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

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1answer
35 views

“a” RKHS or “an RKHS” [on hold]

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
52 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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1answer
99 views
+50

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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0answers
10 views

List of hundreds of elements

In a formal writing I need to list the following elements in order: $a_1=[x_1,x_2,x_3],a_2=[x_1,x_3,x_2],a_3=[x_2,x_1,x_3],a_4=[x_2,x_3,x_1],a_5=[x_3,x_1,x_2],a_6=[x_3,x_2,x_1]$. ...
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24 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 ...
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0answers
22 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 ...
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0answers
67 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 $X$ ...
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2answers
25 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 ...
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1answer
52 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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0answers
36 views

Precedence table for mathematical symbols (like in programming languages, e.g. C/C++)

I want to write long expressions which include the common "standard" math symbols like $\in$, $<$, $\forall$, $+$, $\cdot$, $\land$, $\lor$, $\Rightarrow$, $\sum$, ... Only for $+$ and $\cdot$, I ...
4
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1answer
43 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
70 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
48 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 ...
8
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3answers
404 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. ...
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3answers
74 views

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

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 ...
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2answers
36 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 ...
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0answers
31 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 ...
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41 views

Reference in other languages

In the reference of many papers there are usually papers/books which are not written in English; some German, some French, some Russian, etc. (I seldom see Chinese or Arabic ones, although there are ...
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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 ...
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1answer
36 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 ...
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0answers
37 views

proofs without using symbols/notations

I am looking for a big list of mathematical proofs which only use pure text, without introducing symbols and extra notations.
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1answer
38 views

Formating equations in a scientific paper

When I write derivations that spread over several lines, I use the following format $V(x) = x^2 - 2x + 1$, from (3) $= (x-1)^2$ $> 0, because x > 0$ ...
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0answers
61 views

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

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 ...
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2answers
69 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
67 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
261 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 ...
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0answers
31 views

trends in mathematics

I study mathematical modelling and was asked to prepare a translation of an article for the English classes. So I want to find something up to date, that would help me to choose the direction of my ...
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2answers
114 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
93 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. ...
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1answer
37 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
32 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
61 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 ...
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24 views

What is the established way to write evaluation of function?

Outside of mathematics, we hardly get to see lambda calculus. Thus, showing something like (domain definition omitted) $$(z\mapsto z^2\sin\pi z)(1/2)$$ will probably not make sense to readers from ...
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20 views

Uniform convergence with respect to a parameter

So this is just a notational question. Assume one has a sequence $f_n\to f$ uniformly, where $f_n,f:X\to Y$ for some metric/Banach spaces $X,Y$. Now suppose that $f_n$ and $f$ depend on a parameter ...
3
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0answers
76 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 ...
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0answers
23 views

Phrases for uniform boundedness and uniform convergence

I have some doubts about using prepositions. I. Let $f_a : \mathbb{R} \to \mathbb{R}$, $f : \mathbb{R} \to \mathbb{R}$. Assume that $f_a (x)$ converges uniformly to $ f (x)$, $x \in [0;1]$, as $a ...
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0answers
23 views

Usage of the phrase “constant parameter”

In general, constants are globally fixed, while parameters are a bit more free. But suppose I wish to use the word "constant" as an adjective to emphasize that a parameter is fixed w.r.t. other ...
0
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1answer
28 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 ...
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0answers
44 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
55 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
66 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 ...
0
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1answer
105 views

Writing a chain of implications in English

How to write a theorem of the form $A\Rightarrow B\Rightarrow C\Rightarrow D$ where every $A$, $B$, $C$, $D$ are formulated with words (English) rather than with formulas? One idea: The next item of ...
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1answer
33 views

What is the best way to express a complex modulus squared in text?

I am looking for a way to describe the fact that I am taking a modulus squared in text. E.g. "inserting the potential (Eq. 1) into the expression for the wavefunction coefficients (Eq. 2) and taking ...
5
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4answers
179 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 ...
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101 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
62 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 $Q$): $\forall z\in Z:(P(x) \Leftrightarrow Q(x,z))$ ...
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2answers
281 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? ...
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3answers
100 views

Use of the word “shall” in mathematical writing

Sometimes I really want to use the word "shall" in my writing. But I get unnerved because I got a feeling it's pretentious or outdated. Any opinions? Is it a nice variation on "will"? Other ...
2
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0answers
39 views

On ambiguity in statements expressed in natural language, where the statements use an indefinite article, e.g. “a”.

Please consider the following example statements and judge the meaning of the article "a". Example: A house is a building. Example: A house is being built next to our house. In example 1, "a" is ...