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How to keep one's focus during discussions, meetings and lectures
I noticed that I have more and more serious problems keeping focused, and despite my efforts to fix it the problem is just getting worse over time.
When I'm in a research-related discussion with someone, my mind easily wanders, and I won't be able to recall the last thing other person was saying so I have to politely ask them to repeat it.  Usually this is because I'm still thinking about the last idea they mentioned instead of continuing to listen to them talk, but sometimes it's just as if my mind just turned off for the duration of a sentence of two.
At least when I'm talking to one person, I can always ask them to repeat what they said or ask them to slow down.  But when it's a group discussion or a lecture/talk, this is not possible.  When I was an undergraduate and attended lectures regularly, I didn't have this problem.
Am I alone with this problem, or do others encounter it too?
What strategies can one use to improve concentration and comprehension?  How can I train myself to focus better?
I am very concerned about this problem as it affects my academic work and performance.

You could ask for an example, if you haven't thought of that, depending on your subject. It's not the same as repeating.

@Compass Agreed, although it is possible to sound silly this way, e.g. http://mathoverflow.net/a/62749/1682 :-)

@TrevorWilson I'm not a math guy =.=

When talking with just one person, I ask them to give me time to process what they've said. If you're just zoning out, it might be worth leaving off the conversation for a bit.

The question in the topic can generate some useful answers but the situation as you describe it seems to point more towards a possible medical issue. I'd highly recommend you discuss this with your GP/doctor. Perhaps you're simply struggling to pay attention to discussions you find boring but you'd want to rule out things like an attention disorder or microsleeps first.

This is a common issue I have when attending a talk or discussing on some intense topic with a collaborator. Since English is not my first language, I also happen to spend some time mentally translating it to my internal language (which is a mix of many by now).
Personally, some mental homework and meditation has helped me focus. Looking at the abstract and author bio (if available) before the talk helps. Experience gained from attending more and more talks has also helped.

I think it helps to ask as many questions as you can reasonably get away with asking, about whatever parts of the talk you are able to formulate questions about.  As well as helping you understand the thing itself that you are asking about, it slows down the talk (which might be appreciated by others as well as by yourself) and also may help to keep you engaged.
(Of course, the number of questions that you can reasonably get away with asking may depend on the speaker, the type of talk, and the audience.)

You should first attend to any lifestyle factor that may be disrupting your ability to focus and maintain short-term attention.
Most important is sleep.  Make sure you have regular, consistent sleep of sufficient quality and quantity. This means going to bed at the same time each night, and waking up the same time each day.  Avoid alcohol and caffeine after 6pm. Get some exercise or activity (20 min. walk) each day.
Second is to avoid "multi-tasking".  Stop doing two, three, or four things at once when you study, read, or attend class.  TURN YOUR PHONE OFF. Be in a completely quite place.  No other screens or activity on around you. If you are working on your computer, turn off your email and your messaging apps.  Don't look at them for hours.
Finally, start writing notes BY HAND when you attend lectures and group discussion, and you should aim to catch ALL important comments and points.  If you put this level of attention into written notes, then it's hard to allow space for your mind to wander.

I find that writing - note taking - helps me greatly.  If I'm just listening then my mind wanders (problems of middle-age: one's mind is not as flexible as once it was!)

What you describe sounds remarkably like burnout (http://en.wikipedia.org/wiki/Burnout_%28psychology%29) - the effort and amount of material and time involved after undergrad are often greater than during undergrad.  It may not be possible, but downshifting or taking a break for focusing on other avenues could also help - if it is burnout "pushing through" can exacerbate the situation (you note that it seems to be getting worse).
If it is not possible to take an actual break or temporarily reduce workload/hours, it might help to enforce personal time to focus on other tasks (for instance reading a book for pleasure, going on a hike over a weekend, playing a video game, volunteering at a local charity, etc.).

Sounds to me more like normal life. Burnout is, I believe, more like when you don't even care that you're not concentrating.

