^{\underline{A}...
41
votes
0
answers
1k
views
Homotopy type of TOP(4)/PL(4)
It is known (e.g. the Kirby-Siebenmann book) that $\mathrm{TOP}(n)/\mathrm{PL}(n)\simeq K({\mathbb Z}/2,3)$ for $n>4$. I believe it is also known (Freedman-Quinn) that $\mathrm{TOP}(4)/\mathrm{PL}(...
2
votes
1
answer
400
views
References for the categories: DIFF PL LIP TOP
Is there any survey paper focusing on the study of DIFF PL LIP TOP categories?
3
votes
0
answers
238
views
How to denote a partial derivative?
This question is related to Was Jacobi the first to notice the ambiguity in the partial derivatives notation? And did anyone object to his fix? and Suggestions for good notation .
When there are two ...