Various aspects of writing mathematics such as style, notation, grammar, frequently used phrases and common mistakes.

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27 views

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 ...
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0answers
17 views

Writing finite field notation

I am trying to write about finite fields in a word document, and although usually writing in latex form works, it's not in this case. It works fine here: $\mathbb{F}$: I used \mathbb{F} But it ...
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0answers
35 views

References of papers published in ArXiv

To prove a theorem I use a result of a paper published in ArXiv. This paper has also been accepted for publication in a journal. In reference I must mention the arXiv or the journal where the paper ...
3
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0answers
41 views

In a math paper, what is a remark?

I sometimes see paragraphs labeled 'Remark.' However, papers that include remarks also include unlabeled explanatory paragraphs (i.e. all the other writing in the article) that seem to be remarks. ...
2
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0answers
28 views

Is there a published standard for the sectioning of math papers?

Most papers seem to use sections (e.g. 3) and sub-sections (e.g. 3.1). Is there a published standard that says what sort of thing warrants its own section and what sort of thing warrants its own ...
3
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0answers
40 views

Formulating equation for distances between atoms

I'm trying to formulate notation to describe code that calculates the distances between protein atoms (represented as points in 3D space). Fragments consist of residues (amino acids) and each residue ...
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1answer
28 views

The use of “consistent with”.

This is a simple question about writing but I'm a little bit confused now about the logic in using "consistent with". The context is as follows: We first derive a formula for a special case, say, for ...
2
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0answers
43 views

a.s. for all $t$ or for all $t$ a.s.?

Assume that we have some equality, $$ X (t) = Y(t). \quad \quad \quad \quad \quad \quad \quad (1) $$ I imagine that if I say "(1) holds a.s. for all $t>0$" it means that $$ P\{X (t) = Y(t) ...
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7answers
858 views

Undergraduate Research Thesis

1. General background information ★ At my university [whose name I will omit] the following practices are customary: ● During their third year of study, students have approximately $4$ ...
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1answer
84 views

Is the phrase “recall that…” an abuse? [closed]

I love how in some proofs delivered formally or informally, you would always encounter the phrase "recall that". The irony here is that you precisely do not recall this notion or formula e.g. the ...
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0answers
23 views

What are best practices when writing (sub)equations?

I wonder when it's preferred or better to use subequations instead of normal equations. I.e. when to use 'normally' numbered equations (e.g. (1), (2), ...) and when to use subequations (e.g. (1a), ...
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1answer
34 views

Notation and Quantifiers

I was wondering what is a natural way to write certain formal expressions, without make them look too cumbersome. In particular, what I learned from various books is that, when we deal with the ...
16
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3answers
280 views

Good examples of mathematical writing (structural organization, style, typesetting, and so on)

A very famous question on MathOveflow asks for examples of good mathematical writing. Here, I'd like to narrow down the topic and ask: $\color{#c00}{\text{Question:}}$ Could you point ...
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2answers
80 views

$1,2,\cdots,n$ or $1,\cdots,n$?

In mathematical writing, when should one write "$1,2,\cdots,n$" and when should one write "$1,\cdots,n$"? It seems to me that writing $1,2,\cdots,n$ is actually wrong if $n=1$ is allowed. When ...
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1answer
47 views

“a” RKHS or “an RKHS” [closed]

I am confused if I should use "a" or "an" before RKHS (reproducing kernel Hilbert space). Since "R" is not a vowel, I think I should use "a". But I saw both on Wikipedia. Can you tell me which is ...
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1answer
56 views

A basic question of basic writing

When we define some term by a notation starting with the word "define" or "let", which of the following is correct? Define $A=x+2y$; or, define $A \equiv x+2y$.
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2answers
180 views

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. ...
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4answers
211 views

Checking that a $3$-D diagram is commutative

When proving certain results I need to use commutative diagrams, some of which quite complicated. My question is: Do we need to check every small square all the time to make sure that they are all ...
0
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0answers
29 views

Name the maps in a commutative diagram

When writing a formal paper sometimes one needs to construct complicated commutative diagrams, such as My question is, should one always give names to all maps in the diagram (perhaps except those ...
1
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1answer
105 views

The word “onto” - adjective?

According to Oxford English dictionary, the word "onto" is preposition only but I see it used as an adjective in mathematical writings. I think it is grammatically correct to say that "$f$ maps $X$ ...
0
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2answers
44 views

How to write in mathematical symbols the expression “range over”

My question is really simple, how can I write symbolically this phrase: $x=\sum a_mx^m$ where $m$ range over $\{1,\ldots,g\}\setminus\{t_1,\ldots,t_u\}$ Being more specific, I would like to ...
2
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1answer
53 views

What is the terminology for “lemma of lemma”

Let's say I need to prove a main theorem, to prove which I need three lemmas. Thus in writing the structure is as follows: Lemma 1 Proof Lemma 2 Proof Lemma 3 Proof ...
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1answer
57 views

How to denote sum over partitions?

