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Can I write a book based on my own published papers?
I have published several research papers, from my PhD thesis, in varied journals and proceedings of international conferences. Now I wish to publish a book that shall be utilising the majority of the contents of these papers. Would it be called plagiarism?

As already mentioned, but somewhat unclear, fetching reuse permissions from the journals' and proceedings' publishers is a good start, but there is also the issues from @Buffy's answer. For how to fetch permissions see https://academia.stackexchange.com/questions/65784/can-we-use-a-book-figure-illustration-in-a-review-article-and-cite-the-source-wi, https://academia.stackexchange.com/questions/43770/what-are-the-restrictions-placed-by-copyright-laws-on-reuse-of-figures-in-disser, etc.

If your book is simply reprinting your papers it certainly isn't plagiarism. However, if you are re-writing and re-phrasing them, to bring them together as a whole, you should do it just as if you were writing a book based on the work of others.
In other words, when you quote or paraphrase your old papers, give a citation, just as if it were someone else's paper. This makes your intent clear to the reader. More importantly, however, is that it lets the reader go back to your originals for any context that they feel they might want.
Moreover, if your book contains new material as well as the old, the citations should make it clear what is new and what was previously written.
But just restating what you said before without citation is, today, considered self plagiarism. In some circles it is considered very serious, but mostly as it prevents the reader from finding that original context along with your references and such.
Even a statement at the beginning of your book that says that you will be copying and/or paraphrasing without citation would not be appreciated by your readers.
Treat your own work like you would that of any other scholar. This is true in general, not just for the example of a book.

If your book is simply reprinting your papers it certainly isn't plagiarism — ...but it might violate your publication agreements with your papers' publishers, unless you have their explicit permission to reprint.

@JeffE, true enough.

The book chapters are tailored to the need of target readers, obviously different from PhD chapters. End users of book are expected to be different from that of research papers. In the flow of the write-up, contents of different research publications appear almost as such. The difficulties are  1. It is difficult to rephrase every part of the research papers extracted out of my PhD work.
2. If I provide in-text citation, since there would be large volume of the copied text, how many times I must cite for every research paper?
3. Whether to cite the published papers or unpublished PhD thesis?

One possibility is to state something like "the following section is developed fully in [3]" or whatever, so that you don't keep pointing to the same paper in the same section. But subsequent quotes with ibid is pretty common in other  writing.


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do you know anyone who is over 30 years old, but got admission from top math grad school?
I am going to apply math grad schools this year.
But, the problem is now I'm 30 years old.
Do you know anyone who is 30 or over 30, but got admission from top math grad school?

https://en.wikipedia.org/wiki/Joan_Birman

Knowing an answer to this question won't help you. What will help you is making a good application to a school you'd like to attend showing your skills and potential. No one will say, "Well, this is the greatest mathematician since Riemann, but, alas, he's 30". Age won't play any part at all in an application, not even competitively. Your suitability will be evaluated on what you have done and what can be expected of you.
But in any top school, the competition for a position is fierce and you will have a lot of other applicants that show near perfect records on most criteria. Make sure that you can stand up to the competition, not only in what you write on the application, but what you can say in an interview.
But if you don't apply, you don't get accepted. That rule is almost universal.
If there are gaps in your record, be sure you have an acceptable explanation.

I can't give you any well-known examples from the top of my head, but for postgraduate programs (and many undergraduate programs fwiw) the age of the applicant does not matter that much.  Career gaps are not uncommon. Having a proper job after undergraduate program and coming back to postgraduate 10-20 years later is not uncommon.
I personally know a few academic who started and successfully completed their MSc/PhD studies when they were 60+.

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How many first-author papers should I publish during postdoc to get a tenure-track faculty position?
I'm currently a 2nd year postdoc in mechanical engineering field working on bio-related applications. I have ~9 first-author papers during my Ph. D., but have not been able to publish a first-author paper during postdoc.
For anyone in a similar situation (postdoc in mech. working on bio stuff), what is the reasonable number of 1st author papers to apply for TT? If I have several non first-author papers, would that still "count" as my research output when getting reviewed by the search committee?

The answer depends massively on the subject and profile of place you are applying to. Also, the number of papers is not the best metrics - the quality matters more.

I don't understand how an answer will help you. You have what you have. But an application for an academic job isn't an accounting problem, simply counting up papers. More is better, of course. But hopefully you have other qualities that make you desirable as a faculty member. Work hard, but don't be discouraged. Don't let fear of failure hold you back.

I think quality of the work is more important than number or papers.  Even more important than first-author status.
Of course non-first-author papers count; for exapmle, get the actual first author to write one of your recommendation letters, to describe your contribution to the research.

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Can contacting a search committee for questions about the position hurt your chances?
Most job postings include an email (usually for the chair) to contact the committee's chair. I have so far never dared to use it for fear that i'd get sidelined for asking stupid questions. Things that I've wanted to ask in the past but haven't include:

Could I amend my application by adding document X (after deadline has passed)
Would you be interested in an applicant with a background in X and Y, having worked on Z (with CV attached)
Could I submit one more recommendation letter than the specified number?
Should the "Teaching statement" (or whatever they call it) include student evaluations (if they're not asked for anywhere else in the ad)?

Could asking such questions potentially hurt a candidate's chances?

It is hard to be definitive here, but I don't think the questions you are suggesting will help and might hurt. They are questions about the "candidate" (i.e. you) not about the position. (See the last paragraph here, however.)
On the other hand, my opinion is that a true question about the position and the department in which it is being offered are appropriate. Questions like "Are there frequent/regular seminars attended by faculty and advanced students?" Or: "Do students have an opportunity for independent study and do they take advantage of it?" Here you are asking about the environment of the job itself.
If you have to ask the questions you list, it would be better (opinion again) if you ask them of some higher level authority than the hiring department or the chair of the committee.
However, if a problem arises in your application in which you have a serious need to know the answer, then, yes, ask it. If you already have a problem then you need a resolution.


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How do I think clearly about applying to grad school?
Tl;dr:
I have serious issues with self-confidence and indecision that have already negatively affected my academic career and that persist despite significant improvement. What strategies can I use to prevent these issues from impairing my decision-making when applying to grad school?
Background
I graduated last year from a top-tier college with a major in physics. Speaking only about performance in my classes, I was probably somewhere near the top of my class, and I had a lot of advanced math/physics coursework with a 3.9 (cumulative and in-major). Unfortunately, "great at coursework" might be the only thing I have going for me. I took 5 years to graduate, due in roughly equal parts to a Junior year change of major and burnout.
More seriously, the sum total of work I did in my five years and four summers was a single summer job in my school's administrative department. I think this would look very strange to outside observers, since my school is known undergraduate participation in research. It's difficult to understand how I could think this way saying out loud, but: I had a really paranoid expectation that, not only would no one be interested in taking me on as a student, but that they would chew me out for even bringing up the subject, and confirm my suspicions that I wasn't smart/diligent/disciplined enough to succeed at research. I am also a pretty disorganized person (and I could be pretty lazy as an undergraduate), so the mere thought of this possibility was frightening enough for me not to even try to formulate summer plans.
After I graduated, as you might expect, I did nothing for a while, but eventually applied to a DOE internship program and got in. I approached this with more or less the same attitude that I had toward summer research - "If I don't try to figure out what/who I want to work with ahead of time, I can't fail to live up to my expectations" - with the result that I ended up being chosen to do something I didn't have any interest in. I did well enough that I got offered the chance to stay, which I did, having no other way to make money. It looks like I can get my name on a couple of publications (possibly one as sole first-author), but it's not stuff that I think will be relevant to my future interests, and frankly I'm not proud of it. It's not shoddy work or anything, I just haven't felt challenged. I have been working here for 10 months.
Now
Although it's not my calling, this DOE job has given me confidence that I would enjoy research (and given me some universally-applicable skills). I have done well at finding ways to make my work more interesting, and slogging through it when there's just no other way. Most of the careers I am interested in either require a PhD or seem easier to break into with some graduate education. Also, I'm just genuinely excited about the opportunity to do some cool research for a few/several years. So I think grad school might be for me.
But there are some problems:

I only came to this realization very recently (previously I thought I just wasn't prepared enough), and I am way behind on applications, having not seriously started. I'm taking the subject GRE in a couple of weeks, but that's the extent of my preparation. I doubt that I'll be able to build a solid application in the next couple of months. But if I don't apply this cycle, there will be more than three years between my graduation date and the earliest possible start date.
I am really unsure about what I want to study. There are at least 5 or 6 fields I'm seriously interested in, not all of which are part of a typical physics department, and I don't know how to narrow it down to just a couple, let alone to a manageable number of schools or research groups.
My self-confidence and social problems have improved a lot, but they're still pretty bad. I have a hard time imagining that I'd be accepted by a program in which I'd be happy to work. I definitely don't feel like I deserve it.
Probably the worst: I have no one in my life to talk to about this. I have no friends who live within 1000 miles of me, and few who live further away. I feel uncomfortable bringing it up with my mentors/more senior coworkers, mostly due to pure social anxiety.