Thank you for your answer.  I wish I could blame it on burnout, but I cannot.  This happens even when I am not overworked.  Also, I am not new to this type of work (as a new graduate student would be), but for obvious reasons I tried to omit personal details.

Snap a rubber band on your wrist. If it is a lecture, take notes. You could use the program Lumosity to improve your brain's attention span, memory, etc.  Ask questions, but only good ones... Don't annoy people, or they will hate you forever.  Not really, but still.


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Can being a reviewer for a top journal improve my chances in PhD admissions?
I have got an email of invitation to review a paper in a best journal of my field. I had a paper there and somewhere else almost in that field.
As I must invest serious time and attention to complete the review, I wanted to know if that does any advantage on improving my resumé for getting a better chance of acceptance and scholarship for my future PhD program abroad?
Basically, should I mention in my CV that I am a reviewer of that journal, when I am sending it to other universities?
P.S. I have graduated from M.Sc. two years ago.

I have put the question in the title, feel free to reword it if you want.

If you look for an academic career, that's an opportunity to jump onto.

Yes, this helps.
Regarding the CV, I've seen frequently that people include sections like "Other scientific activity" or "Community service" where there is subsection like "Referee for:" followed by a list of journals (sometimes even with numbers indicating how many reviews have been done). So you can make this service visible in your CV.
There is another way in which reviewing may help your career: If you write a sensible review for a relevant paper it will be read by at least one editor of the journal and it's safe to assume that this editor is a respected and reputable member of the community. In this way, writing good reviews helps to build your reputation (albeit slowly as not many people see your reviews with your name attached, but at least these are the "right" people).

Can I mention the name of those papers in my CV as well?
If the author of those papers are reputable in my field already, Can I tell them I have reviewed your paper when I want to apply at their university, of course after the whole reviewing process. @dirk

No, I would strongly advise against this. As far as I know there is no consensus about whether reviewer may lift their anonymity, but at least to some people this would look strange.

If the journal does not link reviewers to paper (some do), don't reveal which paper you reviewed. I would consider this a no-no (for various reasons). Some reviewers do not review anonymously, but always sign off their reviews - in that case, it's a different story, still I do not think it is a good idea to mention the paper reviewed in the CV, unless the journal itself has this policy.

Another point to consider is that, if you say which journal you reviewed for (depending on the situation), it may be easy to guess what article you reviewed.  I personally don't like to say what journals I've reviewed for, but in your case it would probably help your case to name the journal on your CV.

It can definitely help - acting as a reviewer is a signal that an editor somewhere (and in this case, a decent journal) thinks you qualify as an expert in a particular field - that's a good signaling mechanism for trying to get into a PhD program. It should absolutely go on your CV, and likely stay there - reviewing is a form of service, and that's a way many postdocs and faculty are evaluated as well.
Beyond just the direct benefit, it's also a good way to see "inside" the process of peer review, which I've found generally helps the quality of my own work. "Doing better work", while an indirect effect, can only help.

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Why might my tutors from several years ago not respond to my email request for a meeting?
It has been 3 years since I contacted my former school tutors.
During the past few days in New Year, I wrote 7 emails to them (with contents as shown below), but I have received only one reply.

Dear XXX, Happy New Year. My name is XXX, and then year of graduation,
  student ID... During the xxx course, I had learnt... I hope you can
  arrange a time for a meeting with me... closing greeting Kitty

I am thinking if my tutors have marked my email as spams.

You might get a higher response rate if you indicated why you want to meet with them or gave them more details about who you are. From your question, it looks like you're writing a pretty generic email that is easy to ignore.

I am quite likely to ignore email when the correspondent doesn't tell me what he (she) wants.

Why do you want to speak to your former tutor? If they don't know, why should they schedule a meeting with you?

I have edited the title of the question because the content of the post did not seem to match its title. If you find that the new title misrepresents your question, please [edit] it to clarify what you are actually asking.

