Questions tagged [article-writing]
Various aspects of writing mathematics such as style, notation, grammar, frequently used phrases and common mistakes.
322
questions
-1
votes
1answer
23 views
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 ...
0
votes
0answers
24 views
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 ...
0
votes
0answers
17 views
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 ...
3
votes
2answers
96 views
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 ...
0
votes
0answers
208 views
+500
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 ...
0
votes
0answers
27 views
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 ...
0
votes
0answers
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 ...
0
votes
0answers
24 views
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 ...
4
votes
1answer
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, ...
0
votes
0answers
10 views
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 ...
0
votes
0answers
18 views
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 ...
1
vote
0answers
23 views
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 ...
1
vote
1answer
31 views
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 ...
0
votes
0answers
5 views
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))...
0
votes
1answer
42 views
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 ...
0
votes
2answers
49 views
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 ...
0
votes
0answers
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, ...
0
votes
0answers
32 views
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 ...
0
votes
0answers
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 ...
0
votes
0answers
24 views
Is there a specific term for “algebraic nullity”?
I want a compact way of saying "The algebraic multiplicity of $0$ for the operator $M$ is $2$".
Similar to the way "the nullity of M is $2$" means the geometric multiplicity of $0$ for the operator $...
1
vote
1answer
39 views
Function that is 1 if input is positive, 0 otherwise
I am trying to write a certain matrix neatly for a paper, but I do not know how I would go about writing what I want formally.
I have two variables, x and y, which can assume any value. I want to ...
5
votes
2answers
143 views
Why writing equations in two column explanation is bad math?
A question arised while I was reading "A Guide to Write Mathematics" (by Dr. Kevin P. Lee, p. 5) about writing explanation of steps, in equations calculations or listing some equations, without using ...
1
vote
1answer
30 views
How to write an equation that started with for each where
First of all, it was difficult to find the proper title for my question. Basically, I would like to write an equation for the following:
For each branch $b_i$ where i in 1 to n, the BEC value for ...
0
votes
0answers
25 views
Is it proper style to skip “and” when discussing two mathematical variables?
Suppose we are discussing two matrices $ A $ and $ B $. Furthermore, let us say that $ A, B $ commute with a matrix $ C $. Was it permissible to write $ A, B $ instead of $ A $ and $ B $ in the ...
0
votes
2answers
43 views
Indices, Combining Sum and Product Notation
I have a function
$$ f(x) = (x-a_1)(x-a_2) \cdot \cdot \cdot (x-a_n) $$
I want to express $f'$ with sigma notation. It is clear that $f'$ is the sum of $n$ terms, where each term is missing one $(x-...
1
vote
1answer
31 views
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 ...
3
votes
0answers
47 views
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)?
...
1
vote
1answer
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 ...
1
vote
1answer
74 views
General formula for mth degree polynomial in n variables
The general formula for a $\text{m}^{\text{th}}$ degree polynomial in n variables is something like this:
$$ \sum_{\substack{a_1+ . . .+ a_n \; \leq \; m \\ a_1, . . . , a_n \; \geq \; 0 \\ a \; = \;...
4
votes
3answers
57 views
Right Punctuation in Equivalent Conditions
The sentence "The following are equivalent:" is frequently used in mathematics, and most of the time it is followed by a list of statements.
It was never clear to me how one should seperate these ...
0
votes
1answer
97 views
How can this definition be improved? [closed]
On my new theorem I have to introduce some new notions that may be extrange in academics reading and in order to get it accepted by the reader I would like to be as clear and correct as possible. ...
2
votes
1answer
63 views
How to write this properly, elegantly? Context: expressing a number as a product of its prime factors
I'm striving for proper and standard mathematical writing, elegance being a plus.
Here's what I want to say. If two natural numbers are not the same number, the fundamental theorem of arithmetic ...
0
votes
2answers
61 views
Basis (linear algebra) - ordering of the vectors?
Looking at Wikipedia Basis (linear algebra), it seems that in English a basis is a set of vectors that may be ordered, with ordering not being mandatory. This creates issues when dealing with ...
0
votes
1answer
118 views
When writing a new theorem, is it acceptable to introduce some new definitions concepts? [closed]
Let's say I'm writing a new theorem but I need to introduce concepts, definitions and lemmas, of course valid, in my own way, since I don't know if someone defined them before in the past.
I am ...
0
votes
2answers
66 views
Is it acceptable to write “the function $f_n$ is cts for every $n \in \mathbb{N}$”?
When I have a sequence of functions $f_n$, $n \in \mathbb{N}$, is it OK or acceptable to write
"The function $f_n$ is continuous for every $n \in \mathbb{N}$"
meaning
"For every $n \in \mathbb{N}$, ...
0
votes
0answers
31 views
Is it bad math style to use one letter for indexing two objects? [duplicate]
Is $$\sum_{i\in I_1} a_i + \sum_{i \in I_2} b_i$$ or $$\prod_{i\in I_1} a_i \cdot \prod_{i \in I_2} b_i$$ confusing or bad math?
Should I rather use $j$ for indexing the $b$'s?
1
vote
5answers
146 views
Grammar Mistakes in Math Writing
May be my question is simple. But this question is confused me. In fact, I want to present a lecture and I don't want to have grammar mistakes.
My question: which one is correct?
A: Let $\mathbb{F}...
3
votes
2answers
69 views
Should one include a long standard proof of a small lemma in a paper? [closed]
I have a three page induction proof which is pretty typical but unusually long due to the nature of the formulae. Should it be included in a paper which probably won't exceed more than 30 pages?
0
votes
0answers
29 views
Probability Theory Verification
I am writing some notes on basic probability in my own version, but regarding to many different versions of probability concepts I have found in several books and articles..I would like to ask whether ...
1
vote
0answers
30 views
Reference to named theorem
Assume Theorem 1 is Pythagoras' theorem, I want to reference it and I want to be nice to the reader and tell them at the point of reference both that I'm referring to the Pythagoras' theorem as well ...
0
votes
0answers
25 views
Most clear notation for expansion of functional relations for arbitrary dependencies?
This is a question about notation, and clear exposition in a paper. (I haven't published a paper before).
I have a set of variables $\mathcal Y=\{Y_1,...,Y_n\}$, and a directed acyclic graph $D$ with ...
3
votes
2answers
41 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
104 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?
1
vote
1answer
22 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 ...
0
votes
1answer
97 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
62 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
39 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
110 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 ...
0
votes
2answers
245 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}{...
1
vote
2answers
105 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 ...
