Various aspects of writing mathematics such as style, notation, grammar, frequently used phrases and common mistakes.

learn more… | top users | synonyms

2
votes
2answers
85 views

Should I rephase when quoting a theorem/definition?

Actually I would like to ask two questions and the answers may not be the same. When writing a paper and if one need to introduce a definition, is it alright to just copy-paste from wikipedia/a ...
9
votes
1answer
135 views

Is there a standard name for this “continuous induction” principle?

I am working on a paper, and I want to prove that some statement $P(x)$ holds for every value of a parameter $x \in [0,\infty)$. I plan to proceed as follows: Show that $P(0)$; Show that if $P(x)$ ...
1
vote
1answer
36 views

When is it appropriate to use \rightarrow or \leftrightarrow

When writing papers on maths, when is it appropriate to use \rightarrow or \leftrightarrow, and when should one refrain from using them. For example, would this be appropriate use of ...
1
vote
1answer
22 views

Best practice for naming variables to distinguish chosen upper bound from computed maximum.

Say I have a vector of a matrix's singular values $[s_1, s_2, \cdots, s_N]$, and would like to define two variables, one which holds the maximum value in the vector, and another which holds an ...
0
votes
1answer
41 views

Comma placement inline math

In the following sentence If all $f(x_j), j=1,\dots,N$ are positive, then ... Do you think there should be a comma after the $N$? I always considered the math as a single unit and read the ...
0
votes
1answer
34 views

Placement of quantifiers in a symbolic statement

I have the statement: Let $A_n$ be an indexed set of numbers defined by $A_n = n\mathbb{Z}_{\geq m}$ for $n,m \in \mathbb{Z}$. Consider the claim C: For all $n$, if $x,y$ is in $A_n$, then ...
-1
votes
1answer
62 views

A basic question of basic writing

When we define some term by a notation starting with the word "define" or "let", which of the following is correct? Define $A=x+2y$; or, define $A \equiv x+2y$.
7
votes
0answers
122 views

Use of “I” in mathematics papers

Some people consider the use of "I" in a paper to be a great evil. Others, however, consider the use of the passive voice to be an even greater evil. I will be presenting a paper at a competition, ...
6
votes
0answers
511 views

In a math paper, what is a remark?

I sometimes see paragraphs labeled 'Remark.' However, papers that include remarks also include unlabeled explanatory paragraphs (i.e. all the other writing in the article) that seem to be remarks. ...
3
votes
0answers
54 views

Formulating equation for distances between atoms

I'm trying to formulate notation to describe code that calculates the distances between protein atoms (represented as points in 3D space). Fragments consist of residues (amino acids) and each residue ...
2
votes
0answers
18 views

Additive and Multiplicative Effects: Terminology

I am trying to explain the relationship between several variables. The outcome of interest is $Y \in \mathbb{R}$, and the predictors of interest are $A \in \mathbb{R}$ and $B \in \mathbb{R}_{>0}$. ...
2
votes
0answers
91 views

When should we use `\frak{…}` in LaTeX

I saw in a note that when writing a paper some notations must be written by \frak{ }, in LaTeX, I want to know what the meaning of some notations is, and where I ...
2
votes
0answers
17 views

Changing Notation in Direct Quote

Tried asking this on Academia.SE but the mathjax doesn't render. Direct quote: "...the estimator for the expected logarithmic return, $\hat{\mu} \equiv [\sum_1^n X_k]/h$, will have the properties ...
2
votes
0answers
37 views

Is there a published standard for the sectioning of math papers?

Most papers seem to use sections (e.g. 3) and sub-sections (e.g. 3.1). Is there a published standard that says what sort of thing warrants its own section and what sort of thing warrants its own ...
2
votes
0answers
113 views

a.s. for all $t$ or for all $t$ a.s.?

Assume that we have some equality, $$ X (t) = Y(t). \quad \quad \quad \quad \quad \quad \quad (1) $$ I imagine that if I say "(1) holds a.s. for all $t>0$" it means that $$ P\{X (t) = Y(t) ...
2
votes
0answers
48 views

What is the notation for a sub-expression?

For set theory, we have notation to denote subsets, e.g.: $$S \subset X$$ When working with expressions (arithmetic, Boolean, etc.), is there a notation to denote expression $S$ is a valid ...
2
votes
0answers
88 views

Learning to write the style of mathematics texts

When learning how to write articles in mathematics (in style of articles published in journals) is there a good reference listing things like common outlines, style guides, phrases, common mistakes ...
2
votes
0answers
93 views

Referencing something that isn't a lemma, proposition etc…

I need to reference a fact that is in another paper. It is stated after a lemma, and follows from this, thought perhaps not very directly. I could just reference it as "see [1, Pg. 5]" or "see [1, ...
2
votes
0answers
51 views

How would you write this sentence

I'm writing a short document about an integer programming (IP) problem instance. I've mentioned that IP is known to be NP-Hard, but that being NP-Hard doesn't automatically qualify this particular ...
1
vote
0answers
41 views

The following question is about the expression “The following.”

