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

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13 views

Definition of a function whose codomain is set of probability measure over cartesian product with dependency between sets in the product

I am thinking about the following function: $$ p : A \to \Delta \big( F(x, y(t) ) \times T \big) ,$$ where $t \in T$ denotes continuous time, and $\Delta (X)$ denotes the set of all probability ...
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21 views

$\mapsto$ functional notation and probability distributions

I have a question concerning mathematical writing. If we have a function $f: X \to Y$, we can write it \begin{align} f: \ & X \to Y \\ & x \mapsto f(x), \end{align} where $f(x)$ can ...
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26 views

Expressing Math Equations Image Shifting

I'm confused how to express the following expression in math equations for scientific publication: imagex = shifted version of imagey left with z pixels. I thought about this: imagex ...
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1answer
35 views

How to simplify the equation of combination?

If there are three random variables and three related thresholds, how to simplify the following expression by summation or multiply or other operators? Thank you. ...
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2answers
39 views

Concise description of why rotation quaternions use half the angle

I'm currently writing the report on my master thesis project, where I use Android sensors to perform inertial navigation in a heavy industrial environment. In my application, I make use of quaternions ...
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18 views

LaTeX template for NSF attachments? [migrated]

Does anyone have a nice LaTeX file template for the preparation of NSF attachments, please? I hear they are picky about margin sizes, etc. Thank you all.
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17 views

Proper way of adding a glossary to an article

I am thinking of adding a glossary to an article of mine, I was wondering if there is an etiquette regarding adding a glossary of symbols and notations? To be frank I have not seen one in any recent ...
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0answers
40 views

Formulation: Smooth vs. finitely often differentiable

I treat the cases $f\in C^\infty$ and $f\in C^k$ in different sections of my thesis. While I am happy with the title smooth functions for the first section, I am not so sure if finitely often ...
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28 views

Article writing: How to represent a matrix by its elements?

Intuitively I guess that parantheses with subscript and superscripts is a way of representing a matrix or an array by its elements, e.g., $$ A = (a_{i,j})_{i,j=1}^n $$ (This is taken from here) ...
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3answers
380 views

Should I cite the original source or a book?

In the introduction to my thesis, I cite a lot of classical results from the 19th and early 20th century. Should I try and cite the original source for these results, or does that look like I am ...
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1answer
60 views

Two questions regarding mathematical writing

I am a German mathematics student. I have two questions: First question: When writing several equivalent equations, we usually write this as: $x^2 = 4$ $\Leftrightarrow x = \pm 2$ I have never ...
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36 views

How to formally express a negative statement (in the wording or formulation of a theorem, for instance)

This is a doubt about English mathematical formal language. I would like to know the best way to express a negative hypothesis, in the formulation or statement of a theorem, proposition, etc., using ...
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2answers
54 views

Huge case analysis in an article

I am writing this article on a graph related problem. In an important lemma dealing with classification of a type of graphs, I am undergoing this huge and tedious case analysis involving ...
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4answers
624 views

How to learn/speak “mathematical english”?

Good day! I was wondering if there is a good way to learn "maths in english". I am studying mathematics in Germany (I am from Germany, so english is not my native language) and have recently started ...
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4answers
620 views

Why do single-author math papers use “we” instead of “I”? [duplicate]

Even when math papers are authored by one person, you will see stuff like "We now prove so and so" or "In the following section, we show that...". How come papers with one author use "we" instead of ...
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1answer
21 views

Placement of quantifiers in a symbolic statement

I have the statement: Let $A_n$ be an indexed set of numbers defined by $A_n = n\mathbb{Z}_{\geq m}$ for $n,m \in \mathbb{Z}$. Consider the claim C: For all $n$, if $x,y$ is in $A_n$, then ...
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6answers
1k views

What is an adjective for “weaker than weak”?