The absence of a response can be because of several reasons. Your mail can indeed end up as spam but it is usually the e-mail system that sorts it there automatically, not the person. Sending additional mails will then be pointless unless the recipient actually goes through the spam folder to look for erroneously sorted mails.
A more likely reason for the lack of response is a matter of priority. I think etiquette would dictate at least a brief answer to the effect that the mail was received but cannot be followed up. You are requesting something that is a personal favour to you. As such, and as has been commented, it is only fair and indeed professional to provide a short and clear statement of the purpose of the meeting. After all to meet someone during work hours better be about something work related.
The tutors have probably also tutored many others. From their perspective, you, without any derogatory intent, will be one of many. I often get requests from students who apparently think that because they are out of the program they should be "friends" with me. I would end up with many such "friends" but none that would have any significance either professionally not privately. Hence there is an unbalance between how your tutor has meant something for you and what you have meant to the tutor. This is built into this sort of relationship. Hence, you need to look at the formal role of both parties and evaluate if your reason for contacting the tutors is mostly a professional issue or a private issue. In the latter case, the response may be less than what you would wish for. If your cause is professional, you are far more likely to get a timely and satisfactory reply.

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strategies for sharing teaching information with universities I don't personally have contacts with
A large part of my job is the creation of new teaching materials and methods.  I enjoy it, but I'm noticing a few things:

Some international students struggle with my material, not because of the content tested, but because of the context.  As an example, if I write a large computer programming problem that requires students to understand, say, the workings of a large North American supermarket first, and then understand how to write a program for one, some international students take considerable extra time to understand what is being asked.  Once they get it they can write the code very easily.

I like to provide authentic examples as often as I can, and I feel that having information from non-North American sources would go a long way to provide a greater breadth of examples.

I'd like to foster relationships with educators around the world teaching similar things (math, programming, electric circuits, mainly).  My hope is to better understand:

How are instructional materials designed elsewhere in the world?

What kinds of examples and methods can help my international students?

How can I expose my North-American students to a more global way of solving problems
I've reached out to a few universities but so far my strategy is to just send an email explaining my goals and wait.  No one gets back to me.

What are some strategies I can use to start building these relationships?  Are there any organizations/whatevers around that help with this sort of thing?
EDIT: I'm noticing some upvotes but not many solid answers (thanks to the one answerer though!).  I feel that there might be some interest on this site for a discussion about exchanging information.  If so, let me know in the comments.  If there is enough interest I have no issue sharing my email address to get the conversation started offline.

When you write a large supermarket question then why mention a particular country or you could even have 4 questions with slightly different sets of data in different countries - then the method is the same - at least that’s how I do mine.

@NajibIdrissi one way you can deal with that is to state : make any assumptions used clear as part of your answer, and if I put your question in a quiz, I would accept either result as correct....

@NajibIdrissi well, I would look at the situation as “you should not write questions that are ambiguous” as that leads to confusion on many levels.... And a question with two possible correct answers is ambiguous...

This discussion is exactly what I'm hoping for.  Basically, it's not just about the questions themselves but about making assessments/learning materials that are universal if possible, and that can expose every student to a wider perspective.  So yes, I'm sure I can re-write the supermarket questions to be more clear, but I'm hoping to bring a more global perspective to my questions in general

A remark: The approach to teaching around the world varies a lot, and using teaching material constructed for a certain level in a certain part of the world can lead to a disaster in another part of the world. I discussed a bit the issue in this answer related to a comparison between the UK system and the Italian system.

@MassimoOrtolano agreed.  I'm more interested in knowing how the teaching is done/what is expected/what types of examples are used, not necessarily to use the data

I've reached out to a few universities but so far my strategy is to just send an email explaining my goals and wait. No one gets back to me.

Unfortunately, as other questions on this site attest to, this is probably to be expected. Especially if you reach out to "universities"; my guess is that you won't get help from them at an institutional level. But if you find individual people who share your interests, your chances might be better.
I would recommend starting at your own university. Many universities, at least in the US, have teaching and learning centers, or some variant. Their purpose is to support instructors who want to improve their own teaching. They might be able to answer some of your questions directly, or put you in touch with others who can.
If you go to conferences, I've found those to also be great places to discuss teaching.
You might look for instructional materials directly on the internet. Sometimes the instructors who created these will make them publicly available. (In math this is fairly common.) You can learn a lot by reading these directly, and the people who created them might be more likely to respond to cold e-mails. Perhaps not your big-picture questions, but they might be happy to answer questions about their course materials.

