# Questions tagged [advice]

This tag is for questions requesting advice (e.g. on a suitable publishing venue, presentation strategy, career move, ethical dilemma). It should be used in conjunction with a more specific tag, such as [journals], [teaching], [career], or [ethics].

126
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### Advice on results for balls on regular $N$-dimensional grids

I have obtained some results regarding balls on regular $N$-dimensional grids. I would like expert opinion on wether the results are significant or interesting enough for (trying to) publish them in a ...

10
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3
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### Research in mathematics without a degree in mathematics

This question might not make much sense or be a big deal for someone but I genuinely would like to know the opinions.
I am currently a software developer in a small start-up. I had to drop out of ...

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1
answer

306
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### Amount of mathematical knowledge required for starting Ph.D. in pure mathematics [closed]

How much mathematics should one know before starting a Ph.D. program in pure mathematics? For example what topics one must understand well to pursue a Ph.D. in US University in Number Theory (...

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10
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### What do you do when you're stuck?

I'm pretty sure almost all mathematicians have been in a situation where they found an interesting problem; they thought of many different ideas to tackle the problem, but in all of these ideas, there ...

1
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0
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### Advice on constructing a Non-structural Flood Mitigation Model [closed]

I am not sure if this is the right site to post this. But I seek some valuable suggestions, and I believe I can get them here.
At present, I am in the final semester of my BSMS Mathematics course. I ...

16
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2
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### What should one do before submitting a paper?

Assume I just wrote a paper. Now I would like to publish it in a journal.
What kind of things I should do before its submission?
Should I first give a few talks at seminars or conferences? Upload to ...

14
votes

2
answers

2k
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### How do I, as an undergraduate, find interesting, accessible questions to work on to see if I'd be interested in research mathematics? [closed]

For a little more context: I'm currently an undergrad (sophomore) at a small liberal arts college with a (from my experience so far) solid math program. So far, I've taken Calc I, II, III, linear ...

5
votes

4
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423
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### Funding programs for mathematical research [closed]

In the USA, as far as I know, the main grants available to mathematicians are collected on the NSF or the AMS websites [please, correct me if this perception is inaccurate]. On the other hand, for ...

68
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8
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### What to do after a pure math academic path?

I don't know whether my question is in the appropriate place. I've studied physics, and then did a PhD in (pure) math and 2 postdocs. I definitely love math research, but I am not ready to apply all ...

18
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5
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### How to get a research paper published after the author has died?

Sometimes, a mathematician dies suddenly, leaving behind very good mathematics that didn't make it through the publication pipeline. For example, it is possible they had a paper entirely ready to ...

31
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5
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### How to pass on research posthumously

I've been independently researching math, for a while in the homeless community. While I am generally safe, situational realities (weather, equipment stress, health and especially how cities can ...

9
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2
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### Undergraduate research in Topological Quantum Field Theory

I'm really interested in Topological Quantum Field Theory (TQFT) and am currently planning to focus on it in my undergraduate thesis. My university, unfortunately, does not allow double majors in ...

2
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0
answers

249
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### How does one build and refine strong technical skills relevant to research?

I am an early career researcher working in an area of "hard" analysis but this is a fairly broad question. My technical skills are likely below par and my greatest hindrance to my research ...

9
votes

1
answer

1k
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### Is it OK to send a manuscript to good mathematicians in the field of your paper even if they don't know you before

I am wondering if it is OK to send a finished manuscript to some mathematicians in your field for initial references or feedbacks in addition to just posting it in Arxiv, even if they do not know you ...

0
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0
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181
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### Advice on how to deal with an elementary "long-to-prove" statement

I am not entirely sure if this question totally fits here. If it doesn't, I apologise in advance.
In a paper I've been working on, we have a very elegant result which, when forgetting about the ...

30
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3
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### How can I seek help in preparing a very long research article for publication?

