Questions tagged [article-writing]

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

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4
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0answers
81 views

Research article inspired by a question on MSE?

I am writing a short research article that was inspired by a question posted on this site. Is mentioning this in the article viewed as unprofessional/undesirable? I specifically mention in the ...
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1answer
33 views

the equation (A) vs Equation (A)

Quick question about grammar in English. Consider the equation $$x^2=c \tag{A}$$ Do we say that: For every $c<0$, the equation (A) has no real solution. For every $c<0$, Equation (A) has no ...
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6 views

What is the proper terminology for node/edge output by an algorithm? [closed]

What is the proper terminology for node/edge output by an algorithm? e.g. solution node, selected node?
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1answer
35 views

Using existential statements in informal mathematical reasoning

In symbolic logic, existence statements are normally written as $\exists x P$ where $P$ is some smaller statement. The $x$ is bound by the existential quantifier and the scope of $x$ is $P$. When ...
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1answer
16 views

Summing Term over only edges involving a particular node

I've got a quick notation question. Currently I'm trying to do a sum over all edges of a graph as so: $$ \sum_{i, j\ \in {E}}^{m}\frac{J_{i j}}{4}Z_{i} $$ What notation would indicate I only wanted to ...
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1answer
97 views

How do I write equations for this Fibonacci sequence

The Fibonacci sequence can be defined using the recurrence relations: $F_0 = 0, F_1=1, F_{n} = F_{n-1} + F_{n-2}~~$ for $n \in \mathbb{N} \colon n \geq 2~~~$ (1) $ F_0 = 0, F_1=1, F_{m+2} = F_m + F_{...
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40 views

Summarising a Research Paper

I thought to put this out to the community. I am an Undergraduate student summarising maths papers, firstly to get to grips with reading mathematical research and collecting a body of interesting ...
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1answer
42 views

Compact notation for limit at two different points of interest

Is it acceptable to replace $$ \lim_{x\to a}f(x)=\lim_{x\to b}f(x)=c $$ with $$ \lim_{x\to \{a,b\}}f(x)=c? $$ If not, is there another way I could state such a fact in a compact manner without having ...
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1answer
25 views

Interpretation of “[Numbers] are taken modulo” in scientific writing and best practice suggestions

This is a question specific to scientific writing and not about the modulo operation. The final question will be: Is this expression well-formed, or should it come with clarification? On several ...
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1answer
17 views

Grammatical standard for ordinals of complex expressions

In English, ordinals are usually created by appending a “-th” or “-eth” sound to the end. In mathematics, this extends to variables, hence the word “$n$th”. But the numbers 1, 2, 3, and 5 are ...
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12 views

Proper way of representing “meters per second squared per degree” in a scientific paper

I am having a hard time coming up with a way ro represent "meters per second squared per degree" in a scientific paper. How should I do it? I could do $m \cdot s^{-2} \cdot \circ$ or $\frac{...
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4answers
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Which does “themselves” qualify, “proofs” or “three theorems” in this sentence? (Michael Spivak “Calculus 3rd Edition”) [closed]

I am reading "Calculus 3rd Edition" by Michael Spivak. There is the following sentence in this book: The proofs of the three theorems themselves will not be given until the next chapter, ...
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1answer
42 views

How to write a mathematical expression defining a set with double “such that”?

I have a sentence I am trying to translate as a mathematical expression but I am not sure if the expression matches what I mean. The mathematical expression I came up with: What I actually mean: F is ...
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100 views

When professional mathematicians solve problems, do they use pen and paper or do they type directly into LaTeX? [closed]

When professional mathematicians solve problems, do they type directly into LaTeX or do they solve problems using pen-and-paper? By professional mathematicians, I include those pursuing a mathematics ...
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1answer
64 views

Proper notation for corresponding members in sets

I'm an amateur 42 years removed from academia so I don't always know "the language". In a paper I am writing, I specify search limits like $\;4\le m \le 9\;$ and then show, in examples, how ...
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41 views

Which Mathematical Concepts and Objects Do Not Require Citations in an Article?