I recognize that it's a little crazy and very stupid, but this has all amounted to a gigantic mental block that makes it really hard for me to think clearly about some tough decisions. Does it make sense to wait another year to apply, or is it now or never? How do I narrow my application focus? Who can I talk to for general advice? I have no idea to answer these questions, and it's challenging for me to even ask them. What can I do to make them more approachable?

US, and Department of Energy, yes?

@Buffy: Yes and yes.

As a current doctoral student, I agree with Buffy's comments - particularly about connecting with your DOE colleagues, tapping their academic knowledge/networks, and getting perspective on graduate school, timing, etc. Many of these colleagues would likely be flattered that you're asking their advice on graduate school. If I were in your shoes (and actually, I was in pretty much the same boat 3 years ago) I'd be less concerned about waiting a year to apply to programs than about wasting a lot of time/money/effort/psychic energy on producing a lot of poor applications right now that might only net an offer at a low-quality program or a program that isn't really going to give you the opportunities to do what you want later.
My own grad school application process was a learning experience in itself... I was able to take 6 months to really learn about the culture, resources, structure and focus of various programs even as I was trying to figure out exactly what it was I was looking for. I cold-called/emailed many current students at various programs who listened to me talk about my somewhat-unfocused interests and were able to interpret them into areas/fields that meshed with specific scholars/programs/institutions so I started to see patterns both in my own interests and in the institutions that would be a good fit for me.
Long term, it is much better to be a year older and in a good program that supports students well and places students into good jobs.  Racking up another year of relevant research experience while being surrounded by people who can help you compile a really strong application package sounds like a win-win to me. Rushing to submit a half-baked package because of some self-imposed, imagined life-timeline is definitely a path to less optimal outcomes.
On a separate, but equally important note, it might be extremely helpful for you to consider talking with a therapist (in person, online, whatever works for you) to better understand the source of your challenges with social anxiety and self-confidence. As someone who struggles with both these issues, I can say with certainty that graduate school will only compound your pre-existing challenges, which could lead to burnout, low performance or failure. Even the most successful graduate students question their abilities and performance at some point; emotional/social challenges make the experience even more difficult [gut-wrenching, soul-crushing] by an order of magnitude. Impostor syndrome is real and it's deadly for grad students.
You mentioned several instances in which your coping skills caused you to act (or avoid action) in ways that hurt you academically and professionally. Take this year to understand the roots of your behavior and learn new ways of perceiving/responding to situations so that when you do get into that awesome program, you'll have the emotional strength and coping skills to help you be successful.
If you don't have experience with therapy, I'd suggest a good place to start is by looking for practitioners who offer DBT (Dialectical Behavior Therapy). DBT is similar to CBT (Cognitive Behavioral Therapy) in that it is solution-focused (you'll spend some time understanding the roots of your current cognitive thought patterns, but more emphasis on developing & practicing new skills/techniques to help you going forward). However, DBT differs in that it also helps you address the emotions attached to your current thought patterns that often keep you from actually adopting those new behaviors.
Grad school is a marathon, not a sprint, so take the time (and action) to prepare well. I wish you the best of luck in your journey.

This doesn't sound like typical burnout or Imposter Syndrome. Maybe a bit of anti-climax and a let down. But, I think you have more resources than you think you do.
I'm guessing that the people you work with at DOE have a lot of ideas, suggestions, and, more important, contacts in the academic world. Talk to them. See what they think of as options for a young scholar. See if you can leverage their contacts.
But, as to the indecision about which field to study within, say, Physics, many US universities won't require you to choose a specialization instantly to join a program. If you choose a university with a large program/faculty where there is a lot of things going on, you could start out and spend some time looking around for an advisor and a specialization. Most US universities will require some coursework for a person entering with a BS degree so you can use those to evaluate both faculty and interests. You might have to initially rule out a few of the possibilities when you apply, but you will probably also have lots of options when you arrive. Look for a university with a large and diverse faculty who support a lot of different sub-fields.


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Asking professor for recommendation after rejecting his PhD offer
I did my undergraduate thesis with a professor A in a foreign country X. It went well and he offered me a direct PhD in his department afterwards [1]. I was not too keen on accepting the offer due to a variety of reasons, and to avoid saying an unequivocal no (lest he feel bad), I ended up saying (untruthfully) that I could not join the PhD program as I did not want to settle in a foreign country. Having matured much more since then, I now realize in hindsight that this was perhaps not the best way to handle that situation. At the time, I instead asked him to recommend me for a different research job in my home country (I am currently at this position).
Presently, I am being considered for a research job in a foreign country Y, and it checks a lot of the boxes of the ideal job that I have in mind. It provides great opportunities for my future career as well. The recruiter for this new job has asked me to provide references. Professor A is a really good reference for this as the work that I did with him is similar to what I will be doing at this new job, and he was impressed by my work too.
The question is, would it be reasonable to ask professor A to recommend me for a job in a foreign country, when I had declined his offer to apply for his PhD program stating that I don't want to settle/work in a foreign country. If he were to ask me why I am applying to a foreign country, what could I possibly say to him as a reasonable explanation for this seemingly contradictory behavior? I have considered coming clean about it, but it seems that he would just be even more upset that I wasn't honest with him at the outset.
[1] Well, he not so much "offered" it as "suggested" it - he told me that they had a program to take PhD students directly after their bachelors if the students were deserving, and he said he liked my work and felt that I was deserving enough to clear the bar of this program to be selected.

Is this Professor a reasonable person?

I don't see any issue at all. Just ask and be honest. What was true in the past may not be true now. You don't need to go into all of the reasons that you refused in the past, but changing your mind about going abroad is not an issue.
If s/he supported you in the past, they are probably a good person to support you now. Don't let this hesitation work against taking advantage of an opportunity.


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Asking to present paper as first author, when the second author's travel has already been booked
I recently published a paper at a technical conference in computer science as the culmination of my bachelor thesis. I'm the first author for it, and my 2 supervisors are the other co-authors.
I pursued this thesis in another country A, and after completion went back to my home country B. This paper recently got accepted for oral presentation at a conference to be held in A. Upon requesting for funds to attend the conference, my supervisors said that this is not possible since the conference is local for them and thus it is little to no expense for one of them to go and present the paper.
Since this is my first scientific publication, I am very excited for it and wish to attend the conference to present the paper. I searched around a lot and managed to scrape together some financial assistance from various sources. In spite of this, I will still need to pay a large amount of money from my own pocket.
Since this requires a large expenditure from my end, I wish to confirm with my supervisors whether I will get to present the paper or not. I think that since I am the primary/first author, the opportunity should be mine – but I'm not sure what is the norm here. Is it a reasonable request if I ask my supervisor to present our paper since:

I'm the primary author.
I'm spending a lot of my own money to attend the conference.

The primary issue is that one of my supervisors has already registered for the conference – so I fear that they may cite this as a reason for not letting me present the work. Any thoughts/comments?

I think it is certainly appropriate to ask and wonder why you hesitate to do so. I think that a note that you are able to attend and that you would like the opportunity to present the work and that it would be a boost to your future career should be received positively.
Having registered for the conference (the advisor) should mean little or nothing in this situation. Whether it is good politics to demand your right to do this is a matter of personalities, of course.
But the fact that you are spending your own money likely won't count for a lot. Your presence at the conference should, however arranged, count in your favor.
But, yes, it is reasonable to ask, and I think it would be unreasonable for the advisor(s) to refuse you.

I'll also note that there are a lot of reasons to go to CS conferences beyond presenting something. Your advisors should recognize this. They haven't "wasted" money if you present in their stead. There are normally a lot of ideas floating around and a lot of interesting people to interact with.

"I think it is certainly appropriate to ask and wonder why you hesitate to do so." Thank you, this is exactly what I was looking for. As I mentioned, this is my first experience dealing with a conference and I was very unsure about what is suitable and what is not in such situations.


