Questions tagged [mathematical-writing]

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18
votes
2answers
2k views

Can the place of publication be harmful to one's reputation?

What can be said about publishing mathematical papers on e.g. viXra if the motivation is its low barriers and lack of experience with publishing papers and the idea behind it is to build up a ...
3
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1answer
440 views

What are some efficient ways to keep a note of results when reading a research article in mathematics?

I learn and produce mathematics. In that process, I had to read quite a number of research articles. Question : What are some efficient ways to keep a note of results when reading a research ...
3
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2answers
557 views

What does the abbreviation “p.p.” mean in the context of convergence [closed]

What does the abbreviation "p.p." mean when referring to convergence? E.g. in the following paper by Harry Pollard THEOREM. If $f \in L^p$ for some $p$ in the range $\tfrac{4}{3} <p < \infty$,...
9
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0answers
343 views

Including alternative proofs

Suppose I have found two or even more proofs of a theorem and I prepare a paper on it. Is it considered to be a good practice to write down all of them? Or is it considered to be my job as an author ...
2
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0answers
104 views

Specific versus general in titles of papers [closed]

It may not be possible to use mathoverflow in the way I'm hoping to, but my question is this: Should the title of a research paper in mathematics be as accurate and specific as possible (at the cost ...
2
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0answers
97 views

Comma usage when defining symbols [closed]

Consider the following sentence that introduces a symbol, $f$, used later in the text (not shown): A classifier is a function $f$, which takes an image as input and produces a label as output. ...
26
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1answer
2k views

How can I improve my formal definitions?

I am a Software Architect and not very familiarized with standard notation in mathematics. Nonetheless, I would like to write a paper explaining a normalization of a computing model for expert systems....
24
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2answers
1k views

Why would one number theorems, propositions and lemmas separately?

When it comes to numbering results in a mathematical publication, I'm aware of two methods: Joint numbering: Thm. 1, Prop. 2, Thm. 3, Lem. 4, etc. Separate numbering: Thm. 1, Prop. 1, Thm. 2, Lem. 1,...
22
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8answers
3k views

How do we explain the use of a software on a math paper?

Suppose one has written a math/computer science paper that is more focused in the math part of it. I had a very complicated function and needed to find its maximum, so I used Mathematica (Wolfram) to ...
1
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0answers
185 views

When writing a research paper, what is the acceptable format for acknowledging my advisor?

I am writing a paper for an independent study course I am enrolled in. I have contributed all of the work to the project. My supervisor has been a guiding force during this research, suggesting things ...
1
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0answers
84 views

What exactly is and is not a concentration inequality?

Hoeffding's inequality is surely a concentration inequality. It can be written in the form: $\Pr(\bar X + f(n,\delta) \geq \mu) \geq 1-\delta,$ for some function $f$, where $X$ is a set of i.i.d. ...
47
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9answers
4k views

Examples of Mathematical Papers that Contain a Kind of Research Report

What are examples of well received mathematical papers in which the author provides detail on how a surprising solution to a problem has been found. I am especially looking for papers that also ...
2
votes
2answers
703 views

Would a journal such as Bulletin of the AMS accept an article from a student? [closed]

I am a masters student, and am currently writing an expository article on an area of applied maths for a class project. I plan to work on it for several more months. One of my major goals is to ...
14
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2answers
764 views

How to handle results from an unpublished paper?

I am writing a paper right now, and part of the paper makes use of a (trivial) generalization of a number of really nice theorems and constructions from a paper that was never made public. The author ...
7
votes
2answers
707 views

How Much Flesh to the Bones does an Initial Online Publication need?

Background of my question is the following: I have found a solution for my question Smoothness Conditions for Planar “Mock-parametric” Spline Interpolation and while developing the solution, I ...
33
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6answers
5k views

Obsessive editing/revising of math papers

I've been wanting to ask this question, because I have no insights into the way other mathematicians prepare papers (for eventual publication). How much are editing, revising, updating, adding to, ...
21
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8answers
3k views

Mathematical Writing: Proof Outlines/Overview in a Paper

While my question topic is that of mathematical writing of papers, which is a broad subject, the particular question is specific. I am writing a paper, in which we have a section called "Outline of ...
42
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5answers
3k views

Explaining the Main Ideas of Proof before Giving Details

I'll be the first to admit that this is a risky question to try to get away with on math overflow, but I'm going to give it a shot anyway. Roughly speaking, the question is this: Is it good to try to ...
29
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2answers
1k views

Is it possible to cite a page in n-Lab in a research paper?

