Tagged Questions
2
votes
3answers
92 views
Should I put interpunction after formulas?
I am presently doing my first substantial piece of mathematical writing, hence this, probably somewhat silly, question.
How does display-style mathematics interact with punctuation?
More ...
1
vote
0answers
32 views
Is there a common notation for the labelled degree of a vertex?
Let $G$ be an undirected graph with labelled edges. The labelled degree of a vertex $v \in V(G)$ is the number of edges incident to $v$ with distinct labels.
The definition of the labelled degree ...
6
votes
1answer
241 views
What are $\Sigma _n^i$, $\Pi _n^i$ and $\Delta _n^i$?
Sometimes reading on wikipedia or in this site (and in very different context like topology, arithmetic and logic) I have found these symbols $\Sigma _n^i$, $\Pi _n^i$ and $\Delta _n^i$. They are ...
6
votes
1answer
216 views
Is there a rigorous theory of context, whereby sets can gain additional structure within a context?
Consider sets $G$ and $H$ and a function $f : G \rightarrow H$. So far, it doesn't really make sense to ask whether $G$ and $H$ are groups (technically, the answer is "no, they're not groups"), and ...
2
votes
1answer
75 views
Diagrammatic (Postfix) Composition of Functions
Consider the functions $f : X \to Y$ and $g : Y \to Z$. According to the Wikipedia articles on Function Composition, the application of $f$ to an input $x$ can be written as $xf$ (as opposed to the ...
2
votes
2answers
53 views
Why is $S/R$ a ring extension?
If $S$ is a ring and $R \subset S$ is a subring it's common to write that $S/R$ is an extension of rings. I frequently find myself writing this and read it quite often in textbooks and lecture notes. ...
1
vote
0answers
26 views
Enumeration of symbols in grammatical expressions or vertices in tree graphs
I have expressions (type of a function) like e.g.
$$f:(A\to B)\to C \to (D\to E)\to F.$$
(Where I understand $A\to B\to C$ as $A\to (B\to C)$, in case that is relevant.)
There might be information ...
3
votes
2answers
130 views
Generalization of a product measure
Let $(X,\mathfrak B(X))$ and $(Y,\mathfrak B(Y))$ be measurable spaces and further let $\mu$ be a measure on $\mathfrak B(X)$ and let $K$ be a kernel, i.e. for any $x\in X$ we have $K_x$ is a measure ...
4
votes
1answer
139 views
Inverse function notation
Suppose $f$ and $g$ are functions that fail to be one-to-one, but $f+g$ is one-to-one. Has anyone ever seen the notation $(f+g)^{-1}$ for the inverse function in that situation? (I find myself ...
1
vote
1answer
119 views
Logic about systems?
In Godel's Incompleteness Theorem, his theorem is about a system of logic. Where can I find more about this study, especially the notation?
EDIT
I mean logic about systems in general. I worded the ...
3
votes
2answers
100 views
Original papers on the subject of group actions
Does anyone if there are any original paper(s) that first introduced the notion of group action or permutation representation, and who the author(s) were? Any references I have found so far on e.g. ...
3
votes
2answers
84 views
Relation-preserving maps as morphisms of a category
What is the canonical name for the category whose objects are all pairs $(X, \rho)$, where $X$ is a set and $\rho$ is a binary relation on $X$, and whose objects are relation-preserving maps? That is, ...
0
votes
2answers
76 views
Weak Partial Complete Lattice and Homomorphisms
What is the proper nomenclature for a generalization of a lattice $L$ such that not all subsets of $L$ may have a join/meet, sometimes not even for finite subsets? This paper calls it a "weak partial ...
3
votes
2answers
87 views
Textbook determinant convention
My text book is called "Linear Algebra and its applications" by David C. Lay.
I am just wondering why the textbook uses the absolute value symbol when it wants us to compute determinants. For ...
4
votes
2answers
175 views
Resources to learn the meaning of any math symbol
There is lots of symbols and may be operators like || in this expression
$$ 3^k||n$$
that I would like to be able to quickly find the meaning of. I tried Wolfram|Alpha but I think it expects the ...
7
votes
1answer
174 views
Why do they print the number of Illustrations on some mathematics books? [closed]
Why do they print the number of Illustrations on some mathematics books? For example:
In my whole life, I've seen this only on maths books and I can't figure out why they do this or why it's ...
3
votes
2answers
103 views
What letter should I use to denote an ideal?
In commutative algebra, there seem to be two rather different notational conventions for ideals: either $I,J, \dots$ or $\mathfrak{a}, \mathfrak{b}, \dots$.
By itself, it is hardly surprising - after ...
5
votes
1answer
140 views
History of Lie algebra notation (in Fraktur)?
Does anyone know how it has become the standard to express Lie algebras in fraktur? I'd also like to know how it's established for each era and region, not only the origin.
It doesn't seem that ...
3
votes
2answers
249 views
Notation to work with vector-valued differential forms
What it the standard notation used while working with vector-valued differential forms?
I tried using abstract index notation, for example denoting a $1$-form valued $2$-form as $P_{i[bc]}$, but I'm ...
