Questions tagged [article-writing]
Various aspects of writing mathematics such as style, notation, grammar, frequently used phrases and common mistakes.
3
votes
2answers
34 views
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. (...
0
votes
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?
0
votes
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 \...
1
vote
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 ...
1
vote
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,...
0
votes
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 ...
0
votes
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 "...
1
vote
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 ...
1
vote
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 ...
0
votes
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}{...
2
votes
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 ...
3
votes
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 $$(a,b,c) < d?$$
1
vote
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
votes
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
votes
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 ...
0
votes
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, ...
0
votes
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 ...
0
votes
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 $K$ ...
2
votes
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:
...
0
votes
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
votes
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 ...
1
vote
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 ...
0
votes
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{\...
0
votes
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 ...
0
votes
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^...
2
votes
0answers
30 views
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 ...
1
vote
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 ...
1
vote
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
votes
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
votes
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
votes
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 $v_i$?
8
votes
0answers
197 views
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 ...
1
vote
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 ...
0
votes
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 ...
0
votes
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
votes
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 ...
5
votes
0answers
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 <...
0
votes
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 $A^* = A.k$ ...
0
votes
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 ...
-1
votes
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
votes
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 ...
3
votes
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
votes
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 ...
1
vote
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 ...
4
votes
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\...
0
votes
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, ...
1
vote
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 ...
0
votes
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);
...
0
votes
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 $...
1
vote
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 ...
