article writing - How to briefly mention that you answered someone's question without seeming dismissive?

I'm writing my first paper. I would like to mention at the end that I have answered someone's question that is related to the subject of the paper. The proof is really short and doesn't use any original techniques, so I probably will not include it. The question is, how do I mention that I solved the problem without seeming dismissive, as if the solution was not worth the ink?...Read more

Grammar Mistakes in Math Writing

May be my question is simple. But this question is confused me. In fact, I want to present a lecture and I don't want to have grammar mistakes.My question: which one is correct?A: Let $\mathbb{F}_q$ denote the finite field with $q$ elements. Considerthe two elements $\alpha$ and $\beta$ in $\mathbb{F}_q$. B: Let $\mathbb{F}_q$ denote the finite field with $q$ elements. Considertwo elements $\alpha$ and $\beta$ in $\mathbb{F}_q$. In other language, I really like to understand how to use the word the in math writing. ThanksEdited based on the @u...Read more

Writing a mathematical work in english

this question is less about mathematics, but I don't know else where to ask.I am native to german and have to write my current thesis in english. This is difficult and new to me so i asked my professor, if there is any help to improve creativeness and variety in formulating mathematical sentences in english. His answer was that he guesses by now there should be such literature for mathematical writing in english but he doesn't know any title. I couldn't find any, either.So here is my question:Do you know any literature or source for this? (This...Read more

article writing - 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 textbook/a paper, or should one at least rephrase it a little bit?If I need to copy a theorem from an old paper, is it better just to copy exactly the theorem as it is, or should I rephrase it to make it in harmony with my notation/modern terminology, etc.?...Read more

Math writing from code- how to write equations?

I have written code (in R) for my research project and am trying to publish a paper. Is there a good guide on how to take the concepts in my code and write them in a paper mathematically?Specifically, I have two questions:How do I write that a number has to be a divisor? Is it: If a|b, then... where a is one of the divisors of b?If I have an array of indices v, how do I define the values of another array, G, at the index values $\bar{v}$? Is it: $G_{v}= \ $ or maybe $G_{\bar{v}}= \ $?For example, in my project, objects exist along an axis Z. Th...Read more

article writing - 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. Here is a sentence taken from Higham's Handbook of Writing for Mathematical Sciences: If $\alpha>-1$ then the integral does not exist.Since the book is intended for writing mathematics correctly and this structure has appeared in many places inside it, lack of a comma in the above sentence cannot be a simple typo. Does anyone know the reason for t...Read more

article writing - The following question is about the expression "The following."

In a mathematical document,it is common to have some English prose leading into a mathematical displayand continuing after it.The display is some computation or equation, written symbolically,centered and with some space above and below.Technically the display can be part of the same paragraph as the writing before and after it.I have found this can be a bit awkward grammatically especially the frequency with which it happens.By the way I'm a PhD student in the process of writing my thesis so I'm thinking about these kinds of things a lot.First...Read more

article writing - How to write concise mathematical answer

I have a question which is: $71\sinh(x)+29\cosh(x)=5$ where $x\in R$At degree level how would I make this as mathematically concise and accurate as possible? Or is this acceptable?$71sinh(x)+29cosh(x)=5$$71(\exp(x)-\exp(-x))+29(\exp(x)+\exp(-x)=10$$100\exp(x)-42\exp(x) = 10$$50\exp(2x)-5\exp(x)-24=0$$\exp(x)={\frac {5\pm\sqrt{25+4*50*24}}{100}}$$\exp(x)=0.7$$x=\ln({\frac7 {10}})$...Read more

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 repetitive. For example"$x$ is the average rate of change of ..."Variable name followed by "is" sounds correct, but this must be frowned upon due to capitalization issues. Perhaps you could write,"The average rate of change of ... is [called] $x$"This is passive voice. We tend to use in proofs,"Let $x$ be the rate of change of ..."But this gets repetitiv...Read more

article writing - Proper way to write a mathematical theorem

Consider the Bernoulli Inequality, for instance. Basically it says the following: For all $x\in\mathbb{R}$ such that $x\geq -1$ and all $n\in\mathbb{Z}^+$, we have that $(1+x)^n \geq 1+nx$. I'm concerned about the equivalent ways to rephrase this result, and if they are correctly written. I'm gonna put here two of them. 1) Let $x\in\mathbb{R}$ be such that $x\geq -1$ and let $n\in\mathbb{Z}^+$. Then $(1+x)^n \geq 1+nx$. 2) If $x\in\mathbb{R}$ is such that $x\geq -1$ and $n\in\mathbb{Z}^+$, then $(1+x)^n \geq 1+nx$.In the item 1), includin...Read more

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 identification of a forbidden subgraph. Even though each individual case is often very simple, but for the sake of rigor, I am pushing the analysis grind day and night. My only concern is that if a referee finds writing these cases involving easy identifications rather silly and picks up a bad vibe about an otherwise good article. Of course, to make sure that t...Read more

The Difference Between "be" and "is" in math writing

When I want to write a paper, two problems bother me in my math writing!First: what is the difference between be and is or are in math writing? For example, when I want to begin a theorem, I do not know if I should start with "Let $X$ be $Y$" or "Assume $X$ is $Y$". In some situations, it is really difficult to decide whether be is better or is.Second: I do not know why but several times I used the expression as follows. For example, when I want to define Vandermonde matrix, I usually write as follows and I do not know which format is better o...Read more

In-line writing of a function and of a particular value of it

Say I have a simple expression such as$$y = \frac{x}{\sqrt{x^2 + p}}$$where $x,y$ are variables, $x> 0$, and $p$ is a parameter.I also want to highlight in the same line that $y = 1$ for the special choice $p = 0$. Added If there's room for such nuances in mathematical writing, this is a sort of additional remark, meant to highlight more the role of $p$ than the final effect that $y = 1$. I am not setting this function myself, it comes from prior knowledge. In words, it would sound like 'and look at this special case, by the way'.So I was te...Read more

article writing - How to use of "the" before known matrices

I am writing a paper and want to use Vandermonde matrices in its abstract.I am confused which of the following sentences are correct? A) One of the important matrices in coding theory is the Vandermonde matrix. B) One of the important matrices in coding theory is Vandermonde matrix. C) One of the important matrices in coding theory is Vandermonde matrices.Thanks for any suggestions....Read more