One of the concepts I need in my paper is best summarized on the n-Lab page. I tried my best to find a similar description of the same concept in a more "classical" reference, such as a paper or a ...
7
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3answers
2k views

Which affiliation to use when publishing, when invited professor at second university

I am a PhD student at one university and an invited professor at a second, i.e. I do not have a permanent position in the second one. Now I need to indicate an affiliation in a journal paper but I do ...
80
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6answers
7k views

What’s the etiquette on using diagrams that need color to be understood?

I’m working on a paper that makes heavy use of colorful diagrams to supplement the text. For most of these it would probably not be possible to create grayscale versions that convey the same ...
21
votes
5answers
921 views

Illustrating mathematics with wysiwyg tools

What tools are out there for creating mathematical illustrations in a what-you-see-is-what-you-get mode? Having struggled with tikz for several years, I've found creating figures in Omnigraffle (...
26
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5answers
2k views

Main statement as theorem or corollary

In a text there will often be a few important results that are usually called Theorems. Intermediate statements are called Lemmas, and statements that follow immediately from previous results are ...
20
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4answers
3k views

Using a known result without a specific reference

This is a question of mathematical writing. Let me know if it would be better suited to academia.SE. I am writing a paper in invariant theory. It uses some slightly heavy commutative algebra. There ...
10
votes
1answer
1k views

How are constants/functions named after their discoverer?

In general, when a paper references an object discovered/defined in another paper by author X, it goes something along the lines of: "Let $\tau$ be the constant defined by X in 1999 [1]$\ldots$", or ...
10
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2answers
673 views

Examples of (Git) open math (texts) projects

I am an active part of a research project on the positive effects of open math projects on the community. With open math projects I have in mind a particular thing, namely a GIT project on mathematics ...
38
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5answers
5k views

How to improve writing mathematics?

My first language is not English. How can I improve my mathematical writing. I feel like the only things I can write down are numbers and equations. Is there any good suggestion for improving writing, ...
2
votes
2answers
207 views

Expanding a combinatorial argument involving permutation coefficients

I have spent more time thinking than I would like to admit because of the following sentence: "Choose $t = c_6X^{1/e}$ and we obtain Theorem 2.". What obvious argument am I missing that allows us to ...
7
votes
3answers
634 views

Notable examples of syntactic proofs whose existence is guaranteed by completeness, but having been found later than a semantic proof?

Question. What are examples (preferably documented and explicitly commented on from this perspective in the literature, preferably in an article dedicated to this aspect alone) of the following well-...
15
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2answers
1k views

Rights to edit “Archives Grothendieck”

The Archives Grothendieck are now "Archives en accès libre", I would like to know if one can edit them... I would like to take an excerpt (split some pages of the archive i.e. from page 10-30 of ...
2
votes
2answers
206 views

Technical term for representing object of a presheaf determined by a left-adjoint?

If $\mathcal{D}$ is a locally-small category, then a functor $F\colon\mathcal{C}\rightarrow\mathcal{D}$ has a right-adjoint if and only if for each object $d$ of $D$, the presheaf $$\mathcal{C}^{\...
19
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4answers
2k views

Reproving a known theorem in an article

Suppose one wants to use a theorem that was published quite a long time ago (+80 years) in a paper that is using a terminology and notations that are very much out-dated (making the paper very hard to ...
2
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0answers
110 views

General treatments of the problem of extending a functor from a small category to its power set to an endofunctor on it?

Suppose you analyse a small category $\mathsf{C}$ whose set of objects you again denote by $\mathsf{C}$. Suppose you have found a natural categorical structure on $2^{\mathsf{C}^{\mathrm{op}}}$ (...
3
votes
1answer
252 views

Usual technical term for replacing a set by the set of singletons of its members?