I very much want to give credit where credit is due and avoid accusations of plagiarism. Obviously certain mathematical concepts (e.g., addition) and objects (e.g., the set of Fibonacci numbers) are ...
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34 views

How should I denote vectors and matrices in equations when accessing contents within in a scientific paper?

I come mainly from a software background and my math is not as strong as my programming. I am writing a paper and cover the basics of neural networks. As an example, here is what I have in terms of ...
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1answer
25 views

Should Two Unrelated Remarks Be Presented in One “Remark” Section, or Two?

Suppose at a certain point in my article I would like to make what are essentially two unrelated observations, where each pertains to the topic of discussion but neither is of sufficient importance to ...
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46 views

How to Avoid Abusing the Terminology of Interpretations and Representations With Respect to Formal Languages?

I find myself floundering in terminology, with the result that I fear the article I am writing will only appeal to readers afflicted with masochistic tendencies. At the very least, there is the ...
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1answer
35 views

In a Discussion Involving Formal Languages, Can a Word Be Regarded as an “Expression”?

In order to avoid sounding repetitious by too frequently using the word "word," I would like to be able use the word "expression," writing, e.g., "Applying the function $f$ to ...
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38 views

Can I Use Subscript Notation in an Unconventional Way If I Explicitly Note Its Usage?

I am writing a mathematical article in which I identify certain sets as subsets of another very famous set, the latter very commonly symbolized by an uppercase script letter, as in $\mathcal{B}$. I ...
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14 views

How to Present a Simpler Definition as a Prelude to a More General But Complex One?

I intend the paper I am currently writing to be of interest to professional mathematicians while also being accessible to students at the undergraduate level. One difficulty I face is how to ...
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1answer
25 views

What is the common usage for “let” for multiple variables? [closed]

Should I use Let $x$ be (...), let $y$ be (...), ... or Let $x$ be (...). Let $y$ be (...). ... or Let $x$ be (...), $y$ be (...), ... or even something different? What variant is commonly used in ...
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28 views

Suggestion of article to work in degree work

Hello, I am looking for an article to work on my undergraduate project, I am currently finished undergraduate, I want to guide my thesis on something that deals with germs, whitney topology, if I have ...
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28 views

Asterisk Symbol Meaning On a Particular Paper

hope you are all doing well. I am currently reading an article about quadcopters and on dynamic equations there is an asterisk symbol operation which I do not understand. I know that it does not ...
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10 views

Extending a weight function in a formal paper

For the first time, I am writing a research paper on my own. (I previously did so with some supervision of a professor during a summer internship) I would appreciate the opinion of someone with ...
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0answers
11 views

How to reference a paragraph?

Whats the best way to reference a paragraph. Basically, I don't want to say by line ___ on page ____ ... On the other hand the paragraph in question is a bit long and not formal in the separation of ...
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52 views

Mathematical Writing: Can objects in a definition be assigned any name, even though this name is used elsewhere in the text?

Consider the following example: On page 1 of my paper I write: Let $R$ be a finite commutative ring with $1$. ...[some text where I use $R$]... On page 3 of the paper I write: $\textbf{Definition.}$ ...
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1answer
15 views

Word to describe “semi-optimal” solutions

I have an algorithm (based on heuristics) that solves for a quantity $x$, producing a practically good result but not guaranteed to be optimal. What adjective can I use to describe this "solution&...
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1answer
32 views

How can I rewrite equations with conflicting indices?

I am writing a paper where I have to define theoretical background of the techniques I've used (I'm from the field of Computer Science). However, since I have little mathematical writing background, ...
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12 views

Should one include already cemented proofs of related principles in one's paper?

In a paper I'm writing (purely recreationally, nothing fancy), I state that "an odd number minus an odd number = an even number". I also state that "an even number minus an odd number = ...
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17 views

How to talk properly about stability, reachability, feasibility?

In proper English, should we say : "Proving the stability/feasibility/reachability of ..." or "Proving stability/feasibility/reachability of ..." ? I have found both versions ...
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43 views

Is it standard to write $2>1>0$?

Is it standard to write $2>1>0$ or we should write $2>1$ and $1>0$?
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25 views

What is the convention for referencing matrix indices with values greater than 9?

