Questions tagged [article-writing]
Various aspects of writing mathematics such as style, notation, grammar, frequently used phrases and common mistakes.
394
questions
2
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0
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20
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Book or article on Bernoulli numbers and polynomials
I am looking for a book or article that deals in detail with the Bernoulli numbers and polynomials.
- 149
1
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0
answers
35
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In which cases can the article "the" in sentences be eliminated? [closed]
In the sentence "Geometric interpretation of the non-commutativity of unit quaternion multiplication", can we just write "... of non-commutativity of ..." ?
- 149
1
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1
answer
35
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Measurement or measure of a complex number?
In math, do we write "measure of an angle of two vectors" or "measurement of an angle of two vectors"?
- 149
1
vote
1
answer
65
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How to write maths
In the sentence below, which expression is better to choose: "their multiplications" or "their multiplication" :
"This identification allows us, first, to present a new polar ...
- 149
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0
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63
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Why do we say a non-negative real number
In some articles, we write "non-negative real number". Why we don't simply say "positive real number" ?
- 149
1
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0
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8
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Cross-references in a LaTeX document [migrated]
When I click on the link of a reference (equation, image, section...) it sends me to the beginning of the page where the reference is and not to its exact location.
- 149
0
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0
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13
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How do I express that something is distributed over an interval?
I have a set of states between $t=0$ and $t\to\infty$. I'd like to write the following:
The states are distributed over $t=\left(0,\infty\right)$, so the intervals in $t$ between them are ...
0
votes
0
answers
47
views
Mathematical English in PDE's type paper
I am trying to write some materials in PDE content. However, my English is not very good. Do we have some PDE's type papers or books that is well-written? I am reading the book by Trinduger, but I can ...
- 523
0
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0
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25
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Is there a name to refer to point $A$ / point $B$ when discussing vector $\overrightarrow{AB}$?
In a code, I am writing a concise documentation of a function that needs 2 vectors defining a triangle $ABC$. The function performs an operation which is invariant up to a translation, so two vectors ...
0
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0
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13
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Rephrasing statement: Let $S$ be a set of eigenvalues of an operator $T$. Then $S=[1..n]$
How can I write the following statement in a concise English sentence, using the expressions commonly used in math context (e.g., unique, if and only if)? My question is about the exposition of the ...
- 165
3
votes
1
answer
79
views
How can I say "$T \to \infty$ implies ..."?
I would like to know a better way to say "$T \rightarrow \infty$ implies ..." when writing / speaking.
I tend to write this as "Limiting $T$ to $\infty$ implies ...",
but others ...
- 424
0
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0
answers
18
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Correct description/numbering of formulas across multiple pages
I don't want to discuss a mathematical problem here, I want to ask how to meaningfully present formulas that extend over several pages.
Attached is my suggestion where on the first page the equation ...
- 31
3
votes
1
answer
105
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Can I change a Lemma to a Proposition?
I am getting confused about one thing:
I am reading a paper say X. Paper X has a Lemma in it. I am also writing a paper for my dissertation. I want to use the Lemma from Paper X in proving a theorem ...
- 1,662
0
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0
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14
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Writing mathematical expression for limit on allowed repetitions
I have to write the expression explaining, in $0\leq C_1 \leq C_2\leq \cdots \leq C_r$
"There are no more than $l$ numbers (i.e. $C_i$'s) that can have the same value."
How do I write the ...
- 505
0
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0
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16
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When to use "in" versus "into" when talking about embeddings?
Let $A$ and $B$ be mathematical structures of some kind. Consider the following statements:
$A$ embeds in/into $B$.
$A$ does not embed in/into $B$.
There is an embedding of $A$ in/into $B$.
We say $...
- 288
4
votes
1
answer
96
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How to write an equation and its simplification next to it (math etiquette wise)?
I always have this problem where I want to write an equation then immediately its simplification after it. I used to use the imply or equivalent symbol such as:
Therefore we end up with
$$
\frac{a^2}{...
- 419
0
votes
0
answers
5
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Denoting Repeated Value from First Column of Table
In a manuscript I am preparing, I have a large table with entries that are repeated along some rows. For example, including all numbers would look like
Main Column
Column 2
Column 2
1.03
1.03
1.03
...
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1
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0
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42
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What is the equation for the standard deviation of the set of all odd integers?
I have a set containing all of the odd integers in the integer set. It is denoted by $O=\{2n+1\mid n\in \mathbb{Z}\}$. I want to write an equation that equals the standard deviation of the set. If I ...
- 11
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0
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42
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Would you demand a proof that this is a cyclic subgroup of $(Z/NZ, *)$?
I'm mostly looking for advice on how to say, how to write this, how to prove it. I think it probably dispenses a proof. I'm writing this to a small number-theory audience, so I don't think they need ...
- 121
7
votes
1
answer
116
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"Theorems 1 and 2 imply" vs. "Theorem 1 and Theorem 2 imply"
To convey that
$$\text{Theorem 1} \wedge \text{Theorem 2} \implies A$$
which style is better?
Theorems 1 and 2 imply $A$.
Theorem 1 and Theorem 2 imply $A$.
Which style manuals prefer which form?
(...
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2
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0
answers
89
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How do I write mathematics?
Currently, I’m teaching myself mathematics as a part of my self-study. I’m working on Calculus, and I plan to do so for the next few months or years (I’m in first year of high school, so I have time). ...
0
votes
1
answer
92
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Set definition problem
I want to write in a Proposition:
"There exists $x_1$ and $x_2\geq x_1$ so that
(a) If $x\in [0,x_1)$, then $A>B$.
(b) If $x\in [x_1,x_2)$, then $A\leq B$.
(c) If $x\in [x_2,\infty)$, then $A&...