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How to recover one's career opportunities after a period of poor performance
I read this question about falling behind, but my question is more about the long term.
I find myself becoming depressed at lack of overall opportunities in graduate school (in mathematics, specifically, though this question is more about the general case). I had a bad relationship that messed up a few semesters for me at the beginning of grad school. I'm more or less recovered now, but I'm having difficulty trying to support my progress in any way outside of classes.
My field is computational, so I really want to get a summer internship at a software company, government agency, or some other place where I can get exposure to research and skills that are not immediately available in the department (like coding). My advisor's perception of me formed during my period of low performance, too, so he hasn't invested much in teaching me. I have some mediocre grades on my transcript from this time, so the profs from these classes so far don't have such a good impression of me, either. I don't know who to ask for recommendation letters or networking opportunities. I had shining recommendations from undergrad, but that was years ago, which will raise obvious questions on any application.
Meanwhile, my friends are doing interesting projects they can associate with their name. They're giving talks, going to conferences with their advisors, being awarded fellowships, etc. Feeling like I have nothing going on except for classes and an advisor that doesn't believe in me is no good, and though I'm performing better than before, I am still far under what I know to be my potential.
In other words, I feel like I'm stuck in a cycle of poor opportunities, and I'm not sure how to break out of it. I had a lot of momentum when I came here. People were offering me all manner of things, I had many side-projects in different areas, and I was beginning to make a name for myself in research. Now, all I do is try to get my homework in on time. I'm just bored, and don't know how to get back to a successful state of mind.
How could one recover from this type of setback?

Not 100% the same, but check out this post for certain: http://academia.stackexchange.com/questions/2219/how-should-i-deal-with-discouragement-as-a-graduate-student

In my opinion a good supervisor/advisor is also concerned with the well-being and career of the students. Did you talk with them about this issue yet?

As I understand this is not your first year or second year. Why do you still have classes to attend? Also, this "I am still far under what I know to be my potential" is working against you. You were an excellent undergraduate but you are now a mediocre PHD student. You should focus on improving your current state and not compare yourself with the ideal picture you have of yourself and your abilities based on your limited undergraduate experience.

The summer internship sounds like a great idea.  Spiff up your resume and start applying!  //  I'm glad to hear you're putting effort into your homework despite your ennui.  //  You may be a late bloomer.  Don't think about comparisons with other students -- focus on what you find most interesting about your studies.

You've got a few problems here, so I'm going to try to address each in turn.
Depression: As has been noted before on several occasions, depression is very common among graduate students and faculty.  The important thing to remember is that you're not alone.  Most universities have counseling centers that are available to students for free - take advantage of that.  Psychotherapy is effective for most individuals, and a trained professional can help you come up with strategies that are tailored for you.
Adviser Troubles: It's unfortunate that your adviser seems to be less interested in your progress because of some poor grades early on.  The trick now is how to make your adviser regain interest in you again - whether that's through more frequent meetings with them (out of sight, out of mind, so stay in sight) or by being proactive and finding interesting research directions to pursue is something you'll have to decide.  As a last resort, consider finding a new adviser - it may mean losing several years worth of work, but if it can rekindle the adviser/advisee relationship, it may be worth it.
Letters of Recommendation: One option is to consider alternative sources - are there professors of not-as-relevant courses that you can go to?  Past internship employers?  For networking - are there career centers or fairs at your school that you can leverage? Think outside the box.  Moreover - don't give up on the professors that you've had so far.  Asking for a letter of recommendation, with an acknowledgement that you may not have done as well as you hoped in the course, but you still learned valuable material may yield at least an "okay" letter of recommendation.  And there's always the possibility that their opinions of you are not as poor as you think they might be.
Boredom: This may be the biggest problem of all.  You can see a therapist; you can meet with your adviser weekly; you can cobble together LoRs - but if you're still bored stiff and have zero motivation to do anything, you've got a problem on your hands.  Generally, I've found there are two solutions to boredom:

Power through and do the best you can do.  As Randy Pausch (late Prof. at Carnegie Mellon) said, "The brick walls are there for a reason. The brick walls are not there to keep us out. The brick walls are there to give us a chance to show how badly we want something. Because the brick walls are there to stop the people who don’t want it badly enough. They’re there to stop the other people."  Show that you aren't "the other people".
Find something else to do.  Sometimes there's nothing you can do about it - you're bored, and no amount of self-negotiation will change that.  In those times, you just have to find something else to do.  Here that could mean a new research project, or even just a new angle on the current one.

Which solution is the "correct" one is entirely dependent on you.

Summary: My overall point is that it's going to be an uphill battle for you.  If you want this degree, you're going to have to prove it, and ultimately only you can decide what's best for you.
Here's a little inspiration to get you through your day:

Optimist: Someone who figures that taking a step backward
  after taking a step forward is not a disaster, it's a cha-cha. ~Robert Brault

Best of luck!

I was in a similar situation as I worked on my PhD. I had been through some stuff in my life and was depressed for a while and just unmotivated, and I was doing unrelated stuff that was taking up a lot of time. I had taken too long already and basically the message was "finish your degree or get out".
So I pulled my socks up, made a list of all the goals I would have to fulfill to complete my degree and worked on crossing several things off my list every day.
It's better to write the steps down on the list and then cross them off than just to do them without writing them down, because then you get a boost every time you look at your list and see all the things that are crossed off. Of course, you'll also be adding to your list as you go on and realize there's more to do, but as long as you cross more things off than add to the list as you go, you'll eventually get there.
Your own supervisor wants you to succeed, so if you show enthusiasm and willingness to complete your project, you will have the support you need. It has to be you that takes the first step though. Nobody else is going to motivate you so for that you need to look within and ask yourself what topic really interests you and work on that.
There's really nothing quite like having "Dr" in front of your name (I assume you are a PhD student), so hang in there!
BTW, it is over a decade later, and my PhD supervisor is still happy to write me reference letters as I need them.


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Is it acceptable and ethical to access journals via my previous university's account?
I switched universities for my master's, but I still have access to my old bachelor's university accounts. Now, sometimes it happens that I can only access a journal via my old university account, since my new university does not have access to all online libraries (I cannot see studies which are in the Wiley Online Library, for example). I cannot visit ScienceDirect by Elsevier, but with my old uni's account I can.
Is it allowed to still read and use those journals using my old/previous account?

Maybe, maybe not. Check with your old library.
Example

Access thousands of journals through your My Oxford Online account exclusively for alumni
...
Conditions of Use
These databases are being made available to you to support your ongoing research and study. Use of University database subscriptions are subject to strict licence agreements. For your protection, and for the protection of the University of Oxford, we ask that you observe and agree to the following requirements:

These Information Databases may be used for study and research but not for commercial purposes
Under no circumstances are you permitted to share your password, or otherwise make available, any content from these resources to anyone else
Systematic downloading or viewing of excessive amounts of data is strictly forbidden
Failure to comply may result in the loss of your right of access to the databases and publishers withdrawing content from the whole university.

I'm curious if you know of any examples of "not", where the university forbids journal access to alumni with active accounts, but doesn't actually block it.  I would tend to assume that if your account has access, then it's legitimate to use it.

@NateEldredge that's a fair assumption. But "not" can happen if e.g. you are intending to use the information for commercial purposes (which would be prohibited as in the quote).

Since some pedants seem to be willfully misreading your question and my answer here, I'll briefly update with the following:
You have not indicated in your question what you mean by "allowed", which is decidedly vague. Allowed by whom? Allowed for what purpose?

The government. If you obtain a copy of a piece of written academic work that is not somehow otherwise legally restricted, you may always read it and cite it. You are probably not legally allowed to make copies and distribute them. You may be able to quote a certain amount of the content under terms of fair use.

