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

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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
29 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
100 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
85 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
32 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
31 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 $r$ ...
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1answer
54 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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0answers
21 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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15 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 ...
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56 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
16 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
22 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 ...
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1answer
25 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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3answers
231 views

Is there an adjective appropriate for describing mathematical terminology that you feel needs to be phased out? [closed]

Let me firstly apologize; this is more of an English language question, so posting it here is perhaps slightly inappropriate. But I couldn't think of a non-mathematical example, so here we are. ...
2
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0answers
41 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 ...
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3answers
49 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
61 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 ...
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1answer
74 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
30 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 ...
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4answers
117 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
42 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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0answers
98 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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0answers
43 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
256 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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1answer
61 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 ...
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0answers
32 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 ...
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0answers
38 views

Strict rules for determining whether defined objects are necessarily distinct - related to mathematical writing.

I am not a native speaker and I very often wonder whether there are rules (which are still unknown to me) for determining the exact meaning of mathematical statements/sentences. Currently, for many ...
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0answers
124 views

Writing an abstract for a conference

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 ...
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3answers
37 views

Is this form of finite induction correctly called “downward induction”

In a paper I'm writing, I have a lemma of the following form: If $a_1, a_2, \dots, a_n$ is a sequence of type X and $a_n$ has property P, then $a_1, a_2, \dots, a_n$ all have property P. As you ...
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1answer
26 views

Restrict edge set to certain nodes only

Given a graph $G=(V,E \subseteq V \times V)$, an edge set $D \subseteq E$ and a subset of nodes $W \subseteq V$, is there such thing as an established operator for the "restricted" set of $D$: $$ \{ ...
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3answers
685 views

Starting sentences with mathematical symbols.

I apologise if this is a duplicate in any way or is too opinion-based. To what extent is it best not to start a sentence with a mathematical symbol? I find that when trying to solve a problem or ...
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0answers
69 views

Learning to write the style of mathematics texts

When learning how to write articles in mathematics (in style of articles published in journals) is there a good reference listing things like common outlines, style guides, phrases, common mistakes ...
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1answer
86 views

Writing my first mathematical paper

I'm an undergrad student at a community college, and I am currently taking differential equations. My professor is offering people to hand in math papers for either extra credit or even complete test ...
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39 views

When to write the introduction to a paper

Writing the introduction to a paper is obviously a fine art, since it sets up everything that follows. I have often heard it said that you should write the introduction last (or perhaps second to ...
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0answers
18 views

Proper way to mention convergence to zero in continuous text?

What is the proper way to state, that a series/integral/variable/sequence converges to zero in continuous text in academic papers? Would you say "...therefore, the sequence $(x_n)_{n \in \mathbb{N}}$ ...
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7answers
2k views

LaTeX/TeX Vs. Mathematica for Typesetting

I know Mathematica like the back of my hand, but I do not know a speck of $\LaTeX$ or $\TeX$. With regards to mathematical typesetting, is there something significant I can do in $\LaTeX$/$\TeX$ that ...
3
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1answer
60 views

Commas between adjectives [duplicate]

Is it correct to use these expressions without commas (as written below)? A finite simple group. A finitely generated abelian group. A finitely generated torsion-free abelian group. A ...
2
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0answers
48 views

Referencing something that isn't a lemma, proposition etc…

I need to reference a fact that is in another paper. It is stated after a lemma, and follows from this, thought perhaps not very directly. I could just reference it as "see [1, Pg. 5]" or "see [1, ...
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11answers
10k views

Using “we have” in maths papers

I commonly want to use the phrase "we have" when writing mathematics, to mean something like "most readers will know this thing and I am about to use it". My primary question is whether this is too ...
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0answers
35 views

how to write references

How to write the reference number and the page number at the end of Mathematical proof or definition or any mathematical work I mean [number of reference , number of page] or [number of reference ...
3
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2answers
179 views

When writing a mathematical model for non-mathematical audiences, how do you begin a sentence defining a variables and parameters?

Say you are writing a mathematical modeling paper in a science journal. How do you write your variable and parameter definitions in paragraph form so that you keep active voice but do not sound ...
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0answers
65 views

Are forward references in a book OK?

In a math book I wrote, there is one forward reference (I'm sure not a proof loop). Should I work hard to eliminate forward references, or one such ref is OK?
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1answer
2k views

How could I type “not exist” by Latex? [closed]

How could I type "not exist" by Latex? (I can type ``$\exists$''.) Thanks for your help.
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0answers
37 views

Handwriting of special symbol in maths [duplicate]

What are standard ways of writing the symbol ${\mathbb R}$ in handwriting?
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0answers
57 views

What is the best way to express a set in a scientific paper?

I found the bold representation is overly strong, because it really distracts the readers when you have a lot of sets in bold like so: I have a set $\boldsymbol{S}$ and a set $\boldsymbol{P}$ and ...
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0answers
60 views

Is this notation acceptable for sums and integrals?

I prefer to use this notation : $$ S = \sum_{1\leq k \leq n} a_k \\ I = \int_{x_1 \in [a,b]} \int_{x_2 \in [c,d]} dx_2 dx_1 $$ over this: $$ S = \sum_{k=1}^{n} a_k \\ I = \int_{a}^{b} \int_{c} ...
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52 views

Is this sentence OK?

I'm starting to write a paper. This is the sentence which I want to put first in the paper. It is well known that diagonal properties are useful in estimating certain cardinal invariants of a ...
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0answers
272 views

Papers with unorthodox writing style

I'm not sure if this is the right forum for this question, in any case probably CW is appropriate? I've been looking around the mathblogosphere for the past few weeks and ran into mathgen. It's ...
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1answer
38 views

publish in a conference and journal publication [closed]

what's the difference between the same article that are submitted to conference and journal? can someone help me? Thank you in advance
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2answers
124 views

Is readability ignored in mathematics? If so, why? [duplicate]

Most of the math equations use single character as variables name and functions name, there are also Greek alphabets as well. This is not acceptable in programming since it is too difficult to ...