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Do I have an "anti-research" personality?
I am a second year Ph.D. student in a North American university who is mostly working on applied mathematics with a supervisor/advisor/PI. I have been troubled by a pattern of my own behaviour that seems to go against the seemingly correct way to succeed in research and I wonder if I have some sort of an "anti-research" personality.
Here are the problems:

I study whatever is interesting and cool (within a reasonable range of my discipline) and this causes me to lack a solid focus. It seems to me that people who wind up obtaining a PhD learn to abandon so-called academic freedom early on and drill into a tiny research area. For example, while other people's research could be about different types of seahorses, my research would be about seahorses, pipe fish, shrimps...you get the picture.
Since I work in applied math, therefore I often demand more proof of applicability, where my supervisor is totally happy with toy models. He thinks it is completely sufficient for publishing a paper while I think it is fake applied research. This seems to generate some conflict between us and usually I am the one who gives in at the end and do some simulation on these toy models to make him happy - I never care about these problems. Most other people in my field only simulate toy models as well, not really "real-world" applicable in any sense, but hey, it is sure pumping out a lot of papers.
I never collaborate or ask for help from my peers no matter how stuck I become. I often see my colleagues collaborate with each other in the office. A part of me is jealous that they are taking advantage of each other's knowledge, another part of me almost thinks that this is like cheating. I feel that my thesis and my ideas wouldn't be mine if it was interfered or influenced this way. It wouldn't feel authentic
I move on to a completely new topic immediately after I finish my old one. Usually the way I see how other people work is that they try to do something tangentially similar to what they have done before, i.e., blue-tailed seahorses, then yellow-tailed seahorses. I jump to studying pipe fish immediately after I warp up my research on seahorses. I think my advisor must dislike me immensely for starting from scratch after every project.
If a problem seems to have an easy or existing approach that solves it, I find the problem less attractive to the point that I get physically sick from reading about other people's approach. However, a lot of times in research I find that other people would simply adapt other people's method for their own problem and then publish a paper that way. I try to solve it in my own way every time and most of the times it gets to a point where my supervisor intervenes and tell me to do whatever other people are doing. Again, I give in at the end.
I don't even try to follow my advisor's vision of my project. My advisor seems to have his own vision and ulterior goals that are not completely aligned with mine. I think a good PhD student should just listen to him like a father-figure and do whatever I am told. But I don't agree or sometimes don't even care about his specific vision. For example, why should I do a research on the dorsal fin of a seahorse (for your "dorsal fin grant") when I can study pipe fish instead? I understand that he is the one who is funding me, but I also care deeply about my own academic freedom.

Given these habits, am I doomed to fail my PhD? Do I have an anti-research personality?

"I get physically sick from reading about other people's approach."  This is a pretty striking thing to say and suggests something deeper is going on.  You come across as rather hostile to people in general, which is going to make things tricky in any career.

some of that seems like general workplace/professionalism issues. Have your work been hurt yet? What do you want to achieve in life?

Honestly? It sounds like you prefer "problem-solving" to research and would probably be happier in industry than academia.

"1. ... It seems to me that people who wind up obtaining a PhD learn to abandon so-called academic freedom early on and drill into a tiny research area." I can't speak for what type of maths you're doing, but I do pure maths (discrete probability), and this is not what happens. Sure, I specialise in a particular field, but it's not like I just do one thing the whole time. My supervisor has worked on stuff to do with Brownian motion, BitTorrent algorithms, percolation, random walks, random graphs -- and I would say her research is quite narrow compared with some!

Maybe you actually have got a personality which is averse to some parts of how research is practiced at certain institutions ;) but if you pay attention to stay diplomatic, that does absolutely not mean you are doomed to fail. (Please remember, there is a large social component in doing a PhD, no matter what the technical regulations say.)

Regarding point 3,is it also cheating when you build on someone else's work, or when you cite someone in order to strengthen an argument? You can't research in isolation of everyone else.

Isaiah Berlin's The Hedgehog and the Fox bears some relevance here. Speaking as a thematic, not specialist, researcher who is values by self and others it is worth considering. It's a good question, and you do not need to be a joyless toiling drudge to be in research.

@Elizabeth Really? Someone who wants to work on their own, can't follow direction from their boss (good luck with that) and doesn't see value in iteratively improving things should prefer working in the industry? Each one of those seems like a showstopper to me.

@Voo "Industry" covers a very wide range of positions, and it's a lot easier to take direction when you're aligned with the goals and style of the work.

Having a broad set of interests and knowledge is fine, and can lead to some 'outside of the box' solutions. Yes, you will find periods where anything else is more interesting than your PhD work, irrespective of how interesting your PhD work actually is. You'll find that as you come closer to the end of your PhD, your concentration on the problem at hand will sharpen, and while a PhD deadline isn't quite as good at sharpening a mind as an impending duel, you probably will find your ability to concentrate improve as the ending comes into sight.
Furthermore, don't assume what you're researching your PhD on is what you'll be doing for the rest of your life. Having a wide set of skills and a shallow knowledge of many things will often help you out when you (most likely) realise you don't have the desire to become an academic, and need to search for a different job (which, let's face it, given your background means probably going in to Data Science)
I don't know too much about the culture of applied math to make an informed comment on this, but in general, finding a good real-world application of a concept, and carrying it out, is difficult. It can involve a lot of time mucking around with real world datasets, which are often messy. You have an obligation to show that your results and methods are useful, but to what degree is up to taste, and I don't think is an issue with any kind of 'anti-research' personality.
This sort of thinking is by far your most serious problem. If asking fellow students for help and collaborating is cheating, then so is using Stackexchange or reading from a textbook. Modern civilisation rests on the ability to record our thoughts so every human doesn't have to derive all the rules from scratch. There is nothing dishonourable about asking for help. If someone gives you helpful ideas, thank them in your thesis. Even if they do clever novel work on your problem, you still have to at the very least understand it and synthesize it into your own work.
There is a certain kind of person who is reluctant to ask questions. I would count myself as one. If you feel uncomfortable doing do, I recommend working on that skill until you do feel more comfortable. Stackexchange is the perfect place for that -  even if it isn't a question about anything to do with your research.
This behaviour is fine. One can get a certain fatigue when working on certain projects for a while.
& 6.  It does really seem like you have a need to derive and understand everything from its foundations. In real life, this is rarely necessary.
I did a PhD in organic chemistry. After that, I decided I didn't like chemistry anymore and went on to be a Data Scientist. At first, I would spend a lot of time trying to mathematically understand the techniques I was using, and I wouldn't feel comfortable using them if I didn't understand the underlying linear algebra. Then I slowly got more comfortable using techniques whose underlying mechanics I don't understand. We by and large don't understand the inner workings of a car or computer. We do know, roughly, its outputs when given certain inputs. The inner workings are a problem already solved by someone else.
As you grow older and read more, you'll be continuously struck by the sheer quantity of stuff out there that people have figured out. The sheer amount of knowledge that goes into, say, building an aeroplane or a computer game or a treatment plan for a specific disease or a skyscraper or a hadron collider. Letting go of the need of having to understand all aspects of a certain thing is an important skill. Practice triage with the information you receive and the problems you encounter. Trust in the expertise of others who have come before you. Know when to expend your brainpower, and know when to conserve it.

So in summary, apart from issue 3, I don't think you have any significant "anti-research' personality issues.

To add to issue 3, the academic world relies heavily on networking and collaborations are a key element of that. Even if it is just a short chat about common research interests over a cup of coffee, people are much more likely to remember you and your research if you work with them. And if no one knows you, your papers are far less likely to be read and people will far less likely consider you when they have open positions to fill or grants to give.

Agree. To further point 3, I find it helpful during a brainstorming period to sit and talk through the problem with someone else. Having to formulate the problem in words understood by someone else helps me actually understand it too. Much like you don’t really understand your results until you write the paper such that someone else can too.

I, Pencil — https://www.youtube.com/watch?v=IYO3tOqDISE — lots of effort goes into even the simplest things.

Good, thorough answer. The only thing I’d add is that if you struggle to ask good questions, start by trying to answer the questions of others. Other people may well provide the perfect "real world" problems that you (the OP) crave, and if you can give them a good explanation of the method, you don’t have to go through the "boring" fine details of implementation and thorough evaluation.

Let me preface my answer by challenging an unwritten assumption of yours: that you have a fixed "personality" which is hampering your potential as a researcher. This simply is false. Nobody is born a good researcher. It takes hard work to become one. Sure, some people have predispositions that help them. But in the end, you cannot avoid doing the work, including work on yourself.
You have discovered that you lack certain skills, or that your aptitude for them is currently insufficient. Blaming this on your personality as something that you cannot change is lazy. It is up to you to improve in these areas. If you refuse, then you are to blame, not some god-given "personality" that was forced upon you.
I will now answer point by point, but if you are honest with yourself, you already know what I am going to say.

