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Questions tagged [article-writing]

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

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When is it appropriate to add a title to a theorem?

I am writing a paper and I have proved a couple of theorems and three propositions. Is it appropriate to add titles to these theorems and propositions for more clarity? For instance, say Theorem 2. (...
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1answer
23 views

How to cite a theorem in the proof of another theorem?

I want to prove a theorem using the result of a well-known theorem. Should I write the well-known theorem as a lemma since it aids the proof of my theorem or as a theorem?
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0answers
8 views

Proper way to write a theorem with approximation result.

I have a lemma that shows that we can approximate $a$ with $b$ if $n \gg 1$ and I use the result to prove a theorem. Which one of the following ways is better to write this lemma? Provided that $n \...
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1answer
15 views

Right terminology for time series associated to a variable

I am in the process of writing a paper and I have a doubt. I am not sure that this is the best stackexchange site where to post since it is more a terminology problem than a mathematical one. Please ...
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1answer
45 views

Writing the Dijkstra Algorithm in Mathematics

I would like to know about writing the Dijkstra Algorithm properly and efficiently using mathematical notation, which may simplify the process to writing the proof. Assume that the graph is unweighted,...
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0answers
58 views

Two simple questions regarding typesetting maths (in LaTeX)

The first question I have regards endomorphisms, especially in differential geometry. Everyone who had worked a little in (complex) differential geometry will know that it is very common to write the ...
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0answers
31 views

Interesting mathematical topics to discuss in the essay

I need to write an essay about some interesting math problem. Does anyone have any idea which problem, theorem, questions I can use? I thought about discussing "The history of number zero" or "...
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4answers
107 views

How to use of “the” before known matrices [closed]

I am writing a paper and want to use Vandermonde matrices in its abstract. I am confused which of the following sentences are correct? A) One of the important matrices in coding theory is the ...
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0answers
50 views

Master thesis: in how much detail should mathematical principles be described [closed]

Writing an engineering thesis, I'm sometimes wondering how detailed the used equations should be explained. The section below (equations and italic parts) shows a simplified quote from the main ...
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2answers
52 views

\times vs. \cdot vs. parentheses vs. nothing while writing fraction multiplications

Is there a convention around writing multiplication of fractions. Let us take two examples to be specific. Example A: $ 2 \times \frac{1}{2} $ Here are some ways to write this example: $ 2 \frac{1}{...
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2answers
42 views

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 ...
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2answers
52 views

Is it correct to write $(a,b,c) < d$?

I want to say that the scalars $a$, $b$, and $c$ are all smaller than $d$. Is it mathematically correct if I write it like $$(a,b,c) < d?$$
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2answers
39 views

How important is to use the $\forall$ notation in the optimization frameworks?

Consider I write the following optimization in my manuscript: $$\min_{X,Y} f(X,Y)\\s.t. ~x_{ij},y_{ij} \in \mathbb{R}^+,$$ where $X,Y$ are matrices, and by those constraints I mean their entries ...
0
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1answer
41 views

Should we use parentheses to delimit inline math expressions appearing in text?

Consider this snippet: After adding $1$ to $2^n + 1$, we get $2^n + 2$. Then this: After adding $1$ to $(2^n + 1)$, we get $(2^n + 2)$. Is there any writing style convention that prefers one ...
0
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1answer
27 views

Calculus based or calculus-based?

I've noticed something strange in the literature. Regardless of context, there seems to be a trend where some authors will say 'calculus-based solution' or 'calculus-based physics' whereas others will ...
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0answers
9 views

Managing complexity and how to avoid errors?

How to manage complexity and how to avoid errors? Particularly in "dense" equations. Yeah, intuitively, check everything. However, I've sometimes fiddled with problems that "deviate" into directions, ...
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0answers
24 views

Notation suggestion for modeling discrete random variables in model

I am developing a set of linear difference equations to model labor hiring. In each equation, there are two variables that take on values from a stochastic binomial random variable with $n$ trials and ...
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1answer
32 views

Writing a set of functions

Let $A$ be a countable set of subsets of $\mathbb{R}$ $f:A \rightarrow \mathbb{Z}$ be a bijection $O= \{x_k:\mathbb{R}\rightarrow \mathbb{R} \mid k\in [1,\dots, K]\subset \mathbb{Z}\}$, for some $K$ ...
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2answers
72 views

Using terms “necessary” and “sufficient” when writing proofs for logical equivalence?