Some background first.
I recently graduated with a master's degree in applied mathematics. During graduate school I began working on a paper, which I continued to work on post-graduation. A complete ...

9
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3
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### Should every modern day mathematician care about category theory? [closed]

As far as I know, category theory is used mainly in topology. I have a dislike towards category theory, similar to my dislike of Bourbakism, and want to avoid it as much as I can. However, the head of ...

13
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2
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### Math overdose? Professional advise how to cope with it [closed]

I'm a PhD student, currently working on my Thesis. Over the years I have many time encountered a problem. Maybe professional mathematicians know what I'm talking about?
When I study a math topic, ...

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votes

1
answer

409
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### Rejection of a paper because of not suitable level of rigor without a single example of a mathematical error/imprecision [closed]

Question 1. A paper was rejected because of 'not suitable level of rigour' without a single example of a mathematical error/imprecision. What can the author do in this situation?
It sounds a matter of ...

8
votes

1
answer

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### Advice: What topics to study now in analytic number Theory( And if there are video lectures( Open Online course) / Course notes available on website)

I am a person living in a 3rd world country and completed my masters in mathematics in July 2020. Then I began to study some additional topics in Pure Mathematics as I was applying for Ph.D. abroad( ...

2
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0
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360
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### I want to enter graduate school in pure math. Is doing REU in “mathematical modeling” a good idea? Is it essential skill to learn?

(please let me know if this question is not suitable here)
Hello! I'm an undergraduate rising senior majoring in mathematics and it seems that I got rejected by REU that is held in my university over ...

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1
answer

338
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### Soft Question: Asking for advice: how to study math? [closed]

(I am aware that some people might frown on this question, but I had no place to ask; this will definitely be voted to be closed in SE. I apologize in advance.)
I am currently a 1st year grad student ...

0
votes

1
answer

504
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### Applying Phd directly after undergraduate [closed]

I'm a math undergraduate and I'm about to finish my second year at UCL. It's time to consider my graduate school, and I have some questions about it. In the UK, many universities provide math PhD ...

14
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2
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### How to structure a proof by induction in a maths research paper?

I am 16 years old at the time of writing (so I have no supervisors to seek advice from) and I have written a mathematics research paper, which I plan on submitting to a journal for publication. I ...

1
vote

1
answer

462
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### What qualities and achievements can outweigh bad grades? [closed]

I will try to formulate my question so that the answer is not opinion-based.
My question: Considering a undergraduate math student planning to pursue a PhD program, what qualities and achievements can ...

7
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0
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1k
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### How difficult will it be to start doing research in pure mathematics in the near future? [closed]

I am a first year PhD student in mathematics (complex differential and Kahler Geometry) and the other day I had a thought about the difficulty of starting to do research. This is my first post here ...

220
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8
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### Need advice or assistance for son who is in prison. His interest is scattering theory

The letter below is written by my son. I have been sending him text books and looking for answers on the internet to keep his interest up. He has progressed so far on his own and now he needs ...

4
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0
answers

212
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### Referring to computer software in a paper

I'm performing a calculation of the Smith normal form of an integral matrix based on the SageMath worksheet. Is it sufficient in the paper to say something like ``Using a software package like ...

9
votes

1
answer

886
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### Is it possible to jump ship to mathematics?

A few years back, I did an undergrad double major in math and physics, and afterwards went to a top-tier university to work on a physics Ph.D. Around about my third year of the Ph.D., I started to ...

34
votes

5
answers

4k
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### 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 ...

11
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2
answers

4k
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### Publishing undergraduate research

Sorry if something like this has already been asked, I searched but I couldn't find anything similar to my question.
I'm a senior undergraduate and currently doing my senior thesis. My senior thesis ...

1
vote

1
answer

825
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### Kashiwara-Schapira Trilogy

I’m going to start reading Kashiwara-Shapira’s trilogy Categories and Sheaves, Sheaves on Manifolds, and Perverse Sheaves with someone soon. Flipping through the table of contents for Sheaves on ...