I would like to reference elements of a matrix $A$ such that each element can be found by its corresponding row and column position. Namely, $a_{ij}$ where $i$'s are rows and $j$'s are columns. The ...
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1answer
47 views

Proper punctuation for cases

Is it more correct or preferable to write $$ x = \begin{cases} a, & b; \\ c, & d;~\text{and} \\ e, & f. \end{cases} $$ than simply $$ x = \begin{cases} a, & b, \\ ...
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42 views

What are the mathematics journals focus on computational research article in number theory or algebra?

I know $\text{Mathematics of Computation(AMS)}$ is journal aiming research articles consisting of lots of computations. But this is one of the highest journals in this area to my knowledge. Is there ...
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0answers
6 views

How to write a 2D convolution with a stride width?

How do I write this convolution formula $$ y[m,n] = \sum_{j=-\infty}^{\infty} \sum_{i=-\infty}^{\infty} = x[i,j] \dot h[m-i,n-j] $$ with a stride width of $s$? Do I need to define the new range of $m$...
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2answers
126 views

Which is the best English term for “the result of a mathematical integration”?

I am writing an academic paper. And I wonder which is the best English term for "the result of a mathematical integration". For example, I have a mathematical integration as below. $$F = \...
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1answer
35 views

Notation for sorting a word

Is there an established notation for sorting finite sequences/words? At the moment, I have written the following definition: For a word $\textbf{a} = a_1, \dots, a_t$, let $\operatorname{Sort}(\...
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1answer
65 views

When Should I Use Symbols in a Proof?

The question I'm about to ask might sound weird, I hope i can deliver the idea. I have noticed that in some mathematics books (especially English ones) the proofs are written in words and symbols are ...
2
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1answer
29 views

Proper punctuation of cases in statement of Lemma

I found a very similar question asked on the TeX StackExchange here but the answer was not as definitive as I hoped for. My question is in regard to how one properly punctuates the following Lemma. ...
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61 views

The name for an assumption made for the sake of contradiction - the marked assumption?

What is the name (or adjective) for an assumption made for the sake of contradiction? To be clear, I'm in search of an expression in the form "a(n) $\underline{\quad \quad \quad \quad}$ ...
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0answers
83 views

How to denote a set of vectors?

I have a set that contains vectors as its elements and would therefore like the vectors to be in bold font. Still, I am not sure if the set should also be bold. Which one is more accurate, 1 or 2? $\...
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51 views

A conjecture about the solvability of rational equations of transcendental functions by elementary numbers

Is my conjecture below mathematically and linguistically correctly formulated and well formulated? How can the conjecture be improved and shortened/simplified and made more intelligible? The ...
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1answer
69 views

Is it okay to mix $\iff$ and $\implies$ in a single derivation?

Say, I have to write down the steps to solve this equation $$ \frac{1 + ax}{a} - x = \frac{1}{a^2}(x - a). $$ Is the following manner a good way to write it? \begin{align*} \frac{1 + ax}{a} - x = \...
3
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0answers
29 views

Writing style for modular arithmetic with multiple equivalences in a single line or split between multiple lines

Is this a valid notation in modular arithmetic? $$ 2 \equiv 12 \equiv 22 \equiv 32 \pmod{10}. $$ If I want to split this into multiple lines (say, I have got expressions that are very long), then what ...
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22 views

What is a concise (and formal) way to say “The performance of algorithm $A$ has the same order as $B$ ”?

Suppose I have two algorithms $A,B$ whose performance is measured by a value that evolves with time and can be positive or negative. For any given performance bound on $A$ it is straightforward to see ...
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2answers
69 views

Soft question regarding math theses [closed]

I'm currently in high school and I am wondering about how math papers a formated. In standard literature studies essays, we are told to "come up with" a thesis statement, present it in the ...
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1answer
49 views

How trivial is this? (Reference Request)

I am writing a paper and at some point I make use of the proposition "Any compact, convex set, may be represented as the set of solutions to a (possibly infinite) set of linear inequalities."...
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1answer
74 views

Correct way to announce a theorem

Reading the following statement : Theorem : An operator $A$ has the property $P$ if $\underset{\lambda \rightarrow 0}{% \lim }\left( A-\lambda \right) ^{-1}$ exists. Does the reader understand that $...

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