Often times in mathematics writing, authors prove the two sides of the implication by showing a proof of necessity and a proof of sufficiency, and the proof takes the following template: ...
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2answers
60 views

Problem in Math Writing [closed]

I have a problem in math writing. Consider $a_i$ with $1\leq i \leq n$ are some elements over a field. My Question: Which of the following statements is correct? A) Let $a_i$'s satisfy the ...
0
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1answer
86 views

Will Math Ever Stop Using Paper? [closed]

This is an odd question, yet I must still inquire: will math ever stop using paper? In the writing industry, paper is dead; we do all our writing on computers. Yet with all of mathematics' complex ...
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0answers
26 views

an approximation to the generalized hypergeometric function

Relating to the article An approximation to the generalized hypergeometric function, I would like to calculated example of the Poisson distribution $Po(10)$. If you have the possibility, please see ...
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2answers
32 views

Writing a partial derivative as a function of time

I have two time-dependent variables $x$ and $y$. Now I want to write $\dfrac{\partial x}{\partial y}$ at particular time step ($t$). What is the correct format to write such expression? $\dfrac{\...
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1answer
25 views

How to write cases with “cases” environment involving both equalities and inequalities

I am writing a document where I have a situation where I need to describe that a function $ f(n) $ equals $ n $ in a certain case but does not equal $ n $ in other cases. I am not sure how to write ...
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0answers
18 views

Using **qualitative** and **quantitative** in the context of singular values in SVD

I am dealing with singular value decomposition of a matrix $\mathbf{A}$ \begin{equation} \mathbf{A}=\mathbf{U}^{}\mathbf{\Sigma^{}} \mathbf{V}^{T}=\sum_{i=1}^{rank(\mathbf{A})}\sigma_i^{}\mathbf{u}_i^...
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0answers
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Best style for using a definition that is only used in one theorem/lemma

I have a theorem of the following form Definition. An object $y$ has property $X$ if... [2 lines...] Lemma. If $y$ has property $X$, then ... I could also simply write Lemma. If $y$ has ...
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0answers
37 views

The name for the class of theorems, propositions, lemmas

Statements such as theorems, propositions, and lemmas are all (mostly) proven statements. They differ from, say, definitions by the fact that they describe consequences of axioms, rather than label a ...
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1answer
34 views

Notation convention for distinguishing uses of equal sign when manipulating equations

When reading (or writing, in fact) a proof, or the resolution of an equation, I often find myself in the following situation. Say, for example, that the writer proves the statement $A=B$, where $A$ ...
3
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1answer
44 views

How to make the description of my probabilistic binary lattice model more precise and succinct?

I am supposed to write up a report on a percolation theory project which I worked on, over the summers. I'm trying to describe my mathematical model below: We report some results regarding certain ...
4
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1answer
128 views

Contributing to a unsolved problem and writing a paper about it

How do I write a paper on the Collatz Conjecture without fooling or making an ass out of myself? Im not affiliated to any University at the moment (my past Uni was like 20 years ago, but I didnt ...
0
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1answer
143 views

How to denote a one-hot vector space, like $\mathbb{R}^n$ but for one-hot vectors?

For real vector $v_r$ we can write $v_r \in \mathbb{R}^n$. For binary vector $v_b$, I think we can write $v_b \in \{0,1\}^n$. But how should we write a one-hot vector $v_i$?
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Examples of well-written scientific papers in mathematics [closed]

I am looking for examples of papers, which are (according to you) an example of good mathematical writing, while I would be interested in some sort of justification what makes you believe so. For ...
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2answers
81 views

Using both $\theta$ and $\vartheta$ in the same statement

$\newcommand{\textand}{\hspace{5pt}\text{and}\hspace{5pt}}$ In a recent proof of mine, I used the two symbols $\theta$ and $\vartheta$ for different variable angles. My supervisor noted that this can ...
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0answers
43 views

Set membership notation for indexed elements in a set

I'm aware that a set of indexed items $X = \{x_1,\dots,x_n\}$ is really a mapping $x: I \to X$, where $x(i)$ is denoted $x_i$ (per this question), but my question relates to mathematical writing using ...
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1answer
28 views

