Questions tagged [article-writing]
Various aspects of writing mathematics such as style, notation, grammar, frequently used phrases and common mistakes.
454
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What word means "the property of being holomorphic"?
As in the title, I am looking for a single word meaning "the property of being holomorphic".
The obvious candidates are "holomorphy" and "holomorphicity" but both look wrong to my eye. "...
7
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2
answers
237
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A better way of presenting mathematical content
Traditionally, mathematical work is presented in a linear fashion. Books, papers and articles are single streams of text meant to be read sequentially, from beginning to end.
However, mathematical ...
7
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3
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759
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Formal writing in math: equations
What is the formally correct way to solve a bunch of equations in math?
Is it \begin{align} 42x = 4324 \\ x = 4324/42 \end{align} or \begin{align} 42x = 4324 \\ \Rightarrow x = 4324/42 \end{align} or ...
7
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0
answers
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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)?
...
6
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3
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862
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How to interpret "let" in mathematics?
Before explaining my issue, I wanted to first explain what things do make sense to me.
So, statements (used at the beginning of proofs) like "Suppose $x$ is an integer" or "Assume $x$ ...
6
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2
answers
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Writing computer code in a mathematics paper.
I have some computer computations (using GAP) in my research which I would like to write in the paper. How should I go about it?
Should I include the full working code or just the major algorithms? ...
6
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4
answers
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Are there rules in the useage of prepositions in Math?
It is often to use prepositions in various expressions.
E.g.
$2$ is in the set of natural numbers $\mathbb N$
The symmetric group on 3 letters $S_3$ is the group consisting of all possible ...
6
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5
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531
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Why does nobody use the deduction symbols $A \Rightarrow B \Rightarrow C \Rightarrow D$ in their thesis/dissertation?
I am studying for a Master's degree of mathematics.
There are some deduction in my thesis is written
as the following form.
$A $
$\Rightarrow B $
$ \Rightarrow C $
$ \Rightarrow D $
But my ...
6
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5
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Is it a very bad idea to write xor in an article? [closed]
In writing a paper or thesis, is it a sign of bad style to use xor in your text as a word having the logical meaning of exclusive or? Or should you always avoid:
.. xor ..
by writing something ...
6
votes
2
answers
444
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Nuances of the word "proposition" (versus "theorem") in mathematical writing
In mathematical writing, the word "Proposition" is often used to label lesser theorems. However, I tend to feel that there's a further difference in the way the words "Proposition" and "Theorem" are ...
6
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3
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Is there a list of typical variable letters to use in a given context?
I try to write math notes as clearly as possible. In practice, this means using letters and notation similar to what the reader is already familiar with.
A real function is often $f(x)$, an angle is ...
6
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2
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Difference between each, every, any etc.?
I'm having a bit of trouble understanding the use of these different phrases. Are there any certain rules for when which of the word is to be used? I feel like they overlap a lot, but can bear ...
6
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1
answer
97
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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 ...
6
votes
1
answer
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How to properly mention names and surnames when writing introductions
I am writing a historical introduction to my master's thesis. Therefore I am mentioning a lot of people and I don't want to write their full name and surname each time. However, I cannot write their ...
6
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1
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531
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Referencing Lemma before introducing it
I am always confused about this:
When I am writing a paper I would like to first provide the big picture and then address some detail issues.
On the other hand, I think it's common knowledge that ...
6
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1
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563
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Should I put commas after my matrices in a paper?
When I need to put a matrix in my paper, I usually use $$ to center it on my page, and I usually describe something about the matrix immediately after, e.g., "which has real entries..."
should I put ...
5
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2
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Is there a sign for "according to?"
There are signs in mathematics for "therefore" and "because," which are $\therefore$ and $\because$ respectively.
However, another frequently-used expression is "according to." Is there any symbol ...
5
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2
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Using Comma in if...then Conditional Sentences
Many English grammar books state that in an "if ... then" conditional sentence, the word then should be preceded by a comma. However, in mathematical writing I often see that this rule is ignored.
...
5
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2
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Notation for multiple elements not equal to each other
I have four elements, $A,B,C$ and $D$. I want to write that none of the elements are equal to each other. Basically, something like this:
$$A \neq B \neq C \neq D$$
However, this is incorrect, since $\...
5
votes
1
answer
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Learning to translate natural-language phrases to formal logic
In natural language, we often use phrases like:
"fix arbitrary"
"such that"
"we have"
In general, how to translate those phrases into formal logic?
One example ...
5
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3
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449
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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 ...
5
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3
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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 ...
5
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3
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Notation for definition and equivalence
I would like some clarification about the usage/meaning of $:=$ and $\equiv$.
I have been using $A := B$ to denote "Let $A$ be defined as $B$." This is akin to assignment ...
5
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2
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370
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Basic guidance to write a mathematical article.
I'm trying to put together a mathematical article on how to obtain certain infinite series for some well known functions by a method of integrals (I like to call it "The Integral Method" - thank you), ...
