# Questions tagged [article-writing]

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

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### Use cases for interval notation

The notation $x \in [a,b]$ and $a \le x \le b$ are equivalent in how they describe the variable $x$. When writing mathematics, when does the use of one take precedence over the other? In the former ...
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### Is it acceptable to cite commonly used definitions from Mathworld.Wolfram.com?

I am writing a document/article for the average layman, with the aim of explaining certain well known results in mathematics while glossing over the more gritty details. I'm going to include several ...
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### Making a “definition” by way of a universal property

This is somewhat a question out writing styles. In a paper, I want to introduce and "define" an object $X$ by just stating the universal properties which is satisfies. Logically, this is not quite ...
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### When referring to a numbered equation, do I capitalise “equation”? [closed]

Suppose, I wrote an following equation: $$f(x)=x^2\tag1$$ NOw I want to refer to it later in my work. Which of the following do I write? Using Equation (1) we can see that $f(x)$ is an even ...
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### Why some kinds of elementary transcendental equations cannot be solved by elementary functions - Conjecture and proof

Are my conjecture and my proof below correct, well formulated and linguistically correct? How can they be improved? It's a new conjecture. It's an extension of Lin's theorem in [Lin 1983] which is ...
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### How should I denote “ignore this column” of a matrix?

I have a question about notation. I have arrived at a matrix, the first two columns of which I'm labeling for future reference. I don't care about and won't be using the third column. It will be clear ...
39 views

### Where can I post my article and get some feedback?

So I was bored (because Quarantine) so I decided to write an article about a random math topic. Where can I "post" my paper for other to see and submit some feedback? Because I thought that I could ...
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### Using abbreviations in mathematical writing

I'm currently writing my bachelor's thesis, and I am using the term "independent and identically distributed" a lot. I was wondering if it is accepted if I abbreviate this to "i.i.d.". Or if I can ...
95 views

### O. Gabber, Non-negativity of Serre’s intersection multiplicities

This article is cited here and there, but I cannot find it anywhere. Gabber, O. (1995), Non-negativity of Serre’s intersection multiplicities, Expos ́e `a L’IHES I checked author's publications, ...
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### Question on describing a formula in text form in an abstract

I am currently writing a paper. In it I proof a formula that has the form $$\prod_{j=1}^k ( |Q|L_j + L_j ) = \left( \prod_{j=1}^k L_j \right) (|Q|+1)^k.$$ In the abstract, I want to avoid ...
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### Correct way to write “to the power” with an indexed parameter

Quick (and simple) question: I'm writing a formula that uses parameters with a subscript, and they are squared. What is the correct way to typeset that? See below. I fear that in (1) the $^2$ might ...
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### Order of constants and variables when typesetting equations

I seem to recall that when writing mathematics, constants appear first (numerals, then symbols in alphabetical order) and then variables follow (alphabetically). A simple example would be: 2 \pi x. In ...
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### How to properly introduce notation in a mathematical article?

The main result I am currently trying to publish is the proof of a classical result in optimization, but with weaker hypotheses. In the introduction of my draft, I intend to explain why this classical ...
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### How to note redefining a function by absorbing some terms in an elegent way?

I start with a function x1new = f(x1, x2, x3); then I redefine f(.) for the case where x2=0.1, and x3=0.9 as x1new := f(x1) then I again define for the case where "something happens" where g(f(x))...
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### Which is better: “Then” or “and”? [closed]

Which is the better sentence style-wise? Let $U$ be an open disc in $\mathbb{R^2}$, and $S=\{{(x,y,0)}\in \mathbb{R^3} \mid (x,y) \in U\}$ be an open disc in the $xy$-plane. Let $U$ be an open disc ...
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### How prove/state things formally (mathematically speaking) [closed]

Lately, I have been trying to prove things by own first, then read the proof. However, it is not the same. Is there any tips or advise for proving/stating things formally? I want to write on math or ...
27 views

### Writing: A term is “absent in” or “absent from” an equation?

Notably, a term x is absent in/from Eq. (4). After consulting Gartner and online common use, I remain confused about how to decide which the correct preposition to use should be? For my colleague, ...
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### Naming (a plethora of) auxiliary variables

I am currently writing up a research project, and I came across the following problem: I am running out of variable names. Most Latin and Greek letters are already in use. In the write-up, we used ...
38 views

### Better notation to deal with matrices, vectors, and pdf?

I am working on a paper where I use lowercase/uppercase for scalars (e.g. $x$ or $X$), lowercase boldface for vectors (e.g. $\mathbf{x}$), uppercase boldface for matrices (e.g. $\mathbf{X}$). I will ...
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### Describe in a sentence to perform Singular Value Decomposition (SVD) for all $t$.

This question might be more of a linguistic thing than a pure mathematical question. However, I am struggling with writing something down in a proper manner. I'm trying to describe that I want to ...
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### Should names of “named theorems” be capitalized?

Should names of "named theorems" such as the following be capitalized (a) when being mentioned? (b) when being enunciated (of course the first letter would normally be capitalized in the latter case)? ...
20 views

### Language to describe that a multivariate function is convex with respect to only certain variables

Consider the following function: $$f(x, y, z) = x^2 + y^2 - z^2$$ I am writing a paper with such a function in which I stated "$f$ is convex only in variables $x$ and $y$". By this I mean that for ...
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### How to use $\forall i$ in a sentence?
For example, when I want to say "we need to make sure $a_i<0$ for all values of $i$". Do I need to put a "," between $a_i<0$ and the $\forall$ notation? or I can plainly write it as: "We need ...