Questions tagged [article-writing]
Various aspects of writing mathematics such as style, notation, grammar, frequently used phrases and common mistakes.
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Should I finish a proof assuming a (possibly not independent) additional axiom?
I am writing a proof and I do not know how to proceed.
In the paper I’m writing, I have assumed four Axioms that I suspect imply one very particular thing. However, the proof contains a step that I ...
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How to begin a list of biconditional statements [closed]
Suppose I want to say that something is true "if and only if" <insert a series of equivalences>. Is this correct, or is it better to say "if and only if the following equation ...
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How to use "given" in expository writing.
In "How to write mathematics", Halmos says the following.
Two digressions about
“given”. (1) Do not use it when it means nothing. Example: “For any given $p$
there is a $q$.” (2) Remember ...
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How do you clearly and concisely describe the union of a particular function's outputs for one of many functions?
I'm writing research and I've encountered quite a specific problem. The following are example sentences I came up with to try to explain a particular concept. Note that the following is analogous to ...
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Confused about using "the" in mathematical English writing [closed]
I am not an English native speaker. In many times, I have seen different authors used "the" or not used "the" in the same situation. I am so confused about this. Here are some ...
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Elegant way to write $g(f(x))$
I've a very ugly expression:
$$
\frac{d^2 g(f(x))}{d (f(x))^2} \, \left( \frac{d f(x)}{dx} \right)^2 + \frac{d g(f(x))}{d f(x)} \,
\frac{d \left( \frac{df(x)}{dx} \right)}{d f(x)} \, \frac{d f(x)}{dx}
...
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How do you explain (in writing) a complicated mathematical object in a general sense whilst avoiding ambiguity?
I'm writing research that involves explaining objects which are fairly complicated and very specific to the research in question (e.g. a new type of mathematical model of something). The objects in ...
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How to properly punctuate "for all" after mathematical expressions?
One thing about mathematical writing that has always puzzled me is how to properly punctuate "for all" after a mathematical expression. Let me give you an example.
A function $f:\mathbb{R}\...
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Referencing a statement with quantifiers in two separate lines
I want to show that a statement with several quantifiers, e.g., "$f(a, b) <= 0$ for all $a\in [0, 3]$ and all $b\in [-\infty, -1]$", is equivalent to another statement with several ...
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Writing style of mathematical paper.
I want to write a mathematical paper that is tailored for applied mathematics. To be more specific, it is using extensively differential equations and integrals. I observed that there are two ...
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What is the proper notation for cartesian coordinates with decimals in your native language? [closed]
For simple integers, (1, 2) is what most people are taught in elementary school. This appears to be true regardless or whether their language's decimal separator is ...
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In English grammar, is a mathematical expression considered a clause or a noun phrase?
In English grammar, is a mathematical expression considered a clause or a noun phrase?
When I read the mathematical proof, I find that it is not uniform for authors to treat the mathematical ...
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2
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Notation for a fraction of $n!$
Suppose I want to write $n!/2$, can I just write $\tfrac{1}{2}n!$ or is that easily confused with $(\tfrac{1}{2}n)!$ and I have to write $\tfrac{1}{2}(n!)$?
Are there precedence rules for these ...
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Is it incorrect to use ellipses when writing an irrational number's approximate value with a $\approx$?
For example, is it incorrect to write that Euler's number is
$$
e \approx 2.718\dots
$$
or is it more proper to write
$$
e \approx 2.718
$$
or, maybe I should just write
$$
e = 2.718\dots
$$
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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 ...
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