Notation for intersection of points with function

Suppose I have a function $f:\mathbb{R}\rightarrow\mathbb{R}$ and a set of points $S\subseteq\mathbb{R}^2$. How can I concisely convey the following idea? All points $(x,y)\in S$ such that $f(x)=y$ ...
2
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1answer
54 views

Language to describe $\forall$

In a document that I am working on, I have written the following definition for a group: Definition: (Group) $\hspace{2pt}$ A group (G) is a set together with a binary operation, usually called ...
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131 views

Help from speakers of English wrt Mathematics: “$-x$” reads as “negative $x$”, for some measure $x$? [closed]

I am trying to write a paper in English, while not a native English speaker, and struggle with the English text illustrating the equations. In English, it is correct to write "negative 1" to mean <...
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0answers
31 views

How to write this “loop” for a methodology

I'm not an advanced maths writer (neither a newbie) and need this help. Working on a methodology and need to write this little example Thinking on vectors $A, B, C$ and $D$ and $A^* = A.k$ ...
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1answer
81 views

Should I write “*a* splitting field” or “*the* splitting field”?

I am studying from Patrick Morandi's Field and Galois Theory, and in section 3, he makes the following definitions. Let $K$ be an extension field of $F$. If $f(x) \in F[x]$, then $f$ splits ...
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1answer
41 views

Can I work only with complete atomistic boolean algebras instead of posets? [closed]

I wrote a book, most of whose theorems contain something like: $\mathfrak{A}$ is a poset with the following properties: ... Then the conclusion ... holds. Now I am "slightly" rewriting my book ...
0
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1answer
26 views

How to write equation for a set of products with specific range limits?

I hope you welcome non-mathematicians here. I am trying to find out how to write the following idea as a math equation, currently it is in computer code but I want to be able to discuss this with some ...
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3answers
80 views

Have seen long proofs in articles some with $15$+ lemmas for a single theorem. How does a writer keep track of and manage so many lemmas?

When someone sets out to prove a theorem, they may be able to see for example a couple results that if proven could give them the theorem. But I don't see how anyone could mentally grasp dozens of ...
0
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1answer
39 views

Referring to a mathematical element: to drop or not to drop the “the”

As a non-native English speaker, this question about style comes back to me every time I'm writing a formal text. Given a certain mathematical element, such as a matrix detoned by M. Which is the ...
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3answers
123 views

When to write something in terms of axioms?

Most mathematical structures are defined according to axioms. e.g. we state: Definition. Monoid. A monoid is a tuple $(S,\cdot)$ where $\cdot$ is a binary operation $S\times S\to S$ that satisfies ...
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2answers
54 views

What is the best notation to write ``equations with reasons''?

I'm learning my analytic number theory course. When I make notes, I find that it is effective to use ``equations with reasons'' as follow $$\begin{array}{rll} \vartheta(x)&\displaystyle=\sum_{p\...
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1answer
99 views

Mathematical Writing, Style: Contractions

I am in the process of finishing up writing my first paper, and I have a question on style. How much should contractions be avoided? Specifically, should "we'll" be avoided? Having looked online, ...
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1answer
38 views

How to Phrase an Induction Proof That Only Goes up to 100?

Say I have a statement $P(n)$ which is true for all natural numbers $1 \leq n \leq 100$, but is nonsensical or false for other values of $n$. If I want to prove that $P(n)$ is true for $1 \leq n \leq ...
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1answer
62 views

How to choose between a set and a tuple?

Sometimes when writing pseudocodes in a paper I need to write statements of the form: $A\gets\emptyset$ (initialization); $A\gets A\cup\{i\}$ (add element $i$); $|A|$ (calculate the cardinality); ...
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1answer
28 views

How can I make probabilities and expectations conditioned on locations?

This is about the use of notations in a paper (the main problem is different and I simplified it here, I don't need help on how to prove it): Points $P_1, P_2,\ldots,P_N$ are placed in the circle $...
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0answers
32 views

Is there a marking scheme for assessing mathematics essays and papers? [closed]

It rather difficult for students to write an essay in mathematics because they are not clear about the requirements. It is also very hard to mark the essays. A marking scheme makes both writing and ...