There is a common saying: "jack of all trades, master of none". In math, you are studying concepts that other people have been studying and refining for decades if not centuries. You are not going to master them by studying them for a few months and moving on to the next target. You are now at the bleeding edge of research, and it takes hard work to get up to speed. Your PhD is the occasion that you get to demonstrate that you are able to become a true expert at something and make improvements to the state of the art. It is unlikely that you will manage that by working on something for six months and moving on to something else afterwards.
However, getting interested in other things is not just fine, it is mandatory if you want to have a successful career after your PhD.
You seem to be confused about what applied math really is. Math that you actually apply in the real world is usually called engineering. It is a one-in-a-million occurrence for something in applied math to find a real-world application. But since you don't know in advance what will work, you have to start somewhere. Toy models are where it's at. You start with something simple. Maybe it works. Maybe you realize it's more complicated than what it appeared (the most common occurrence). Maybe it turns out to be useless. You don't know, because you are not an oracle.
There is nothing "fake" about getting influenced by others. Here is another common saying: in academia, we are standing on the shoulders of giants. You are reading papers, aren't you? You didn't discovered all of applied math by yourself from scratch, did you? Aren't these papers influencing your research, your way of thinking? Have you never read something and thought, "hey, I never thought about it like that", or "wow, this unrelated topic gave me ideas for my current research"? The difference with face to face conversations is that it's happening in real time. That's basically it.
And here's another saying, as I like them: alone you go faster, together you go farther. Other people have a different way of thinking, a different skillset, a different knowledge of the literature, different ideas. By pooling your resources together, you will probably be able to solve bigger problems than if you were on your own.
Finally, collaborating is just fun. Try it and you will see.
See #1. If you are happy with making tiny contributions to the state of the art all the time, good for you. (This is especially at odds with your apparent disgust for people who "pump out" papers, but whatever.) Meanwhile, someone will study seahorses for ten years and revolutionize the field by realizing that seahorses are aquatic poneys, rendering most of your previous research mostly useless.
Solving things on your own is fine and valuable. Being able to use other people's ideas to solve your problem more quickly is an extremely valuable skill, however. While you will be reinventing the wheel, others will go around the world in a plane.
This is something between you and your advisor. As a PhD student, you are supposed to transition from supervised research to autonomous research. If you really feel this way, talk about it openly with your supervisor. Maybe you will be surprised. Maybe your supervisor even thinks that you are not ready for unsupervised research because of your other points (unability to focus, to collaborate, to make use of other people's ideas and applying them to your own problem…) and this is why he is still asking you to work on something where he can directly help you and direct you in your research, instead of letting you work on something with less direction and help.

So yes, if you continue with the mindset that there are certain things about yourself that you cannot improve due to your "personality", you will have a hard time, in academia and elsewhere. You will continue to give up at the first obstacle and never amount to much. And you can continue to think that nature, your personality, your upbringing… is to the culprit, in the end, you are the one who has to live with the consequences.

Just adding some nuance to your statement that "Nobody is born a good researcher.". I think it's the opposite: everyone is born a researcher. Observing babies shows that they are excellent experimental scientists: they will keep trying to do whatever it is they are interested in until they figure it out, then move on to the next interesting thing, etc. It's too bad that we lose this ability at some point in late childhood and have to learn it again later on if we want to become good at doing research.

I'm on @user108161 's side on this: I guess the "natural" thing in everyday life is jumping to conclusions - that's the way selection works: most of the time, our conclusions and preconceptions either hold or are at least (computationally) cheap. Handling (understanding, modelling) counterintuitive relations usually needs some advanced training.

Short answer to complement other longer good ones here.
You do seem really to care about the seahorses of all colors, and the pipefish and the shrimp. So focus now on learning whatever you can in your current environment. Continue  reading stuff that's not directly applicable. Do collaborate. Finish your PhD (toy models are sometimes good places to start). Then look for a postdoc with someone whose philosophy and style better match yours. When you run your own lab, look for students like you.

@SquaringtheCircleisEasy Thank you for the (unexpected!) bonus. When you're ready you might enjoy contacting my son (web page a little out of date): https://ms.mcmaster.ca/~bolker/

“Try to learn something about everything and everything about something.”—Thomas Huxley.
Obtaining a doctorate is much more about the second aim than the first. Your advisor understands the practicalities of this, given the finite limits of time, human ability, and other resources.
I sympathize with you, in that I like to study what interests me—occasionally drilling down deeply when I come across something really interesting and sometimes jumping off to look at something different. Thus I am quite unsuited to studying for a doctorate, as perhaps you are.
You can't have it both ways. Either knuckle down and take your supervisor's advice, for a chance of getting a PhD, or follow your nose (as I would do). Another quote from Thomas Huxley:
“Make up your mind to act decidedly and take the consequences. No good is ever done in this world by hesitation.”

The only problem is the issue you have about networking/collaboration. There are different styles of research and approaches, not everyone "processes" things in the same way. Having a large survey level knowledge of the field is actually very important and its a skill that often some people don't have. I recommend to acquire professional level skills on something practical and useful across fields (programming, probability, numerical methods) and then you can always apply that skillset to different problems.

Few small points about 2 and 5.
2) Toy models probably are often applicible as an inspritation. For example, say you want to change the whole US college admission methodology to better. There is a model for that, i.e. Stable Marriage Problem. Is it applicable directly? No. No one can make a preference list of all schools that one is interested in. But you can apply it in some sense. You can make all the applicants to make a small list, maybe with 10 schools each, and then you can proceed with the ordinary prosedure. What the "toy model" teaches us is that this process is stable if everyone lists every school in order based on desire. Increasing the list length will make it more likely to get everyone in a stable matching.
5) I will only adress a small part of this as it has many issues. It is completely fine to start from scratch ignoring all the previous research. I have heard a similar anectod concerning a famous mathematician. It turns out, when starting on a problem that researcher would ignore all the previous research and would try to solve it by himself for a while. If he fails to make it work then he would read the literature. I don't think there is something inherently wrong with tring to work on the problem without reading others'. The issue with what you say starts, as pointed out by others, when you don't want to read others' work no matter what.

From a research psychologist: there is no anti-research personality. You did a good job identifying various barriers to specific goals, such as completing your PhD. It's up to you whether those goals are worth adjusting the approach to the barriers, either through behavior modification or changes in how you view the problems, e.g., through cognitive behavioral therapy. Such a practice would be helpful to most anyone, regardless of their mental health status. Reading your whole question carefully, it sounds like there are two struggles: 1) not meeting your expectations of concrete goals, and 2) managing negative feelings that might secondarily impede your goals (and reduce your quality of life in the process). It might be worth considering what strategies could help you continue to make constructive progress with understanding your approaches and likely outcomes. You're already doing a good job on this path by asking these questions.


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As a tutor, how should I handle anxious/avoidant adult math student?
I'm a private math tutor, and I have an adult student right now (age 28), who is enrolled in algebra II in a community college. He is both very bright and has a kind of inferiority complex about academics because his siblings were much more successful than him in school and employment. This is his third attempt to pass algebra II.
He seems to struggle with math not because he can't do it, but for two reasons: because that's where he feels most inferior to his siblings, and because he has a hard time concentrating (perhaps has ADD).
The trouble is that when math gets hard for him, or when he's disappointed by a test result, he spends the sessions with me talking about anything but math, changing the topic when I try to bring it back to math. Or if I do manage to get in a couple minutes on math, he starts asking questions on peripheral topics that superficially seem like they are about math, but I think are really another way of avoiding the task at hand.
I've tried different ways of bringing him back to math, starting with using my body language (I'll, say, start writing with my pencil), then verbally suggesting we come back to math, then gently pointing out the pattern so he sees that he has to make a choice, etc.
One thing I don't do is criticize him. He's so vulnerable to shame, and so anxious (his voice trembles sometimes when we do math), that I have a feeling if I'm strict or demanding with him, that will be the end of all tutoring. He'll fire me or become even more intractable.
I've also tried supporting him by pointing out his strengths, and I do it honestly and with integrity : I genuinely see strengths in him and I can point to specific examples, so he knows I'm not flattering him.
As of now, he spends about 50% of our lessons avoiding math entirely like this. There are always other periods in which he learns, and the situation is not completely stuck.
I would like suggestions for how to handle this. Everything from how to more directly suggest or control our session activities, to how to support him in feeling less anxious and inferior so that he would more spontaneously choose himself to put in the effort.

Have you tried a sequence of small problems which he can do easily? Increase the difficulty gradually. Confidence can be built and maintained by experiencing a string of successes.

This may not be the most helpful thing to say, but it‘s worth reminding yourself that you are a math tutor, not a therapist. At the end of the day, it’s the student’s job to learn, and if he doesn’t — especially if he doesn’t because of psychological issues that go way beyond the expertise and training of a math teacher, and you’ve already tried everything you could think of to address the problem — well, then, you have done all you could. As frustrating as it may be to have to deal with such a situation, at least know that you are not expected to have a magic bullet to solve his problems.

@DanRomik That is apropos, actually, and helpful. It may be wishful thinking to hope that I could do much. I try with all my students to be supportive and encouraging at the level of an inter-personal relationship, because it makes our time more pleasant and contributes to learning, but this is not therapy, not only because I'm not trained as a therapist, but also because the students are coming for math---i.e. the context doesn't allow for supporting them in non-math ways.

Sadly, this may be infeasible. Throughout the U.S., community-college students who fail these type of classes are about 90% likely to never pass them, no matter what supports are given. I suspect this is, in many cases, a significant learning disability. (Large U.S. colleges are now removing algebra as a graduation requirement for this reason.) You may find more questions like this on SE Math Educators, e.g.: here.

You might also want to ask this question at matheducators.se, after the answers here are finished.