How does one denote a sum of partitions of an integer when writing an article? For example, I have a formula regarding an integer-valued variable (say q=5), and I need to write an expression of the ...
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2answers
73 views

What is the difference between an **Article** and a **Paper**? [closed]

What is the difference between an Article and a Paper? Is there anybody(or journal) which will evaluate our article? My thought I am thinking that an article is just explaining or giving details of ...
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2answers
50 views

Functions whose codomain's form depends from the element taken from the domain

As in the title, I have a notational problem regarding functions whose codomain directly depends on the elements taken from the domain. Here there is an example. Let $X$ be a set with $x \in X$. Let ...
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3answers
427 views

Instructive examples of elegant, clear, rigorous, terse, but “non-dull” mathematical prose

On the "About" page of the Mathgen project one can read: "More seriously, I think this project says something about the very small and stylized subset of English used in mathematical writing. ...
2
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3answers
79 views

What kind of definitions need be introduced in a PhD thesis? [closed]

For all the terminology in mathematics, I am not sure where to draw a line between those which need to be introduced in a PhD thesis and those which do not. For example, I suppose that in a PhD ...
2
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2answers
45 views

Should I rephase when quoting a theorem/definition?

Actually I would like to ask two questions and the answers may not be the same. When writing a paper and if one need to introduce a definition, is it alright to just copy-paste from wikipedia/a ...
0
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0answers
57 views

RSA and El Gamal Algorithms

I have to write a short report about RSA and El Gamal algorithms in cryptography. I just need to summarize them (how one would calculate the various components, what their strengths and weaknesses ...
27
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4answers
4k views

Why do proof authors use natural language sentences to write proofs?

I haven't read very many proofs. The majority of the ones that I've read, I've read in my first-year proofs textbook. Nevertheless, its first chapter expatiates on the proper use of English in ...
2
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1answer
37 views

Is there any good reason against referring to employed equations over the relation sign when establishing a new relation?

I need to write down a complicated proof for a paper, for which I need to employ equations that I established earlier for almost every new relation I show. I would consider it best for the reader, if ...
2
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0answers
64 views

First hand written draft Or LaTex typed draft; when some one want to publish? [closed]

When some one solve a math research problem and want to publish it somewhere; of course one should type it in LaTex. My Question: What should be the ideal way(time) to type it, I mean first one ...
5
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2answers
77 views

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 ...
2
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2answers
90 views

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 ...
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8answers
292 views

Mathematicians' manual of style

I know that there are many styles to write citations and footnotes and that they are all equally good (as long as the reference is complete), but I would like to know if mathematicians follow some ...
0
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2answers
126 views

Best practices in notation

I have already read A Primer of Mathematical Writing, by Steven Krantz which gives extremely good advice about writing mathematics. But I would like to collect some more specific suggestion about ...
5
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1answer
101 views

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. ...
0
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1answer
40 views

Points 17 and 18 of Section 1 in Knuth's mathematical writing

I have two questions about Point 17 and 18 of Section 1 in Knuth's math. writing http://tex.loria.fr/typographie/mathwriting.pdf In Point 17, he says "Sentences should be readable from left to right ...
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1answer
36 views

Defining a ball

Which are appropriate phrases to define a ball? Let $B$ be the open ball of radius $r$ centered at $x$. Let $B$ be the open ball of radius $r$ around $x$. Let $B$ be the open ball of radius $r$ ...
3
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1answer
65 views

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 ...
3
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0answers
87 views

Program for writing a Bachelor Thesis. [closed]

Hello Im prolly going to start writing my bachelor thesis really soon (on geometric ergodicidy). It will obviously contain lots of mathematical formulas and symbols. Does anyone know a really good ...
0
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1answer
31 views

How to split long fraction?

I have a fraction with long numerator, $$ \frac{x1+\ldots+x50}{y}. $$ What is preferred in typing? Or something different? (1) $$\frac{x1+x2+}{}\qquad\qquad\qquad\qquad\qquad\qquad\qquad(\text{first ...
2
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0answers
45 views

What is the notation for a sub-expression?

For set theory, we have notation to denote subsets, e.g.: $$S \subset X$$ When working with expressions (arithmetic, Boolean, etc.), is there a notation to denote expression $S$ is a valid ...
2
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3answers
58 views

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 ...
3
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1answer
68 views

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 ...
5
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4answers
193 views

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 ...
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2answers
44 views

Is it right to use % symbol in a formula?

I was told when calculating an error term I shouldn't use: $$ Error = 2\% \ast 100kg $$ But that, formally, I should use: $$ Error = \frac{2 \ast 100kg}{100} $$ Which one is right? Or are ...
6
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0answers
105 views

Use of “I” in mathematics papers

Some people consider the use of "I" in a paper to be a great evil. Others, however, consider the use of the passive voice to be an even greater evil. I will be presenting a paper at a competition, ...
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1answer
65 views

Write theorem conditions concisely

Let $Z$ be a set, $x$ be some object. Let the following statements hold (for some logical formulas $P,P_1,\dots,P_n$ and some logical formula $Q$): $\forall z\in Z:(P(x) \Leftrightarrow Q(x,z))$ ...
5
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2answers
307 views

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? ...