5
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1
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693
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On the usage of words instead of numbers to denote numbers
[To the best of my knowledge, I did not find any previous question that deals with this issue. I hope it is not a duplicate.]
I have a problem with the way in which mathematicians sometime use ...
5
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0
answers
138
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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 <...
5
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0
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1k
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The meaning of appendices in a math text
I'm writing a formal math text, a long expository paper (i.e. a short book). The text is divided in sections and subsections (no chapters).
In order to present the subsection X.Y (here X and Y are ...
5
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0
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218
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Writing an abstract for a conference [closed]
For the first time, I'm preparing a 2-page abstract, jointly with a faculty member, to submit to a conference in mathematical logic so that the committee can decide if they allow me to present the ...
4
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2
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What does "of independent interest" mean in math papers?
Often I come across phrases like "We believe theorem $X$ is of independent interest"... I know this a phrase specific to math since I can google the phrase "of independent interest" and get mostly ...
4
votes
2
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562
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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 ...
4
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2
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396
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Can mathematical definitions of the form "P if Q" be interpreted as "P if and only if Q"? [duplicate]
Possible Duplicate:
Alternative ways to say “if and only if”?
So when I come across mathematical definitions like "A function is continuous if...."A space is compact if....","Two ...
4
votes
1
answer
993
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In writing mathematical papers, what qualifies as a "remark" and not just some discussion
Can someone enlighten me as to what qualifies as a "remark" in mathematical writing. What is the difference between a remark, and just some discussion.
Context: I introduce a lemma, and then a ...
4
votes
1
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LaTeX help - multiple answers using set bracket / cases [closed]
I'm brand new to LaTeX and am writing up a dissertation. I have read through several LaTeX guides but have not been able to find the answer there. Does anybody know how to use this ...
4
votes
2
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Let $f\colon A\to B$ be a function
The following sentence is often used in mathematical articles and writings:
Let $f\colon A\to B$ be a function.
I wonder, why this senctence is used often, since it is redundant. It is like I would ...
4
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2
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Smart Pen For Math Writing
Next month I will begin to learn in the university, and I am not sure if to buy smart pen such as Livescribe or Logitech IO 1/2 to write math with.(handwriting is not an option)
The problem is that I ...
4
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1
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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, ...
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3
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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 ...
4
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2
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262
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What is the distinction between $=$ and $:=$ when writing math? [duplicate]
I am persistently confused by the usage of $=$ and $:=$ when reading papers and writing in math. Quick google search on "When to use defined as (symbol)", returned no useful result.
The way I am ...
4
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4
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3k
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Punctuation in mathematical writing.
I am trying to collaborate with a fellow student on a piece of work. Unfortunately we have now reached a creative impasse.
I am under the impression that to include punctuation marks in equations ...
4
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1
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Contributing to a unsolved problem and writing a paper about it [closed]
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 ...
4
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3
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Good way to state, in english, the negation of "$f$ equals zero almost everywhere".
Let $X = (X, \mathcal{E}, \mu)$ be a measure space and let $f$ be a measurable function on $X$. Consider the statement:
$f$ equals zero almost everywhere
Is there an concise, unambiguous way of ...
4
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1
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In mathematical writing, how should I emphasise an equation together with its simplification?
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}{...
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2
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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
$$\begin{array}{rll}
\vartheta(x)&\displaystyle=\sum_{p\...
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3
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91
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Is there a word that encompasses both "definitions" and "theorems"?
I sometimes write sentences like this:
To prove the desired result, the following notions will be handy.
What follows is a usually a sequence of definitions, theorems and proofs. Therefore, I don'...
4
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1
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197
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Soft Question: Good strategies for writing a technical book or textbook
Most people would agree that doing technical work, whether it be pure or applied, and learning the background knowledge necessary to do this work comprises most of the literature and curriculum in ...
4
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1
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Referencing a Theorem in a Paper?
I'm making the final edits for a paper and I have a question more about the etiquette. I want to use a theorem from another paper and its obvious I have to cite it, but do I need to prove it too? I ...
4
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1
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writing papers: definition in word or formula?
If we write papers, is it or is it not desirable to write definitions in formulas AND words.
So if I want to define the following set:
$$S:=\{ x \in \mathbb{N} : P(x) \}$$ where $P$ is some predicate ...
4
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1
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566
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Writing small numbers in Articles [closed]
In primary school I learned that numbers less than 13 should be spelled out in writing.
I am suddenly not sure anymore, how I should handle this situation when it comes to article writing in ...
4
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1
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Notation and Style: Two Subscripts
Suppose $v_0$ denotes initial value of, say, velocity, and $v_y$ denotes the $y$ component of the velocity. Is there common way of writing the $y$ component of $v_0$.
$v_{0y}$ does not look ...
4
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1
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Analytic vs. Analytical [closed]
I am trying write an article.
Little Summary:
I have developed some tools to analyze derivative of some function $f$. This characterization leads to better results than previous works that only ...