I defined a notion (say, some kind of equivalence) in three forms, the first implies the second, which in turn implies the third. I would like to use "strong", (nothing), and "weak" to describe them. ...
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2answers
29 views

Proper use of indicator function

Given a set $X$ and a subset $A \subseteq X$ the indicator function $\boldsymbol{1}_{A} : X \rightarrow \{0,1\}$ of $A$ is defined as $$\boldsymbol{1}_{A}(x) = \begin{cases} 1 & \text{if } x \in A ...
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1answer
67 views

Is there a standard name for this “continuous induction” principle?

I am working on a paper, and I want to prove that some statement $P(x)$ holds for every value of a parameter $x \in [0,\infty)$. I plan to proceed as follows: Show that $P(0)$; Show that if $P(x)$ ...
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3answers
81 views

Formal writing in math: equations

What is the formally correct way to solve a bunch of equations in math? Is it \begin{align} 42x = 4324 \\ x = 4324/42 \end{align} or \begin{align} 42x = 4324 \\ \Rightarrow x = 4324/42 \end{align} or ...
3
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1answer
55 views

Is there a name for this curve? Or, how should I describe the behavior of this graph (in words)?

I simulated some results that look like this: but I don't want to include the plot (my advisor is keeping me to a strict limit on figures and these are minor intermediate results). Is there a name ...
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1answer
23 views

How should I describe this limiting operation in an equation

In the code I've written, I receive a delta between two position vectors, I then limit this delta by a maximum delta and return the value. To be clear: the direction of the vector remains the same, ...
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1answer
70 views

Referencing a Theorem in a Paper?

I'm making the final edits for a paper and I have a question more about the etiquette. I want to use a theorem from another paper and its obvious I have to cite it, but do I need to prove it too? I ...
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0answers
22 views

Writing finite field notation

I am trying to write about finite fields in a word document, and although usually writing in latex form works, it's not in this case. It works fine here: $\mathbb{F}$: I used \mathbb{F} But it ...
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45 views

References of papers published in ArXiv

To prove a theorem I use a result of a paper published in ArXiv. This paper has also been accepted for publication in a journal. In reference I must mention the arXiv or the journal where the paper ...
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132 views

In a math paper, what is a remark?

I sometimes see paragraphs labeled 'Remark.' However, papers that include remarks also include unlabeled explanatory paragraphs (i.e. all the other writing in the article) that seem to be remarks. ...
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0answers
30 views

Is there a published standard for the sectioning of math papers?

Most papers seem to use sections (e.g. 3) and sub-sections (e.g. 3.1). Is there a published standard that says what sort of thing warrants its own section and what sort of thing warrants its own ...
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0answers
43 views

Formulating equation for distances between atoms

I'm trying to formulate notation to describe code that calculates the distances between protein atoms (represented as points in 3D space). Fragments consist of residues (amino acids) and each residue ...
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1answer
29 views

The use of “consistent with”.

This is a simple question about writing but I'm a little bit confused now about the logic in using "consistent with". The context is as follows: We first derive a formula for a special case, say, for ...
2
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0answers
46 views

a.s. for all $t$ or for all $t$ a.s.?

Assume that we have some equality, $$ X (t) = Y(t). \quad \quad \quad \quad \quad \quad \quad (1) $$ I imagine that if I say "(1) holds a.s. for all $t>0$" it means that $$ P\{X (t) = Y(t) ...
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8answers
1k views

Undergraduate Research Thesis

1. General background information ★ At my university [whose name I will omit] the following practices are customary: ● During their third year of study, students have approximately $4$ ...
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1answer
168 views

Is the phrase “recall that…” an abuse? [closed]

I love how in some proofs delivered formally or informally, you would always encounter the phrase "recall that". The irony here is that you precisely do not recall this notion or formula e.g. the ...
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27 views

What are best practices when writing (sub)equations?

