Questions tagged [research]

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0answers
102 views

A taxonomy of proof methods [closed]

I am looking for a taxonomy of proof methods in mathematics. For basic proof methods I would think of proof by contradiction, mathematical induction, structural induction (yes I am a computer ...
32
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5answers
3k views

Advice for researchers outside academia

Perhaps some personal background is relevant to this question. A couple of years ago, I graduated with a master's degree in Applied Mathematics from a good Dutch university. Even though I obtained ...
13
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9answers
2k views

Tools from other disciplines useful to mathematics research?

Obviously, mathematics provides essential tools for physicists, biologists, economists, engineers and many others to use in their research. Equally obviously, physics, biology, economy and engineering ...
35
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9answers
3k views

Why is it still common to not motivate results in publications? [closed]

This is a question about practice and publication of research mathematics. On the Wikipedia Page for Experimental Mathematics, I found the following quote: Mathematicians have always practised ...
15
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7answers
4k views

Learning mathematics in an “independent and idiosyncratic” way

This is a question about learning mathematics outside of the standard undergraduate/graduate education. The following is a quote from Thurston's On Proof and Progress in Mathematics: My mathematical ...
61
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3answers
6k views

Replication crisis in mathematics

Lately, I have been learning about the replication crisis, see How Fraud, Bias, Negligence, and Hype Undermine the Search for Truth (good YouTube video) — by Michael Shermer and Stuart Ritchie. ...
0
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1answer
49 views

Question related to complete vertex, interior vertex and boundary vertex of a graph

All the definition and results which I am using here has been taken from the Garry Chartrand book $\textbf{The Introduction of Graph Theory}$ and the paper $\textbf{On the Commuting Graph of Dihedral ...
9
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1answer
351 views

Basic prerequisite (topics) to read current research in Diophantine equation for an independent researcher

I have completed studying Galois theory, Fermat's Last Theorem for Regular prime and some number theoretic complex analysis (prime number theorem), and basic linear forms in logarithm. What else ...
3
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1answer
193 views

Is there a precise relationship between the goals of moduli theory and the minimal model program?

I want to get into some of the big classification problems in algebraic geometry, but have a very broad question. Ultimately we would like to classify all varieties over some field up to isomorphism, ...
5
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0answers
334 views

How often do you put your research into trash?

A soft question. I am a PhD student, at early stages of my academic career; and have personally experienced the following many times. Sometimes you come up with a result, that you are not quite ...
23
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3answers
4k views

Evaluation of the quality of research articles submitted in mathematical journals: how do they do that?

I would like to know as curiosity how the editorial board or editors* of a mathematical journal evaluate the quality, let's say in colloquial words the importance, of papers or articles. Question. ...
7
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4answers
734 views

References for literature from mathematicians who provided critics and proposals concerning ethical aspects of mathematics research

I would like to know sources, articles, books or other, that provide information on ethical aspects in the research of mathematics, I wondered what is the literature that this community knows about ...
14
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6answers
5k views

The work of mathematicians outside their professional environment

As it is reasonable to think the work of mathematicians will be developed/made in their offices of universities (or in eventual seminars or conferences), here are the colleagues, books and journals, ...
7
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1answer
335 views

Survey article model theory research

I've taken a graduate course in model theory and I like it so much that I can imagine doing research in this area. Are there survey articles or review papers on the current research topics in model ...
37
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3answers
4k views

On math looking obvious in retrospect [closed]

Admittedly, a soft-question. I, being a very young researcher (PhD student) have personally faced the following situation many times: You delve into a problem desperately. No progress for a very long ...
8
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0answers
467 views

When is a paper finished? [closed]

How much truth is there to Chomsky's remark that "mathematicians stop working when things get too difficult"? https://youtu.be/atupfHizJxM?t=453 Is this true in your own work? How do you know you ...
25
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5answers
4k views

Is the field of q-series 'dead'? [closed]

I had a discussion with my advisor about what am I interested as my future research direction and I said it is special functions and q-series. He laughed and said that the topic is essentially dead ...
1
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0answers
191 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 ...
0
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0answers
51 views

Is the exact solution of the wave equation for the scattering of waves by a disk/cylinder an open problem?

The solution exact solution of the Helmholtz equation for the scattering of waves by a sphere is relatively straightforward and has been known since the time of Lord Rayleigh. The exact solution of ...
1
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0answers
153 views

Rate of convergence for difference between conditional and marginal probability

Suppose $X\sim \text{Bin}(2n,p)$ and $X_1,X_2\sim\text{Bin}(n,p)$ are independent, with $X_1+X_2=X$. I'm interested in the rate of convergence for the absolute difference $$ \left\vert P(X>c|X_1\...
2
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0answers
184 views

Research trends on mean curvature flow

It's been a few months since I've been curious about mean curvature flow and now I'm reading Robert Haslhofer's lecture notes. I like the subject and would like to do research on it, but I know ...
1
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0answers
296 views

How to approach a respected researcher? [closed]

I'm developing a theory that (I think) is pretty good and something new. I'm thinking of contacting a respected researcher (one of the best in the field), mainly because I'm not 100% that this has not ...
11
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1answer
750 views

Research semester in math

Admittedly, this is a soft question. My own experience in mathematical research has been of long periods of research, mostly characterized in long "blocks" and sporadic breakthrough. How does this ...
2
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0answers
232 views

Currently active Research Areas in Topological Groups

I have done my Master's degree in mathematics and currently I am doing Ph.D. in mathematics in India. I have completed my course work and my supervisor works in Topological Groups. He suggests me some ...
2
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0answers
334 views

How practical is it to change research areas within math after a PhD? [closed]

The title says most of it really. How constrained are you in an academic career based on the topic of your PhD thesis? Is it plausible for someome to be researching in an area of math vastly different ...
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 ...
82
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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 ...
3
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0answers
688 views

How to find research topics in Linear Algebra in Graph Theory [closed]

Note: My first question in this site. MSE users asked me to post this question here for better response I am a Masters student in Pure Mathematics. I need to do a Masters thesis in "Linear Algebra ...
3
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2answers
2k views

$\log(x)$ or $\ln(x)$ to denote the natural logarithm in research papers? [closed]

Since the natural logarithm, i.e. with base $e$, is very commonly used in research papers and that both $\ln(x)$ and $\log(x)$ are used to denote it, it is natural* to ask which of these notations to ...
2
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2answers
360 views

Names of convex geometry journals

What are the names of the research journals that focus on convex geometry? I know of "Advances in Geometry" and "Discrete & Computational Geometry" but no others. Context of question: I am a ...
41
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9answers
5k views

What problem in pure mathematics required solution techniques from the widest range of math sub-disciplines?

(This is a restatement of a question asked on the Mathematics.SE, where the solutions were a bit disappointing. I'm hoping that professional mathematicians here might have a better solution.) What ...