1
vote
5answers
349 views
Mathematical notation for computer science
Can anyone point me in the direction of good introductory material on the use of mathematical notation in the field of computer science? I often come across notation in research papers that I don't ...
6
votes
0answers
122 views
Articles on ideas in the history of mathematics notation?
I'm teaching a course this term on the history of scripts (writing systems) and rather than talking interminably about Semitic and Chinese and their spawn, I'd like to give students a more varied ...
4
votes
4answers
138 views
Why Does Finitely Generated Mean A Different Thing For Algebras?
I've always wondered why finitely generated modules are of form
$$M=Ra_1+\dots+Ra_n$$
while finitely generated algebras have form
$$R=k[a_1,\dots, a_n]$$
and finite algebras have form
...
1
vote
1answer
128 views
Index notation clarification
Previously, I have seen matrix notation of the form $T_{ij}$ and all the indices have been in the form of subscripts, such that $T_{ij}x_j$ implies contraction over $j$. However, recently I saw ...
1
vote
1answer
106 views
Is the notation for the definition of a set stricly formalized?
In the 800 pages set theory book by Jech, he uncommented starts using
$$Y=\{ u\in X : \phi(u)\}$$
as equivalent to
$$Y=\{ u:u\in X \wedge\phi(u)\}$$
on the first few pages. The fact that, in the ...
4
votes
3answers
503 views
A digital notebook for Mathematics?
When I studied math 15 years ago, I was dreaming of having a math repository with tags to navigate between the different entries.
I imagined it would come eventually to the market, and was hopefull ...
3
votes
1answer
85 views
Co-ordinate axes: What does the $e$ in ${\hat e}_x$ stand for?
In vector analysis for $\mathbb{R^3}$ we write standard basis vectors in various forms like $\{\hat{x}, \hat{y}, \hat{z} \}$, $\{ \hat{\imath}, \hat{\jmath}, \hat{k}\}$, $\{ {\hat e}_x, {\hat e}_y, ...
1
vote
2answers
86 views
Standardized Notation for Well-Known Categories
It seems that every author has rather personal and unique conventions for designating "well-known" categories. This raises the question: Is there a reference available, on-line or otherwise, that ...
0
votes
1answer
165 views
Variable naming convention in mathematical modeling
Is there a guide or source of inspiration I can use when picking variable and constant names for a mathematical formula? I'm in the process of converting a poorly written technical document into ...
1
vote
1answer
51 views
How should I understand $\frac{\partial^2 v_i}{\partial x_j\partial x_j}(x)=\frac{\partial p}{\partial x_i}(x)$?
The formula is from the first paragraph in the paper "Second Kind Integral Equation Formulation of Stokes' Flows Past a Particle of Arbitrary Shape" by Power and Miranda:
... the governing ...
2
votes
1answer
174 views
Is $O(10^{-6})$ an acceptable notation in numerical analysis?
In mathematics, the big $O$ notation is used to describe the limiting behavior of a function. It is abuse of notation to say
$$
f(x)=O(g(x)).
$$
But this is understandable. However, in the class of ...
1
vote
0answers
107 views
Style guide for the use of '$( \ )$' versus '$[ \ ]$' in mathematics?
I'm wondering if there is any definitive style guide for writing mathematics. In particular, I'm looking for rules for when to use '$( \ )$' versus '$[ \ ]$.' For instance, when referring to a ...
2
votes
1answer
67 views
Functors preserving (commuting with) exponentials
I have been unable to find any established names for functors preserving exponential objects in general ($F$ such that $F(A^B) \cong FA^{FB}$) and/or those "commuting" with functors $-^A$ (some ...
1
vote
1answer
116 views
What are the $\ker$, $\mathrm{kei}$ functions?
In a book titled 'Ordinary Differential Equations and Useful Polynomials', under the chapter 'Bessel's function', the author has introduced four new functions $\mathrm{ber}$, $\mathrm{bei}$, $\ker$, ...
4
votes
1answer
99 views
For a ring of char $p$ where $p>0$ is a prime, what does $R^{1/p}$ mean?
If $R$ is a ring of characteristic $p\gt 0$, what does $R^{1/p}$ mean?
I am not sure how to search for it, since I don't know a name for it. From the notation, it seems to be a ring consisting of the ...
6
votes
3answers
2k views
What are usual notations for surjective, injective and bijective functions?
Update: In the category of sets, an epimorphism is a surjective map and a monomorphism is an injective map. As is mentioned in the morphisms question, the usual notation is $\rightarrowtail$ or ...
1
vote
1answer
46 views
Notation for “duplicating” partitions
I'm using Macdonald's "Symmetric Functions and Hall Polynomials" as a reference and did not find what I was looking for -- apologies if I only missed it.
As an example, let us consider the partition ...
5
votes
8answers
699 views
Why are derivatives specified as d/dx?
Is the purpose of the derivative notation d/dx strictly for symbolic manipulation purposes?
I remember being confused when I first saw the notation for derivatives - it looks vaguely like there's ...
