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

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20
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7answers
3k 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
votes
1answer
72 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
54 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, ...
68
votes
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 ...
1
vote
0answers
36 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
194 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
68 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?
5
votes
1answer
3k 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
38 views

Handwriting of special symbol in maths [duplicate]

What are standard ways of writing the symbol ${\mathbb R}$ in handwriting?
1
vote
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 ...
0
votes
0answers
61 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} ...
11
votes
0answers
296 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
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
1
vote
2answers
128 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
352 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
81 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
124 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 ...
4
votes
2answers
501 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 ...
6
votes
1answer
122 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
100 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
64 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
75 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, ...
16
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 ...
2
votes
3answers
69 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 ...
17
votes
7answers
2k 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
204 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
162 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
35 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
81 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
67 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
94 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
237 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 ...
2
votes
3answers
115 views

Should I put interpunction after formulas?

I am presently doing my first substantial piece of mathematical writing, hence this, probably somewhat silly, question. How does display-style mathematics interact with punctuation? More ...
0
votes
2answers
95 views

Is there something wrong with this statement?

Is this sentence OK or is there something wrong? "Hausdorff is a very weak separation axiom for one to discuss whether the space is metrizable." Do you have a better expression?
1
vote
1answer
120 views

Looking for a better way of expressing this statement

I'm writing an article on topology recently. I'm not good at English writing. It may be good for me to post this question somewhere else; however, I prefer to post here, as it is related to math. My ...
6
votes
4answers
500 views

Are there rules in the useage of prepositions in Math?

It is often to use prepositions in various expressions. E.g. $2$ is in the set of natural numbers $\mathbb N$ The symmetric group on 3 letters $S_3$ is the group consisting of all possible ...
2
votes
1answer
106 views

An article for some undergraduate journal

I'm a student and last year I attended some courses about algebraic geometry. Referring to many books, I wrote personal notes explaining the Cech cohomology of sheaves and some of its applications in ...
1
vote
3answers
486 views

Looking for philosophical subject for my Bachelor Thesis

In may 2013 I have to write a Bachelor Thesis for my bachelor Mathematics. I prefer to choose a subject which involves philosophy. At the same time I have the feeling that my university wants me to ...
60
votes
5answers
2k views

How are mathematicians taught to write with such an expository style?

I wasn't sure if this question was appropriate for MSE. One of the major complaints we see in industry is a person's ability to communicate which includes writing. We see the same thing on questions ...
6
votes
4answers
345 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 ...
3
votes
1answer
273 views

Writing small numbers in Articles [closed]

In primary school I learned that numbers less than 13 should be spelled out in writing. I am suddenly not sure anymore, how I should handle this situation when it comes to article writing in ...
1
vote
1answer
717 views

LaTeX help - multiple answers using set bracket / cases [closed]

I'm brand new to LaTeX and am writing up a dissertation. I have read through several LaTeX guides but have not been able to find the answer there. Does anybody know how to use this ...
2
votes
0answers
46 views

How would you write this sentence

I'm writing a short document about an integer programming (IP) problem instance. I've mentioned that IP is known to be NP-Hard, but that being NP-Hard doesn't automatically qualify this particular ...
11
votes
4answers
651 views

Short forms like “haven't”, “don't”, “let's” [closed]

Is it true that short forms like "haven't", "don't", "let's" should not be used in serious mathematical texts?
2
votes
3answers
184 views

Publishing an article after a book?

If I first publish an article, afterward I may publish a book containing materials from the article. What's about the reverse: If I first publish a book does it make sense to publish its fragment as ...
39
votes
5answers
3k 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 ...
3
votes
2answers
224 views

Can mathematical definitions of the form “P if Q” be interpreted as “P if and only if Q”? [duplicate]

Possible Duplicate: Alternative ways to say “if and only if”? So when I come across mathematical definitions like "A function is continuous if...."A space is compact ...
3
votes
3answers
168 views

Shorthand for $0<i<1$ , $0<j<1$, $0<k<1$

Is it good style to write $0<i<1$, $0<j<1$, $0<k<1$ as $0<i,j,k<1$? The following does not seem so clear: $0<i,j<1$ as it may be interpreted as: $0<i $ and $ ...
17
votes
4answers
715 views

Advice for writing good mathematics?

It's been a (far-fetched, possibly) goal of mine to some day write a math Textbook. I've been thinking about writing this question for a while, but reading an exceedingly mediocre text on Mathematical ...