In a mathematical document, it is common to have some English prose leading into a mathematical display and continuing after it. The display is some computation or equation, written symbolically, ...
1
vote
0answers
43 views

How to formally express a negative statement (in the wording or formulation of a theorem, for instance)

This is a doubt about English mathematical formal language. I would like to know the best way to express a negative hypothesis, in the formulation or statement of a theorem, proposition, etc., using ...
0
votes
0answers
14 views

Acceptable notation? $\lesssim_{n} n^{-\beta}$ for constants NOT depending on $n$

I am preparing a paper and found it convenient to write things like $$ |\text{Expression of a lot of variables}|\lesssim_{n} n^{-\beta} $$ when an inequality is true up to a multiplicative factor that ...
0
votes
0answers
23 views

representing a periodic circular shift for a vector formally

I'm writing an algorithm in which the operation of circular shift to a given vector $x=[1 \ 0 \ 0\ ... 0]$ is needed on periodic basis i.e. every $\Delta t$ a circular shift will occur. How this ...
0
votes
0answers
8 views

Simple visualisation tool for small graphs

I am looking for a way to add illustrations to a paper I am currently writing. I want to display very basic graphs (not more than 8 vertices, a few edges). The focus is on the edge crossings - I need ...
0
votes
0answers
24 views

Ordinal numbers

I have a sequence of coefficients. I can obviously write "i-th" or "h-th coefficient", but I'm referring to the coefficient with number n-h. Can I write "(n-h)-th coefficient"?
0
votes
0answers
19 views

line breaking for group actions in latex

When the group $G$ acts on a manifold $M$, we typically use expressions as $M$ is a $G$-manifold, or $G$-action on $M$. If we write those sentences in latex, is it recommended to put $G$ ...
0
votes
0answers
28 views

Symbol for exactness in diagram

When making commutative diagrams there are many symbols one can use and even omit in favours of others. For example in the following short exact sequence $$0\to A\to B\to C \to 0$$ we can rewrite it ...
0
votes
0answers
25 views

How to abbreviate “Check that assumption is not violated for the solution that we got through the assumption”

Note that this is not a math question, but a language one. Nonetheless it requires some understanding of math and I thus hope it is appropriate to be asked here. Also be warned of non rigorous ...
0
votes
0answers
22 views

In mathematical writing, what does the phase “Class of nonlinear system” mean?

In many engineering and applied mathematics resources, author specify his work or theory for "a class of Y , Y={Nonlinear systems, Hybrid systems, discontinuous systems .. etc}" what does this mean? ...
0
votes
0answers
8 views

Tree decomposition (Citation needed)

Recently, I read the statement "Fix $k\geq 1$, Any tree with at least $k$ edges may be decomposed as a union of edge-disjoint subtrees, each having between $k$ and $3k$ edges" Now I was wondering ...
0
votes
0answers
15 views

writing rolling formulas -e.g. average-

Question about writing a formula. Can someone verify if they are correct? Assume Rt = one-period simple return on asset in month t. The average return, Mu, is calculated over the sample from t = 1, ...
0
votes
0answers
28 views

$\mapsto$ functional notation and probability distributions

I have a question concerning mathematical writing. If we have a function $f: X \to Y$, we can write it \begin{align} f: \ & X \to Y \\ & x \mapsto f(x), \end{align} where $f(x)$ can ...
0
votes
0answers
19 views

Proper way of adding a glossary to an article

I am thinking of adding a glossary to an article of mine, I was wondering if there is an etiquette regarding adding a glossary of symbols and notations? To be frank I have not seen one in any recent ...
0
votes
0answers
44 views

Formulation: Smooth vs. finitely often differentiable

I treat the cases $f\in C^\infty$ and $f\in C^k$ in different sections of my thesis. While I am happy with the title smooth functions for the first section, I am not so sure if finitely often ...
0
votes
0answers
60 views

Article writing: How to represent a matrix by its elements?

Intuitively I guess that parantheses with subscript and superscripts is a way of representing a matrix or an array by its elements, e.g., $$ A = (a_{i,j})_{i,j=1}^n $$ (This is taken from here) ...
0
votes
0answers
51 views

Writing finite field notation

I am trying to write about finite fields in a word document, and although usually writing in latex form works, it's not in this case. It works fine here: $\mathbb{F}$: I used \mathbb{F} But it ...
0
votes
0answers
36 views

What are best practices when writing (sub)equations?

I wonder when it's preferred or better to use subequations instead of normal equations. I.e. when to use 'normally' numbered equations (e.g. (1), (2), ...) and when to use subequations (e.g. (1a), ...
0
votes
0answers
58 views

Name the maps in a commutative diagram

When writing a formal paper sometimes one needs to construct complicated commutative diagrams, such as My question is, should one always give names to all maps in the diagram (perhaps except those ...