Let me make a suggestion that may or may not target the real reason. I don't have a way to evaluate its relevance.
I've almost never had to give up on a student, but it has happened. The reason wasn't them or me, but just time. I've had students in math who were really terrible at it and didn't really know why. Nothing seemed to work for them.
But in exploring things, I learned that somewhere in their background some teacher (or several) just failed to do their job and let them slide by. In order to help them learn (I think it was) statistics, I would have had to take them back through elementary school math from the beginning. They had never learned to add or multiply properly.
Even worse, no one ever gave them any incentive to learn math, nor any insight into why it might be important. They never had any experience with figuring out how to translate a problem into symbolic form, much less equations.
I had to give up, just because I didn't have the time to teach them ten or more years of things they'd missed.
It is possible, I suppose, that someone has figured out how to short-circuit that process and bring a student up to speed relatively quickly, but at the time, I had no real idea how to do it.
My action suggestion is to give your student a diagnostic test of some sort, even quite informal, to find out if they are just missing so many basics that the new material has no foundation on which to build.
I'll note that in my personal case, I was neglected by one teacher and didn't learn my multiplication tables. I managed to overcome the problem and finally forced myself to learn them - just after I completed my doctorate in mathematics. Now, I can faithfully recite seven times eight = .........

Thanks for the suggestions. I did ask him to consider seeing a counselor at his school, or approach the office that handles accomodations for disabilities, but he rejected both suggestions. At least, for now. I have a feeling that he will come to see the wisdom of this in time. If not this year, maybe next year.

You may not like this, and neither will he, but you will have to be robotically single-minded in that the next sentence out of your mouth will concern (and only concern) part (a) of exercise 5.2.
Either this works, or else he passes into a realm where he needs a therapist not a tutor.


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Is it usually allowed to use lie detecting technique (maybe using neural activities) during post-experimental inquiry?
When an experimenter want to find out about e.g. what is the hypothesis perceived by the subjects via post-experimental inquiry, if the subjects answered that they did not perceive any hypothesis, it might be helpful to find out if the subjects are speaking the truth or lying out of good intention (so that the experimenter would not know that he/she has wasted time on a potentially useless data point) with lie detecting technique.
Aside from the effectiveness of lie detecting technique, is it allowed by e.g. ethical board?

IRBs in the US might have a lot to say. But how would you do it? Lie detector tests have been proven to be junk science. Individual interviews by trained observers are a subjective but also very expensive. Seems like an impossible task.

Are there new technology which might enable lie detecting? Such as change in brain activation, e.g. EEG?

Possibly, but it seems unlikely that  you could design a valid experiment. Probably better to design the experiment in such a way that subjects have no incentive to lie. Sometimes that is done just by asking indirect questions rather than direct ones.

Even if the IRB allowed it, there would be the problem of getting informed consent from the subjects.

@Buffy How can I find whether IRBs would allow it? I would like to talk about general hypothetical experiments in which lie detecting techniques can be used (not actually conducting such an experiment.)

If you are at an American university then it has an IRB. Talk to them. If you are elsewhere, have a US colleague interface for you. You could also talk to any ethicist in a philosophy department anywhere, I think.


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Why should data mining be minimized in research?
According to this paper by the previous editor of Journal of Finance, Campbell R. Harvey, authors of papers should "convince the reader that there has been minimal data mining". Why is it so?

They have confused data mining with hypothesis mining.

@AnonymousPhysicist, probably an answer. Different fields use terminology differently.

What do you mean by data mining? If it is sifting through all the data to find what agrees with your model, you are doing it wrong (as one example of usage).

It should be pointed out that "data mining" is sometimes used as a pejorative to describe the process of testing large numbers of hypotheses in hopes of finding one that is statistically significant so that you can publish a significant result.  This is a completely different sense of the phrase from its other use to describe the process of building a predictive model that is tested for its predictive ability on out sample data and then used to make predictions on new data.  That second sense is what data scientists do.  The first sense is what bad scientists do.

Data minimization is an important aspect of privacy engineering. When the research relies on data that might have privacy-related implications, it's important to not collect more data than required for the purpose of the research.

Assuming by "data mining" what they really mean is "continually testing hypotheses until you find something significant"...
See:
https://stats.stackexchange.com/questions/310119/why-does-collecting-data-until-finding-a-significant-result-increase-type-i-erro
or a comic depicting the same issue:
https://xkcd.com/882/
Basically, when we perform a hypothesis test (using a frequentist approach), we are asking whether it is likely that the data we observe (for example, a difference between two groups) occurred simply by chance.
However, if you look at multiple possible questions, it becomes increasingly likely that you find a result that, due to the flawed approach, appears unlikely to have occurred by chance. If you use a significance threshold of 0.05, you in fact expect that 1/20 times (in the large number limit) you look at completely random data you will conclude a significant difference.
You can still do this systematically and correct for this exploration without increasing your false positive rate. The problem is when you set these explorations aside and pretend that only the "interesting" ones (based on a flawed measure of statistical significance) occurred, you are likely to report a result that occurred by chance and is not replicable.

This problem is even worse if you use your results to inform further analyses in an unprincipled way. For example, you compare two groups: jelly bean eaters and non-eaters, and find no significant difference in cancer risk, but you look and see that the difference is smaller in a subgroup. You then exclude that subgroup (say, people over 55 years old), repeat your analysis, claim "statistical significance", and write a paper titled "Jellybeans cause cancer in people under age 55".
If you didn't set out to test this hypothesis because you had no a priori reason to expect age differences in jelly bean danger, it is very likely your conclusion is wrong: you have "mined" out a result from the data that didn't really exist in the first place.

@Roland Thanks; fixed.


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If I have a list of abbreviation at the beginning of a paper, do I still need to give the full word when I first mention the term in paper?
Do I still need to write e.g. "willingness to pay (WTP)" when there is already a list of abbreviations containing WTP at the beginning of my paper?

I am not an academic, is it normal to start a paper with a list of abbreviations? Shouldn't that go at the end, e.g. in an appendix?

@stannius In some journals it is common, and usually formatted someplace between the abstract and body of the paper. Others may list them at the end; most commonly not at all, though.

I would say that it isn't essential, but it might be a service to your readers to do that. They will, then, see the term used in context as well as its abbreviation.

Do I have to do this consistently? (e.g. if I have done this for one word, do I have to do this for the other words in the abbreviation list too?)

@Aqqqq I would say yes, consistency is important. If I've seen one acronym expanded and then not the next one, it looks like the authors have been careless.

I agree with Buffy 100% that it is not strictly necessary.  However, the question is raising a red flag for me.
The purpose of academic writing is to communicate ideas as clearly as possible to other human beings.  If you include the full words, does it increase the clarity of the sentence?  If you're unsure, ask a colleague to read over a bit of the paper.  My strong suspicion is that they will prefer to see the word written out the first time, and will want to use the key only secondarily (if they forget an abbreviation.)
Always keep the four C's in mind when you write: Clarity, Clarity, Clarity, and Clarity.  All else is just formatting.1
1 - And as De Novo observed, formatting is also clarity. ;)


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How to italicize technical which is explained in Introduction but defined in another section later according to APA?
I am currently writing a paper, which starts with an "Introduction" which is followed by a "Definition" section.
I plan to briefly explain a technical term in "Introduction" and define it more specifically in "Definition". According to APA, I need to italicize technical term if they appear for the first time. So am I correct that in this case, I only need to italicize the technical term in "Introduction" once?

In general, you should italicize a technical term when (or right before) you define it. And you should define it when it appears the first time. If you don't need to define or explain it, then you are implicitly assuming that your audience is familiar with it, in which case you don't need to italicize it. The difficulty arises here because you are essentially defining it twice, once informally and the second time formally.
I would recommend italicizing the first use in each of the sections. Clearly, you should italicize it the first time you use it. But if you are defining a lot of other terms in the "Definition" section, leaving it unitalicized might make it look odd next to all the other italicized terms you are defining.
This is not what the APA rules actually say, but I would assume that they also believe that informed decisions in exceptional cases should override their rules where it is appropriate.
Another thing you could do is say something like

we now give a more technical definition of thingamabobs

in the "Definitions" section, and implicitly point out that you've already  defined it, which is why you're not italicizing it.


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How to answer your boss's question about your impression on the progress of a project that you took part in as a newcomer appropriately?
I work in Germany. After a group meeting of 5 about a project that I took part in, my professor asked me how do I think about the project progress. I had the impression that we might not meet the deadline, but I think that as a newcomer, it is not appropriate for me to say so. So I just told him what I am going to do for the project.
Would there be any cultural differences in dealing with this (e.g. Asian country vs. Germany)? (Would the answer be different if I am in a non-academic field?)