- 41
1
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2
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81
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Feedback on Proof of Squeeze Theorem
I wrote out a proof of the Squeeze Theorem for my personal notes as I study AP Calculus. This is my first time really writing out a proof using a combination of natural language and logic. I would ...
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0
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45
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Meaning of "a particular case of" and "special case"
When people says that function $f$ is a particular case of function $g$, does this mean that $f$ is a special case of $g$?
Are "special case" and "particular case" the same thing?
...
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1
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1
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71
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What do you call the set definition part of a formula?
Suppose I have a formula with two parts: First is a description of the element and set on which an equation will depend, and the second is the equation itself.
Example:
First, the formula quantifies ...
- 13
0
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0
answers
26
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How to simpilfy a function $ f(x_1^1,x^1_2,...,x^1_q,x^2_1,...,x^N_q)=0 $ in a correctly way?
I have a function $f(.)=0$, with respect to $x^{I}_i$, where $I=1,2,...,N$ and $i=1,2,...,q$.
We can write the function in the way:
$f(x_1^1,x^1_2,...,x^1_q,x^2_1,...,x^N_q)$=0.
It looks very ugly.
I ...
- 103
0
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0
answers
30
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How to express orthogonal basis of space spanned by some vector in a correct way?
I have a series of vectors, suppose ${a,b,c,d,e}$. These vector span a space.
$span \{a,b,c,d,e\}$.
I have the orthogonal base of the space, supposed called $u,v,x,y,z$.
How can I express the ...
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1
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1
answer
26
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Does the choice of variable matters in area function using definite integrals?
Consider the following context and definition from the sub-section 7.8.1 Area function of the chapter Integrals from the NCERT textbook
We have defined $\int_{a}^{b} f(x) dx$ as the area of the ...
- 2,209
1
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2
answers
87
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A+B is sufficient and necessary for C. C is unnecessary for D. Is it flawless to formally write that "A and B are unnecessary condition for D"?
Condition A+B is sufficient and necessary for condition C. Condition C is sufficient but not necessary for D.
Is it flawless to write that: "A and B are unnecessary condition for D "?
I am ...
- 2,986
9
votes
1
answer
289
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Mixing fraction notation with slash notation
I am writing a theorem, and in it, I mix $\frac ab$ and $a/b $. The reason for this is that I find
$$\lceil a/b \rceil \tag{1}$$
better-looking than:
$\displaystyle \biggr \lceil \frac ab \biggr \...
- 826
0
votes
1
answer
56
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Representing the total derivative
This is a quick question about syntax.
I have the function:
$$\hat{x_i} = \frac{x_i - \mu_\beta}{\sqrt{\sigma^2_\beta+\epsilon}}$$
where $\sigma^2_\beta$ is an intermediate function:
$$\sigma^2_\beta =...
- 7
1
vote
2
answers
51
views
Can you say "The inequality B encompasses A"?
I know this is a silly question for English speakers, but as a non-native speaker, please help me communicate in math.
I am about to report in a formal academic paper on inequality B, which is a ...
- 595
0
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0
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21
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What is the most common and appropriate way to express sub-matrix
Suppose I have this matrix A, I am wondering if this is the correct and formal way to express the red rectangle submatrix, S=A1,2;2,4
Also looking forward if there is a better solution.
Thanks in ...
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2
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0
answers
47
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Remark inside a proof
It is a good practice to define a remark inside the proof of a theorem to highlight a necessary observation to go on the proof?
Edit (the scheme that I imagine is the following):
$\textit{Proof }$
...
...
- 999
9
votes
2
answers
270
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The best way to use notation in the proof
I have two simple questions regarding the writing styles.
Assume that I make a remark~$1.1$ and I define two sets say $A:=\text{something}$ and $B:=\text{something}$. My question is that I will use ...
- 2,153
0
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0
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84
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The use of definite and indefinite articles in math (the vs. a/an)
This question has been on my mind for a while now. Not being a native speaker and coming from a country, where grammatical cases are used to modify nouns and nominal parts of speech, the use of ...
- 159
2
votes
2
answers
60
views
Is writing $m=\text{undefined}$ formally correct?
I often find some of my students write $m=\text{undefined}$ in their answer sheets. Is it formally correct? Should I suggest them to write $m$ is undefined instead?
For example the question is
...
1
vote
1
answer
28
views
Conventional notation for congruence to multiple numbers
Is there a more concise notation for the following sentence?
"Thus $ f(n) \equiv 0 \pmod{12} $ for all $ n \equiv x \pmod{12} $ where $ x \in \{ 0, 1, 3, 6, 7, 11\} $."
Is this an acceptable ...
- 1,132
0
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1
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82
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Logic symbols in a math paper? Is this correct?
I am writing a mathematics paper with the intent to publish it in a peer-review journal. I have written something along the lines of
Theorem 2.
(1) something
(2) something else.
(end of Theorem 2).
...
- 45
1
vote
1
answer
115
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Multiset/Set/List initiation and use in pseudocode
I'm writing a paper and I've come across interesting problem. In my algorithm, I create a list of 0's (example [0,0,0,0]), where the number of 0's is given by parameter "x". Later I want to ...
- 193
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votes
1
answer
65
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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 ...
- 257
0
votes
1
answer
52
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 ...
- 21
0
votes
1
answer
22
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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 ...
- 163
0
votes
1
answer
127
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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_{...
- 509
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0
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88
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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 ...
- 1
1
vote
1
answer
42
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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 ...
- 152
1
vote
1
answer
47
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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 ...
- 113
1
vote
1
answer
20
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 ...
- 221
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votes
4
answers
58
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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, ...
- 6,137
0
votes
1
answer
48
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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 ...
- 165