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

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31
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4answers
2k views

How to write a good mathematical paper?

I hesitate to ask this question. However I read many advices from math.stackexchange, and I couldn't find anything similar. A good time always goes too fast! Two years are fled. In the third year of ...
6
votes
0answers
83 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, ...
0
votes
0answers
34 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 $Q$): $\forall z\in Z:(P(x) \Leftrightarrow Q(x,z))$ ...
3
votes
2answers
139 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? ...
0
votes
1answer
53 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 But I get unnerved because I got a feeling it's pretentious or outdated.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
votes
0answers
24 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 ...
5
votes
0answers
114 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 ...
2
votes
0answers
28 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 ...
15
votes
3answers
536 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 ...
0
votes
3answers
32 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 ...
1
vote
1answer
23 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 $D$: $$ \{ ...
2
votes
0answers
60 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 ...
0
votes
1answer
71 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 ...
20
votes
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 ...
1
vote
0answers
37 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 ...
1
vote
0answers
13 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 $(x_n)_{n \in \mathbb{N}}$ ...
65
votes
11answers
9k 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 ...
3
votes
1answer
44 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
votes
0answers
40 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, ...
1
vote
0answers
34 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
votes
2answers
142 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 ...
1
vote
0answers
55 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?
4
votes
2answers
338 views

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 ...
2
votes
1answer
168 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.
1
vote
0answers
36 views

Handwriting of special symbol in maths [duplicate]

What are standard ways of writing the symbol ${\mathbb R}$ in handwriting?
6
votes
4answers
314 views

Should I include obvious steps in mathematical paper?

I am writing a formal school paper (by formal I mean, with an abstract, a bibliography and 20 pages in length) on mathematics (it is called 'Extended Essay,' for those having knowledge of the ...
1
vote
0answers
53 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 ...
0
votes
0answers
56 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} ...
0
votes
0answers
49 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 ...
14
votes
14answers
2k views

What are better words to use in an article than “obvious”?

I've heard often than it is ill-form to use the word "obvious" in a research paper. I was hoping to gather a list of less offensive words that mean generally the same thing. For example, one that I ...
10
votes
0answers
211 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 ...
0
votes
1answer
36 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
1
vote
2answers
106 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 ...
7
votes
1answer
138 views

What is “observation”?

Often in mathematical writing one encounters texts like ''..we observe that this-and-that..''. Also one may find a review report basically saying ''..the paper is just a chain of observations...''. ...
1
vote
1answer
64 views

Shouldn't we refer to an inequality as an 'inequality' instead of an 'equation'?

As far as I'm concerned, an equation is any mathematical statement of the form LHS=RHS, an inequality is any mathematical statement of the form LHS?RHS (where ? is a placeholder for some inequality ...
0
votes
1answer
82 views

Lattice Squares; Basic Interesting Facts and Problems

I'm going to write an article in an educational magazine for middle school students, about the game Square It. The purpose of the game is to make lattice squares: I want to introduce the game, and ...
5
votes
1answer
97 views

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 ...
0
votes
6answers
96 views

Which one is preferred: $r2^m$ or $2^m r$? [closed]

Which is preferable to write: $r2^m$ or $2^m r$?
1
vote
1answer
58 views

Mathematica code as reference?

I am preparing a paper wherethere are a lot of algebraic simplifications needed. One of them takes 3 pages to get the result. Instead of consuming all the pages can I cite a mathematica code which is ...
1
vote
0answers
74 views

Stylish Academic Writing [duplicate]

I don't know that this question belongs here, but I'd like to know of any references out there anyone here might recommend for writers of mathematical ideas, be it a book, an article, a dissertation, ...
2
votes
3answers
68 views

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 ...
16
votes
7answers
1k views

Mathematical writing: why should we not use the phrase “we have that”?

In Knuth's Mathematical Writing, he writes on page 2, at number 8: Don't omit "that" when it helps the reader to parse the sentence. Bad: Assume $A$ is a group. Good: Assume ...
3
votes
1answer
158 views

Commas separating adjectives to describe mathematical objects.

Is there a convention which rules that in mathematics an object with some properties should be referred to as a "property 1 property 2 property 3 ...object" rather than a "property 1, property 2, ...
3
votes
2answers
114 views

When to begin a new paragraph?

When writing a mathematical article, when should someone begin a new paragraph? Is there some specific rule or convention? And more generally, what rules are there about articles-writing?
0
votes
1answer
29 views

Is $X$ has a strong rank 1-diagonal?

Definition 1: A space $X$ has a strong rank 1-diagonal \cite{5} if there exists a sequence $\{\mathcal U_n: n\in \omega\}$ of open covers of $X$ such that for each $x\in X$, $\{x\}=\bigcap ...
0
votes
1answer
32 views

How could I define this $\mathrm{nw}(X)$ by using only one sentence?

A family $\mathcal N$ of subsets of a topological space $X$ is a network for $X$ if for every point $x\in X$ and any neighbourhood $U$ of $x$ there exists an $M \in \mathcal N$ such that $x\in M ...
5
votes
1answer
75 views

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 ...
0
votes
1answer
62 views

Could someone help me to improve the proof writing?

I will prove the following claim. I'm not a native English speaker. Could someone help me to improve the writing? A regular pseudocompact Moore space is ccc and first countable. Prove: I will ...
0
votes
1answer
89 views

What is the most appropriate way to cite others' results as a Lemma?

Recently I am writing something up for possible publication. I am struggling with this question: What is the most appropriate way to cite others' results as a Lemma? For example, this is a ...
1
vote
1answer
164 views

Math Behind the Game “Quoridor”

I'm going to write an article for middle school students to introduce them to the game "quoridor". Tha game certainly is interesting, but it will be great to add to the article some serious "math ...