90
votes

5
answers

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### Note rejected from arXiv: what to do next?

Short version: A note of mine was rejected by the arXiv moderation (something I didn't even know was possible) on account of being “unrefereeable”. The moderation process provides absolutely no ...

32
votes

6
answers

8k
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### Pros and cons of specializing in an esoteric research area

If a mathematician specializes in a popular research area, then there are many job positions available, but at the same time, many competitors who are willing to get such job positions. For an ...

3
votes

1
answer

650
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### What are some problems for research in functional analysis that can possibly be solved by someone with basic knowledge of the subject? [closed]

I wanted to know are there any problems in Functional Analysis (FA) that can possibly be successfully tackled by someone like me who does not have any expertise in this area but is only familiar with ...

2
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0
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263
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### What kind of work experience should be included in a math CV?

I am applying to numerous PhD programs in number theory for admission next Fall and I want to have a CV prepared, in part because I want to attach a CV to emails I send out to professors at some of my ...

203
votes

14
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56k
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### Why doesn't mathematics collapse even though humans quite often make mistakes in their proofs?

To begin with, I am aware of these questions, which seems to be related:
How do I fix someone's published error?, Examples of common false beliefs in mathematics, When have we lost a body of ...

5
votes

2
answers

522
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### Tricks for getting a creative idea [closed]

Caveat: I fear that people will criticize me for asking this potentially inappropriate question here, but I guess that the community here is quite unique in the ability of potentially answering my ...

24
votes

5
answers

5k
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### 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
vote

0
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### Doubts related Shifting from Pure to Applied math [closed]

I am a second year (Pure) Math and (Theoretical) Physics undergraduate in India. I want to do a masters in Applied/Computational Science or Math, for which I have apply after next 7 months.
I have ...

42
votes

3
answers

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### Publishing a Simple Paper as an Undergraduate

First off I apologize if this question does not belong here, I would be happy to hear about any better locations to post this on.
I am a (first year) undergraduate mathematics student, and I recently ...

57
votes

16
answers

8k
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### What are examples of books which teach the practice of mathematics?

One may classify the types of mathematics books written for students into two groups: books which merely teach mathematics (i.e., they present theorems and proofs, ready-made, as it were) and those ...

80
votes

18
answers

25k
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### What programming language should a professional mathematician know? [closed]

More and more I am becoming convinced that one should know at least one programming language very well as a mathematician of this century. Is my conviction justified, or not applicable?
If I am right,...

2
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0
answers

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### 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 ...

3
votes

1
answer

589
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### Where to find "Families of curves on a surface of general type" (MR0457450)?

I am currently doing some research on surfaces of general type and I need some results from Bogomolov's paper:
Bogomolov, F. A.
Families of curves on a surface of general type.
Dokl. Akad. Nauk SSSR ...

0
votes

1
answer

257
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### What are problems at the center of geometric topology of 2 dimensions? [closed]

I am working on Geometric Topology in 2 dimensions but I don't know which problems are important and make many connections between different areas. I hope Mathematicians can give me some ideas? Thank ...

3
votes

0
answers

826
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### 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 ...

1
vote

0
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101
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### I am seeking advice for a general audience expository journal [duplicate]

Prefatory note: This be off-topic for this site and, if so, I apologize and seek direction. I am seeking advice for a general audience expository journal to submit my article, “An Application of a ...

28
votes

17
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### Research-only permanent positions worldwide

Most academic jobs involve some amount of teaching. Post-docs generally do not, but they are only short-term positions.
Question: in which countries can one obtain a research-only permanent ...

2
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0
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### Advice on research ideas on Non Linear Dynamics [closed]

I am interested in Non Linear Dynamics.
I am just a beginner to this research area in the sense that I am starting to read the research papers.
My aim is to make my project to a research paper.
But ...