What is a standard technical term in axiomatic set theory for the operation which sends a given set $A$ to the set $A':=\{\{a\}\colon a\in A\}$? (Replacement implies that $A'$ is a set.) Some ...
44
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3answers
2k views

Citing exercises in an article

I'm writing a paper in which I cite a lot of results that appear in Schikhof's Ultrametric Calculus. Some of these results are exercises in Schikhof's book. These exercises are not difficult, but are ...
1
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1answer
221 views

“Pointwise” defintions in category theory

In category theory it is often said that certain operations are defined "pointwise". For example, limits in a functor category $[\mathcal{C},\mathcal{D}]$ can be defined "pointwise" (if $\mathcal{D}$ ...
52
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12answers
4k views

Examples of advance via good definitions

In my research I came across a case where I could derive a known theorem with rather straightforward way by choosing "non-standard" definitions using my knowledge from a related field. This particular ...
1
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0answers
746 views

Proof of the ABC conjecture - how feasible would it be to automate some of the deciphering of Shinichi Mochizuki’s proof?

This is a question I will come back to. I am very interested in Shinichi Mochizuki’s proof, and in particular, the idiosyncrasies of his notation, which I understand to be at the root of why it is ...
5
votes
1answer
355 views

Why are affine functions called “affine” functions? [closed]

I am learning about affine functions and I do not understand why a certain type of function (functions that are in the form of $f(x)=ax+b$) are called affine functions. I read about the word "affine" ...
15
votes
1answer
499 views

Arrangement of the introduction of a paper

In my understanding the introduction of a paper is a very important section because it not only gives a concise summary of the results, but it is also the only section most people will read at all. ...
7
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3answers
386 views

Given alphabetical ordering of authors, how to establish level of contribution? [closed]

I learned recently that in mathematics, the authorship order is virtually always alphabetical. I have recently collaborated on a paper where I did the vast majority of the work (everything but the ...
13
votes
2answers
1k views

Is it acceptable to use the citation references like [1] or [Joh] as nouns in mathematical writing?

I have seen this enough times that I thought it was common practice, but I recently saw someone on a website about writing tips (can't find the link now) say that this was not good. I am hoping to get ...
1
vote
2answers
627 views

Use of ternary operator in formal writing

I would like to write $$ f(x) = \begin{cases}1&\mbox{if }x = 1\\ 0&\mbox{otherwise.}\end{cases} $$ However, this eats up a lot of vertical space for a very simple statement. Is there agreed ...
8
votes
1answer
254 views

Style guide for referring to past work

Has anyone written or expressed a coherent position on how to refer to mathematical results (theorems, proofs) by past authors? Even if there are no hard and fast rules, I find it helpful to have a ...
-2
votes
1answer
327 views

Correction symbols used for mathematical texts [closed]

When proof reading and correcting a mathematical text, I sometimes see people use special notation symbols in the margin to indicate correction, deletion, replacement and so on. Is there any standard ...
6
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0answers
220 views

When do you use “s” apostrophe to refer to authors ($e.g.$ of inequalities)? [closed]

I remarked that there does not seem to be a general rule whether one should use or not an "s" apostrophe for inequalities For example, we can encounter Hölder's inequality, but Minkowski or Sobolev ...
22
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6answers
2k views

How to cite authors from any country correctly?

It has always seemed to me that the Mathematical Community gives a high importance to the act of properly citing an author (Do not write Erdos! It's Erdős. Cauchy must be read as in French, not as in ...
5
votes
3answers
696 views

“Let” versus “for all” [closed]

I have noticed that many authors tend to use "let" instead of "for all". For example, they write something like this: Let $n$ be an even natural number. Then also $n^2$ is even. I wonder, why they ...
53
votes
33answers
11k views

Most intriguing mathematical epigraphs

Good epigraphs may attract more readers. Sometimes it is necessary. Usually epigraphs are interesting but not intriguing. To pick up an epigraph is some kind of nearly mathematical problem: it ...
12
votes
1answer
2k views

Mathematical writing : using an “out-of-date” notation

When I wrote my master's thesis, a professor who read it said that I should not use the phrase "A function of class $k$." but instead "A function of class $C^k$". I am not an expert about mathematical ...