Assuming your professor is a reasonable person, there is nothing wrong with truthfully sharing your view of the progress in the project. They wouldn't be asking if they did not think your opinion matters. Of course, if you are concerned about the project progress, you want to stick to the facts and not over-dramatise the situation of the project. It may also be a good idea to come equipped with at least some ideas how to go forward (since this will likely be the follow-up question if you share that the project currently could be in trouble).
I am sure there are cultural differences related to this, but I don't feel qualified to reason about what the correct way of framing this in an Asian country would be. However, the difference between academia and industry (in Germany) isn't very large - in both cases there is an expectation that you politely raise issues as you see them, rather than pretending everything is great until the car hits the wall.
Edit: one important thing I forgot to mention - this is under the assumption that this is more of an internal meeting. If the meeting also includes external people, most importantly representatives of the funding body behind the project, the only correct answer to "how is this project going?" is "great, we are going to achieve all of our goals." Letting whoever pays the bills know that it may be time to pull the plug on the project is unlikely to go over well.


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How to use "can" or "could" when referring to a methodology?
If I say "This methodology can/could be used in the research in this area, e.g. (the relevant paper)", should I use can?
If no examples is given, should I use could? (to emphasize possibility?)

For generic word choices like this, I think you should look to the English stack exchange instead of Academia. As you can find there, the two words have somewhat different meanings. Generally, 'can' would work if it's known that the method would apply, and 'could' if you propose that it the method might apply.

You can use "could" or "might" as an alternative to "can" when suggesting less force or certainty. It is THAT SIMPLE. The answer to this question (or any question like that i.e. about the usage/meaning of any specific word) should be looked up in a dictionary (best option). Another option is advice from an American/British/Canadian/Australian colleague. The Stack Exchange English is mainly used by ESL students, and ESL students are giving answers there, which is 100% unreliable when compared with the options I suggested. It's a serious fault of the system.

This seems like a fine line with no objective answer. It depends how ready you are to defend your point of view. If you believe firmly (i.e. have good evidence that the method is valid, even if it hasn't been used yet), you can use can. Else, if you consider that your opinion (that the method is valid) may be contested, and you are not sure that it's defensible, use could.


text:
How to in-text cite a series of paper with nothing in between in APA?
E.g. Would it be OK if I write:
The papers by Bechara, Damasio, Damasio, and Anderson (1994), Bechara, Damasio, Tranel, and Damasio (1997) and Bechara, Damasio, Damasio, and Lee (1999)  shows that .....
?

Why not write "X affects Y (citation1; citation2; citation3)"? Why is it necessary to write these out front?

I do not believe there is a rule that covers this. the best I can find is on the APA Style Blog:

When multiple studies support what you have to say, you can include multiple citations inside the same set of parentheses. Within parentheses, alphabetize the studies as they would appear in the reference list and separate them by semicolons. In running text, you can address studies in whatever order you wish. Here are two examples:

The running text example has each citation in a separate sentence so it is not a perfect match. I think the main point is that in the text, you can do what you want. That said, this is one I would either let the copy editor deal with or more likely try and write the sentence in a way that allows the citations to be parenthetical material.


text:
Would it be OK to in-text cite a paper without mentioning the name and year explicitly in APA?
For example, would this be allowed in APA:
Ohme, Reykowska, Wiener, and Choromanska (2009) showed...; in the next year, the same group of researchers conducted an experiment which also focused on ... to show...
Or do I have to add (Ohme, Reykowska, Wiener, & Choromanska, 2010) at the end of this sentence?

I think this is covered in the APA style blog. The example they give boils down to instead of using

This idea was recently explored by Palladino and Wade (2010). Palladino and Wade’s (2010) results indicate that “a flexible mind is a healthy mind” (p. 147).

you can write:

This idea was recently explored by Palladino and Wade (2010). They noted that "a flexible mind is a healthy mind" (Palladino & Wade, 2010, p. 147).

So yes, you need to give the full names and year of the reference in the body of the text.

On the other hand, without more context, the second reference could also be needed just for the page number of the quote.

@henning I am confused. In the first example, the parenthetical part only has a page number and the rest of the citation is in the text.

Hmm, the first example really supports your conclusion better than mine.

"instead of using ... you can ..." implies that the second option is optional and better. I would hesitate to say if it's better, but can clarify whether it's required?

@AzorAhai it is not required. The only thing APA requires is the full citation information in the sentence. Nominally the style manual lets you choose which you think is best, but copy editors may try and force their personal preferences on you.


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Is it unnecessary to write "Please refer to xx paper for detail" after talking about framework presented in this paper?
I wrote a paragraph about a framework from a paper xx. Is it still necessary to mention "Please refer to xx paper for detail" at the end of this paragraph?
It is a thesis.

Since most people would understand that anyway, no, it isn't really necessary. It might be different if it were necessary for the reader to explore that detail before continuing with reading your work, of course. But in that case, you might want to make it more explicit.


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Is it appropriate to have two tables side by side in an academic thesis?
I have about 5 relatively small tables which will be shown in the same part of my thesis. I think it might be a waste of space if I place one table per line, but I am not sure whether one should put e.g. 2 tables side by side in an academic thesis as I have never seen someone do this.
What is the convention?

The convention is what is clear to read or what is specified by your institution and/or advisor.

Don't forget the whitespace. It makes text easier to read. A busy page looks intimidating, and is usually harder to focus on.

The only rule here is to do what is best for your reader.  Try it different ways and see which presentation is simplest for the reader to interpret.  Some considerations to bear in mind are simple labelling of your tables and close proximity of the tables to any textual explanation of their contents.  Try to allow the reader to see the tables and accompanying textual explanations without having to flip back-and-forth between pages.  Your supervisor might be able to give you some guidance here, but the goal is to make the dissertation as clear and simple as possible.  The fact that you have not seen this before in a dissertation is not determinative of any problem with it.
If you find that you are presenting large amounts of information in tables, then another thing to bear in mind is that tables are usually a poor way to present large amounts of information, relative to appropriate graphs.  Consider whether you can present the same information graphically in a simple and clear manner, and relegate the accompanying tables to an appendix.  Again, you should be driven by consideration of what is best for your reader.  Always ask yourself: if I was reading this and had not seen it before, how would I want it presented to me?

For a dissertation, first follow any university and department rules about the format. Those take precedence over everything else, even readability.

Heaven forbid we create educated thinkers that would violate rules!  ; )

In general*, it is a bad idea.  Even a two column table will look fine when centered on the page and with 1+ inches of white space between the columns.  It is the norm*, for thesis style to have lots of white space margins, double spacing, non-wrapped tables and figures, single-column, etc.
They are not usually set with anything approximating the layout in a journal.  (Even for journals, they often have an easier time type-setting articles that have simple "white paper" style formatting with figures/tables at the end, etc. versus attempts to make the thing look like an article ahead of time.)  In addition, I think you will find it easier to maintain the formatting of the document over time (as you write it), if you don't do some complicated setting of two tables side by side.
I did my thesis with the tables/figures at the end of each chapter and used endnotes versus footnotes for the citations (like a white paper or journal submission...and several chapters were sent to journals almost as is).  This was received fine in terms of the review committee and the "ruler lady" (grad school format czar who checked white space and such).  In general, I advise to write clearly and simply and truthfully and with good content.  Elaborate typography is not desirable and can make your life a hassle as you work with a large document over time (distracting you from the core content).
*Of course follow your local thesis style guide.  I am giving you general advice.


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Is it appropriate to mention lack of expertise in certain area as limitation for master's thesis?
I'm currently finalizing my master's thesis and am working on the discussion and limitations part.
I did some relatively standard statistical tests on my data, which gave promising results. My supervisor suggested trying some machine learning to create a predictive model. While I did take a basic machine learning course during my master's, I am by no means an expert in this area.
Now, my machine learning model performed pretty okay. But, since I only know some basic machine learning, I'm sure better results might be achieved with other machine learning methods I have not tried due to lack of expertise. Is it appropriate to mention this lack of expertise as a reason why I did not try to further improve these models?
Note: I tried 2 different ML methods/algorithms, which were suggested by another member of staff.

Rather than describing this as a limitation, I would present this as an area for future research. For example,

Machine learning methods X and Y produced promising results for predictive modeling. An area for future research would be to optimize these as well as explore methods, a, b, and c.

and then build upon this with details to be an appropriate length (probably a paragraph or two).

Like in the other answer by @RichardErickson, I would suggest you frame this as a future direction rather than a limitation per se.
However, your general question seems to be whether you should reveal your own personal limitations in your thesis, and for that I would strongly say no, never. It's normal and reasonable to not pursue every possible avenue around a research project: time is simply finite.
That said, your lack of experience or understanding of a technique should never be used as an excuse. Part of doing research is learning new techniques. In your specific circumstance, it sounds like you've already covered that base fairly well by applying two different machine learning techniques; your supervisor can help you determine whether this is completely sufficient or not, depending on the results. Your thesis (and any publication) should make clear how you applied those techniques and allow a reader to assess the appropriateness of your approach based on their own expertise.

