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

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0answers
36 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
45 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
54 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
44 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
26 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 ...
3
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4answers
101 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
41 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 ...
6
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0answers
97 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 $Q$): $\forall z\in Z:(P(x) \Leftrightarrow Q(x,z))$ ...
3
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2answers
221 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
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1answer
57 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
29 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
35 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 ...
5
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0answers
117 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 ...
0
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3answers
34 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
24 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 $D$: $$ \{ ...
15
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3answers
623 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 ...
2
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0answers
64 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
80 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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0answers
38 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
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0answers
16 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 $(x_n)_{n \in \mathbb{N}}$ ...
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 ...
3
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1answer
53 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
44 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, ...
67
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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
162 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
62 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?
3
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1answer
725 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
36 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
56 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} ...
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0answers
51 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 ...
10
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0answers
244 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
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1answer
37 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
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2answers
114 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
218 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
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1answer
70 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
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1answer
89 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
407 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
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1answer
109 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
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6answers
98 views

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

Which is preferable to write: $r2^m$ or $2^m r$?
1
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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
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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, ...
16
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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 ...
16
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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
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1answer
175 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
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2answers
130 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
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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 ...