I wonder when it's preferred or better to use subequations instead of normal equations. I.e. when to use 'normally' numbered equations (e.g. (1), (2), ...) and when to use subequations (e.g. (1a), ...
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1answer
36 views

Notation and Quantifiers

I was wondering what is a natural way to write certain formal expressions, without make them look too cumbersome. In particular, what I learned from various books is that, when we deal with the ...
16
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3answers
304 views

Good examples of mathematical writing (structural organization, style, typesetting, and so on)

A very famous question on MathOveflow asks for examples of good mathematical writing. Here, I'd like to narrow down the topic and ask: $\color{#c00}{\text{Question:}}$ Could you point ...
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2answers
81 views

$1,2,\cdots,n$ or $1,\cdots,n$?

In mathematical writing, when should one write "$1,2,\cdots,n$" and when should one write "$1,\cdots,n$"? It seems to me that writing $1,2,\cdots,n$ is actually wrong if $n=1$ is allowed. When ...
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1answer
52 views

“a” RKHS or “an RKHS” [closed]

I am confused if I should use "a" or "an" before RKHS (reproducing kernel Hilbert space). Since "R" is not a vowel, I think I should use "a". But I saw both on Wikipedia. Can you tell me which is ...
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1answer
56 views

A basic question of basic writing

When we define some term by a notation starting with the word "define" or "let", which of the following is correct? Define $A=x+2y$; or, define $A \equiv x+2y$.
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2answers
315 views

Using Comma in if…then Conditional Sentences

Many English grammar books state that in an "if ... then" conditional sentence, the word then should be preceded by a comma. However, in mathematical writing I often see that this rule is ignored. ...
12
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5answers
239 views

Checking that a $3$-D diagram is commutative

When proving certain results I need to use commutative diagrams, some of which quite complicated. My question is: Do we need to check every small square all the time to make sure that they are all ...
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38 views

Name the maps in a commutative diagram

When writing a formal paper sometimes one needs to construct complicated commutative diagrams, such as My question is, should one always give names to all maps in the diagram (perhaps except those ...
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1answer
127 views

The word “onto” - adjective?

According to Oxford English dictionary, the word "onto" is preposition only but I see it used as an adjective in mathematical writings. I think it is grammatically correct to say that "$f$ maps $X$ ...
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2answers
120 views

How to write in mathematical symbols the expression “range over”

My question is really simple, how can I write symbolically this phrase: $x=\sum a_mx^m$ where $m$ range over $\{1,\ldots,g\}\setminus\{t_1,\ldots,t_u\}$ Being more specific, I would like to ...
2
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1answer
54 views

What is the terminology for “lemma of lemma”

Let's say I need to prove a main theorem, to prove which I need three lemmas. Thus in writing the structure is as follows: Lemma 1 Proof Lemma 2 Proof Lemma 3 Proof ...
4
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1answer
85 views

How to denote sum over partitions?

How does one denote a sum of partitions of an integer when writing an article? For example, I have a formula regarding an integer-valued variable (say q=5), and I need to write an expression of the ...
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2answers
88 views

What is the difference between an **Article** and a **Paper**? [closed]

What is the difference between an Article and a Paper? Is there anybody(or journal) which will evaluate our article? My thought I am thinking that an article is just explaining or giving details of ...
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2answers
58 views

Functions whose codomain's form depends from the element taken from the domain

As in the title, I have a notational problem regarding functions whose codomain directly depends on the elements taken from the domain. Here there is an example. Let $X$ be a set with $x \in X$. Let ...
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3answers
476 views

Instructive examples of elegant, clear, rigorous, terse, but “non-dull” mathematical prose

On the "About" page of the Mathgen project one can read: "More seriously, I think this project says something about the very small and stylized subset of English used in mathematical writing. ...
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3answers
88 views

What kind of definitions need be introduced in a PhD thesis? [closed]

For all the terminology in mathematics, I am not sure where to draw a line between those which need to be introduced in a PhD thesis and those which do not. For example, I suppose that in a PhD ...
2
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2answers
58 views

Should I rephase when quoting a theorem/definition?

Actually I would like to ask two questions and the answers may not be the same. When writing a paper and if one need to introduce a definition, is it alright to just copy-paste from wikipedia/a ...