It is not generally appropriate to cite your own lack of expertise for failing to pursue a particular line of analysis in research.  The reason is that an academic work is supposed to be an objective analysis of the problem, and so the reader will want to learn about what methods are scientifically useful to deal with the research problem at hand, not about the personal skills of the authors.
Of course, there are certainly cases where authors of an academic work do not have the skills to extend the research in a particular direction.  That is what is happening in your case.  Instead of mentioning the limitations on your expertise, you should simply state the method you used, and then note that other methods might be applicable to the situation, and these constitute an avenue for possible further research.  It is not necessary for you to be the one that does that future research ---since you lack the necessary expertise--- but you can still point out that other methods might fruitfully extend the analysis.


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Short publication as a letter and then more extensive as an article
I have written some paper, that is quite extensive, that I would like to submit.
However, the journal that I would like to submit to (with the highest impact factor) accepts only short letters that can be up to 4 pages.
With such a low limit I am not able to describe everything precisely and I am not sure what to do.
Is it good idea to try to publish some short letter in the journal with good impact factor and then try to submit extensive version to different journal, or maybe it would be better to submit the whole article to the journal with lower impact factor but without such low limit on the number of pages?
I also wonder how the journals are going to consider my idea to publish the same thing twice, but the second time in much more extensive way.
This is the first time I try to do such thing and I do not know if it is a common practice, and how much ,,knowledge'' should be included in the short letter.

This is common in my field, physics, to the extent that at least one publisher has an explicit policy encouraging it:

The submission of an expanded version of a PRL to a topical Physical Review journal is an established practice that provides readers with easier access to important additional information. If authors simultaneously submit a Letter to PRL and a regular paper to one of the Physical Review journals, the two manuscripts are then reviewed coherently, typically by the same reviewers. If both papers receive favorable reviews, we aim to publish them at the same time, unless this leads to undue delay for one of them. We also ensure that the paper and the Letter cite each other.
Submitting a joint publication couldn’t be easier. Simply alert the editors by mentioning the companion papers in your cover letter.

For example, consider the case when you have come up with a great new method to calculate something. Then the letter would tend to introduce the method, and show results from an example application or two. (Naturally, these examples are usually the ones  with the most impressive or surprising results.) The full-length article wouldn't so much repeat what was stated in the letter as it would extend it. It might provide more details and justification, applying the method to a wider set of systems, and showing some less central conclusions. The idea is that it should still be a different paper, but there is less need for the letter to be fully self-contained.
That said, it's even more common to first write up the more "exciting" results, submit that as a self-contained letter, and then submit a more extensive follow-up as a regular article later. I don't know how universal either practice is, so you might want to check with an advisor, or mentor, or colleague to figure out if this is an accepted practice in your field, and what the expectations would be.

Fully agree - I did just this more than a few times with PRL and PRB or APL and JAP.

@Anyon Do you use the same title for both?

@AlBundy Following the "should be different papers" logic, I'd say go for distinct (but usually thematically related) names that match the distinct contents in each. You could also use subheadings, like in "On X: Y" and "On X: Z", but using the exact same title for two papers released the same year just seems like it would cause unnecessary confusion.


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What latex template to use when you do not know the journal you are going to submit
Usually distinct journals have their own templates for latex, some of them  require you to use specific format for pictures etc. However sometimes you write an article and you do not know what journal will be your target for submission. What temples do you use in such scenario? Do you have any custom ones or do you prefer one provided by some journal?

are you just asking for opinions?

"However sometimes you write an article and you do not know what journal will be your target for submission": more often than not this is a bad idea, which is frequent a cause of rejection. My 2 cents: when you write a paper, try to have a clear understanding of the target journal and audience.

Write TeX, submit as pdf.

Duplicate of this question on TeX stacckexhange
https://tex.stackexchange.com/questions/514898/how-can-i-format-a-document-for-submission-to-analysis-journal/514906
My answer:
If the journal doesn't give you style files I suggest just vanilla arrticle class. If the paper is accepted they will format it. If not, you haven't cluttered it with formatting some other journal won't like.

To add to the answer I've rarely used templates. An editor of your choice and conversion to pdf seems ok. I never got a formatted paper to review, too. Or so few that I don't remember.

In general whichever software you use to write the paper, word processor or LaTeX, make sure that it is easily adaptable. That said, most journals will have very specific requirements and it is difficult to make a generic file which suits all. In my experience the text is easier to adapt than the format (but this of course depends on the field).
Beyond using the most basic template, there are some pitfalls which are worth considering beforehand:

The article is still a draft so focus on making it as readable as possible for the reviewers rather than fancy.
Avoid elaborate packages that will make exporting the paper to different software impossible if needed. I recently had to submit a LaTeX paper to a journal accepting only .doc files, and it took a while to realise that I needed to revert to an old citation package in order to export to RTF. I think this is a specific case of the general point that you shouldn't rely on specific environments for your paper.
Figures should follow basic rules of readability (font size, colours, etc) and this should keep you safe for most journals. It can also be handy not to rely on colour if not necessary.

Keep it simple, elaborate only when necessary.


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Writing out numbers in ranges: between 5 and 50 or between five and 50?
In a manuscript, when defining a specific range that starts below ten and ends bigger than ten, is it written as numerals for all, for the number below ten or all in numerals?
Example:

We detected between 5 and 58 genes.

or

We detected between five and 58 genes.

Previous discussions on this topic don't really answer this specific case
When and why should you write numbers less than 10 in words?

I'm voting to close this question as off-topic because this a question about English language and usage ...

Or “between five and fifty “...

For measured values, you should use "5 and 58". For enumerations "five to fifty reasons"

@virmaior why is this off-topic but the linked question not?

Okay alternately that question contains your answer.

No answer in the linked thread discusses this topic. Stop being pedantic. Thank you for answering my question. If you had done so as an answer and not a comment, I would have marked it as accepted.

I agree with the OP - if the linked question is on-topic, so should this one.

For the sake of consistency, you have one more choice: "We detected between five and fifty-eight  genes". I personally prefer your first one , i.e. "We detected between 5 and 58 genes" Consistent, concise and clear.


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Would it be seen ok to change PhD more than once?
Last year I was doing a PhD in an area I happened to not be interested in after a while, and I decided to change PhD project which end up taking me to a different university and different country.
At the moment my topic is good, of my interest, but I don't like the way my supervisory team works, more specifically, I am not making too much progress on my PhD thesis, because I'm helping with other stuff and my supervisor already said that is the way in which the department works, so is either accept their system or quit.
Plus, I've been having a hard time to adapt to this place, my work is all in English but I am in a non-English speaking country so my life is not that easy in that sense. I don't speak the language of this place, and I am trying to learn it but it would take me a while, plus I feel isolated as well and with very few friends, therefore I am deeply missing the city in which I was doing my former PhD.
Due to those reasons I've been thinking on applying to a project of my interest in a city nearby where I used to be, but I don't know if this would be seen badly by supervisors. And instead of being helping myself, start being considered as quitter and not suitable for PhD research.
What is your advice? Should I just endure here and try to finish on time despite the way of working of my supervisors, and then leave?
If you were a supervisor and I tell you this story would you take me on for a project or you'd consider me as a student that is better not to accept?

Do other students who work with your supervisor/around your supervisory team tend to graduate on time? Helping with other stuff can be quite normal, an important part of training, and should only really be a problem if its not leading to graduation.

No, people usually tend to submit a year or sometimes two years after the official deadline has passed. And I know some students here consider that quite normal, but I wouldn't really be happy to keep working on my thesis after the official ending date.

Did you ask about that before you accepted a position there? Not learning about that ahead of time is kind of your responsibility.

Wouldn't changing research groups and projects presumably also mean that you lose a year or so?

Only you can decide how unhappy you are in a given situation, so what action you should take is up to you.
I can tell you how such a CV would come across to me, though.  It wouldn't be positive.  It would look like your decision-making process doesn't have enough thought behind it, and that you're likely to make important decisions and then change your mind.
The quality of work you've done might get you an interview after someone has drawn such conclusions, it may not.

Once graduated, as a hiring manager of PhDs, I certainly would not get a warm fuzzy feeling about hiring the OP either. If they get 'not interested' in things so quickly and don't see them out it will be a major problem in the workplace.

You lay out a lot of the problems you would face. Most potential supervisors would be at least a bit skeptical of you and your commitment. You would have to find someone who would accept you and only he/she could make a decision.
Before you jump, you should talk to potential supervisors in person and lay out what your problems have been and what your potential is. Only they can really answer this question. It is likely that you would have to have some special skill that the professor needs.


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How is it best to put an unfinished PhD if you want to continue in academia?
I left a PhD position that I did for a year and then changed to a different area in psychology, the subject I do my PhD in. I am just wondering how to put that unfinished PhD on my CV. After my current PhD, I would like to continue on academia and apply for postdoc positions, maybe even in the same university in which I dropped out but on a different department. So I don't know how could I put that antecedent on my CV so that does not really affect me later on. Or would you think that with my achievements during my PhD the previous academic history remains irrelevant? I was thinking I could just leave it as one year of research internship, but I am not sure about this.

