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

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2
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2answers
73 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
111 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
32 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
20 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
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1answer
38 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
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1answer
29 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
59 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 $A \equiv x+2y$.
14
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0answers
519 views

Papers with unorthodox writing style

I'm not sure if this is the right forum for this question, in any case probably CW is appropriate? I've been looking around the mathblogosphere for the past few weeks and ran into mathgen. It's ...
7
votes
0answers
118 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
341 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
85 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 ...
3
votes
0answers
51 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
34 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, ...
2
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0answers
16 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
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
36 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
112 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
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0answers
86 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
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0answers
87 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
50 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

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
32 views

Translation of a book

I am an undergrad studend, my professor told me that a good work I can do is to translate a book on universal algebra (subject which I like a lot) in my language. I'm asking if this kind of work is ...
0
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0answers
21 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
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0answers
6 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
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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
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0answers
26 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
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0answers
43 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
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0answers
47 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
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0answers
35 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
33 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
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0answers
54 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 ...