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

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67
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 ...
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 ...
34
votes
5answers
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 ...
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 ...
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 ...
16
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 ...
15
votes
3answers
658 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 ...
15
votes
4answers
671 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 ...
11
votes
4answers
631 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?
10
votes
8answers
814 views

Book about technical and academic writing

I'm in the process of writing my Master's Thesis on automata theory. The writing must be in English which isn't my mother tongue. So the question is, given that this is my first time long (hundred ...
10
votes
0answers
257 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 ...
7
votes
1answer
262 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...''. ...
6
votes
4answers
336 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 ...
6
votes
4answers
455 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 ...
6
votes
1answer
112 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 ...
6
votes
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, ...
5
votes
2answers
257 views

Basic guidance to write a mathematical article.

I'm trying to put together a mathematical article on how to obtain certain infinite series for some well known functions by a method of integrals (I like to call it "The Integral Method" - thank you), ...
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 ...
5
votes
0answers
122 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 ...
4
votes
2answers
239 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? ...
4
votes
4answers
115 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 ...
4
votes
1answer
1k 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.
4
votes
2answers
451 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 ...
3
votes
2answers
175 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 ...
3
votes
2answers
221 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
2answers
144 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 $ ...
3
votes
1answer
190 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
143 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?
3
votes
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 ...
3
votes
1answer
59 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 ...
3
votes
1answer
57 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 ...
3
votes
1answer
259 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 ...
3
votes
0answers
54 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 ...
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 ...
2
votes
3answers
114 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 ...
2
votes
2answers
138 views

Is it bad math style to use the same index symbol in different indexed objects?

The title says it all (I'm referring to the case, when writing for example an article to be published or something similar - something where the writing itself should also be of quality). Example: ...
2
votes
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 ...
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 ...
2
votes
1answer
105 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 ...
2
votes
0answers
63 views

Igor Pak on priority of results in citation [on hold]

Today I saw Igor Pak's post on his issues with citation of priority http://igorpak.wordpress.com/2014/09/12/how-not-to-reference-papers/ I know this is a very human feeling. How important is ...
2
votes
0answers
40 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
votes
0answers
31 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 ...
2
votes
0answers
66 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 ...
2
votes
0answers
47 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, ...
2
votes
0answers
37 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 ...
1
vote
2answers
120 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 ...
1
vote
3answers
457 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 ...
1
vote
1answer
491 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 ...
1
vote
1answer
63 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
3answers
222 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. ...