What about something like this?

Education

2016-present, PhD student, psychology

2015-2016, PhD student, underwater basket weaving

2012-2014, BSc, underwater basket weaving

I think that since it will never be finished, put the work you did as "pursued PhD in  and did the following:  item1, item2" etc.  I don't think it is required to put in the word "unfinished", as that is implied, but if someone asks, always be honest.
If/when the other PhD is finished, this should add credibility, not detract from it.
Have a friend/colleague review for suggestions.


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How can I finish my algorithms research project in 3 weeks?
So I'm doing a research project on a problem in graph theory and my conference deadline is just 3 weeks away. I need to develop a novel approximation algorithm for this problem and test it on synthetic data. I've already read a bunch of papers and have done a bunch of experiments to discover certain properties of graphs, but I haven't started writing the algorithm nor the paper. The good news is  Is it possible for me to do this in 3 weeks (assuming I work a total of ~200 hours)? A deadline extension is completely out of the question. The good news is that I have an expert professor mentoring me and he'll help make the paper more mathematically rigorous. Does anyone have some advice as for how I can finish this in 3 weeks? Thanks!

The main thing is don't skimp on sleep. You will get less done if you work over-long hours than if you get enough rest.

I'm still sleeping for at least 5-6 hours per night, but I'll also be working at least 10-12 hours per day.

Ask your advisor. We don't actually know about your project, and are merely random people on the internet, so...

Management would typically schedule a miraculous breakthrough in week 2. The real answer is to learn from this and not overpromise to such an extent in the future!

The topic isn't too mathematically heavy and the paper is mainly experimental. We're only shooting for about 10 pages. So is it possible for me to at least get something done? It doesn't have to be miraculous, but it must be solid.

That’s 5 hours gone on here...

Does anyone have some advice as for how I can finish this in 3 weeks? — Sure.  You can be extremely productive and extremely lucky.  (If I were your advisor, I would tell you to forget about deadlines until you've actually done the work.)

You won’t know if you can do it until you give it your very best shot. All we can say is that what you are asking about doing is very difficult. Some people might be able to cobble something together in 3 weeks. It won’t be as good as it might have been if they had, say, 3 months, but some rare very talented and hardworking people might produce something halfway decent.
Other people won’t come up with something good even in 3 months, or 3 years. It depends. We don’t know you, and we don’t know how hard this goal is.
I suggest that you give it your best effort. Even if you “fail” (in the narrow sense of not producing a minimum viable paper by the deadline), I believe it will be an educational and very rewarding experience to work extremely hard for the next few weeks in an attempt to meet this deadline. It will both advance your research substantially, which will yield some useful benefits in the future regardless of whether you meet this particular deadline, and teach you a lot about yourself and what you’re capable of. In my opinion, most people (especially younger, less established ones) use maybe 15% of their true intellectual capacity. Learning how to make the most of your potential is an incredibly important life skill that separates almost all successful people from everyone else, and trying to meet a crazy, impossible-looking deadline is a fantastic way to get on the path to acquiring this skill.
Finally, I don’t want to be guilty of giving you any more reasons to procrastinate by giving you long psychology blogs to read, but here is something that might give you a bit of hope/inspiration. Good luck!

I will be honest: If you expect to do real research starting from zero within 3 weeks, then you are probably on the wrong track. If that was so, then research would be easy and we would live in a world where we know and can do much more than we actually can right now. Research is difficult and takes time.
To your particular question: We of course don't know. We don't know what your concrete research project is, and we don't know how much you already have. I suspect that just implementing and debugging an algorithm you already have thought about in detail will take 3 weeks unless it is trivial. But you seem to still be in need of some of the thinking, the testing, the evaluating, the writing up results, etc.
The only person who can really help you with this is your adviser. Talk to her -- in fact, I may suggest to travel back in time and go to her about 3 months ago so you can work out what needs to be done in the time between then and now!

So are you saying that it takes 480 hours to do? Can we cut that time in half and get something done in 240 hours?

I've already conceptualized the algorithm and now I just need to get to the specifics.

I spoke to my advisor and he says it's possibly doable. It will probably take 25 hours to implement test the algorithm (once it's complete) and another 25 hours to evaluate the results write the research paper, so that's 50 hours. What I'm unsure of is how long it will take to do the thinking.

The algorithm is based on a conjecture I came up with. The conjecture (which is somewhat trivial, but quite powerful) is accurate about 90% of the time and it would be surprisingly simple to implement it, but it might not be rigorous enough. It's still a cool conjecture though.

How are we supposed to know whether the number of hours you quote is enough? I've implemented algorithms for which I suspect I've spent 240 hours just getting the implementation right, not counting evaluation. These were of course worth many thousands of lines of code. Maybe you have something trivial -- though usually trivial also means that someone has thought of it before.

I'll provide some context. I'll reveal that I'm a senior in high school and I'd like to submit to a very prestigious competition for which the deadline is in 3 weeks. Most semifinalists and finalists complete research over the course of 100-350 hours. The vast majority of the projects either involve lab work, applications of machine learning, or pure mathematics. Theoretical computer science projects aren't very common so that's why I'm trying to seek some advice. Though I doubt that it will take thousands of hours. I'm being judged on the quality of my research and scientific creativity.

The project needs to be at the graduate level, but the paper and depth requirements aren't quite as rigorous as those of journals. 250-300 lines of code should be sufficient. I just need to develop some type of algorithm and somehow show that it's more efficient than the state of the art. The initial algorithm I developed with my conjecture was only 25% accurate, so I just need to spend a lot of time modifying it. My mentor said just to use my intuition. The thinking involved in my initial algorithm is on the right track, but the implementation is probably bad.

To put your number of lines in context: A good programmer with several years of experience writes about 100 lines of (correct) code per day.


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Math Research after undergraduate degree and before graduate school
I graduated with a bachelor's in math a few years ago and this year I've applied to several graduate programs and have been rejected. One of the graduate coordinators gave me some very helpful feedback and one of the things suggested was to try to get some research published.
I've found many places for undergraduates to publish, but I am technically not an undergraduate anymore, nor am I a graduate student.
Is it feasible for me to get something published given my circumstances?
Are there any places that would accept research at my level from someone who has their undergraduate degree?

One way would be to publish with a colleague who has the know how, a former teacher. Publish something on magazines, local magazines.

This seems rather strange advice to me, at least for someone familiar with graduate programs in the U.S. That said, you can find a lot of examples of suitable journals and examples of possible research topics in Thomas J. Osler's list of papers, many of which I believe he co-authored with his undergraduate students.

@DaveLRenfro He had more advice that you would probably consider more typical, but this was the piece of advice that wasn't as straightforward for me. The other big piece of advice he gave me was to take another semester of each Algebra and Analysis. Is that more typical advice? Would you say that my effort would be better spent on other aspects of my application?
Thank you for the link.

Taking another semester of algebra and analysis is much better for you. For one thing, there is little risk of failure, unlike research which could wind up not going anywhere even if you put in a lot of effort. For another thing, you have the opportunity to do VERY WELL, which would look very good on your application as well as allow one or two teachers to write a very positive recommendation for you.

@DaveLRenfro You make an excellent point; it would be risky. I think I've been interested in pursuing it since I have some time to kill before the classes start, but I could instead take that time to prepare for those classes.
I've reread the email, and I the advice was to participate in research. That may be a little more realistic than publishing. Either way, I think I'll take your advice and put my effort toward preparing for those classes.
Thank you for the advice.

Yes, of course, there are many places you could publish research at your stage. For one thing, many undergrad journals will accept papers from recent graduates as long as the research was started when they were an undergraduate. Another option would be to team up with some other undergraduate and write a paper together.
There is also the Graduate Journal of Mathematics (full disclosure: I am an editor there). You don't need to be a grad student to get published there. The website explicitly states that a good bachelor's thesis project could be acceptable. And, of course, if you do work at the level of a professional journal like the Journal of Pure and Applied Algebra, you could publish there. They have published papers by undergraduates and recent graduates of Reed College (students of Kyle Ormsby), for example.
All that said, I agree with Dave Renfro that a better way to strengthen your application for a PhD program is to demonstrate success in graduate level courses. You could do a post-bac program like Smith's. You could audit grad level courses at a local university (and try to get a letter of recommendation from the professor who can speak to your potential). You could apply to master's programs instead of PhD programs. As Dave said, the upshot of showing depth via coursework is that it's more likely to succeed than showing depth via research (after all, grad school is meant to teach you how to do research), and also the coursework you do will help you pass your qualifying exams when you do eventually get into a PhD program.

Unsurprisingly, this answer came much too late to affect my decision, but I think it is a good answer, and hope that it will be useful to other people. For what it's worth, I did extend my search to masters programs, got accepted to one, did well, and now I'm most of the way through a PhD program.

Yay, that's great to learn!

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