Your old university. Since your old university account still has access to this material, your old university is allowing you to access it. Possibly they do not intend for you to have access to it, but it's not your responsibility to figure this out unless you think some kind of abject IT mistake has been made.

The publisher. They are allowing your old university to grant access to copies, which the publisher probably distributes. You have no business with the publisher.

It sounds to me like you're acutely overthinking this question. You have access to these documents. They are presumably not state secrets, or accessed via a deliberate attempt to circumvent access restrictions. You cannot be prevented from obtaining, reading, and citing them.
There is a very long academic tradition of getting your hands on relevant materials in the cheapest way possible. There may be formal text of whatever licensing agreements your old university has with various publishers. Those will indicate that there are restrictions on whom the university should give access to and not. This is not your responsibility to enforce.
Even more generally, there's no way to discover that you've "inappropriately" obtained a copy of any given work unless you publicize that fact rather widely. Typically the thing that will get you in hot water with publishers is redistributing their copyrighted or licensed works such that it substantially undercuts them. That is illegal, and could get you sued for money damages.
As an example, what if you had downloaded copies or printed copies of papers whilst you were a student? There's no mechanism or expectation that you'll destroy those copies once you've graduated.
In short: Just download whatever you need that you have access to, it's extraordinarily unlikely to be a problem.

This does not address the actual question above.

@JonCuster With due respect, that's patently incorrect. The asker wants to obtain copies of something via account access that they have. Is it allowed? Either the question is extraordinarily simple: Yes it is allowed, because they still have access via their account. Or it is a question about copyright or similar. In which case: Yes, it's still allowed. This is a Stack where we're supposed to answer realistically about how academia works. An addiction to legalism in this case would not just be inappropriate, it'd be misleading.

@JonCuster I've updated the answer in case it can shock you to read both the question and the answer more closely. Though I'm somehow skeptical.

Truly fascinating to learn that this community prefers to obscure the reality of how this system works in practice the name of legalism on behalf of...the publishers? University IT departments? I didn't quite realize we were an opinion board.

"It sounds to me like you're acutely overthinking this question." I agree.

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Is source code provided in the appendix of a thesis copyrighted? [US]
I'm contemplating including source code in the appendix of my thesis. Although, I will not be strictly required to, I think this would be something that my committee would like to see.
Will I run into any copyright issue for this? Will the university own the rights to the code if I include it? The project was not funded so the university didn't pay me to write the code and no one else has contributed to it or even seen it.
Also, if the university is to own the right to my code, another concern of mine would be that I have used various open-source libraries and I would worry about running into license issues for using those as well.

What is your institution's policy on the ownership of copyright of the thesis?  Are you allowed to keep the copyright or must you transfer copyright to the university?  It is typical that the student retains copyright but must grant permission to the university to publish the thesis.


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To what extent should a reader be required to read a paper to understand a chapter?
I am doing a master thesis and have more or less written my report. My supervisor has from time to time read my paper and from the feedback I get she wants to be able to skip to a later chapter and read it without necessarily reading exactly everything else before. This seems a bit odd to me, but I have not thought about it before as the papers I've read I read from the introduction and onwards.
My outline is introduction, related work, method, results, discussion, conclusion.
So, to what extent should I expect/force a reader to read previous chapters that are relevant but not critical for understanding the paper? Should the method chapter be written in a way that you don't have to read the related work and introduction chapter? Should you be able to skip to the results and discussion and understand them without reading the method chapter?

Since your supervisor is grading it, I think you should, within reason, do as she wants. Ask her directly.

What is for example very common, and good practice, is to repeat the research question in the conclusions, so your conclusions have the form: "this is what I wanted to know and this is the answer". Similar repititions can be meaningful in other places of your article. Remember, scientific articles are not meant to earn you a nobel price for literature; They are professional communication, which means that quite often people read only the parts relevant to them, and read in more detail only if interested.

Arguably, a fairly experienced professional in a closely related field might expect to read later portions directly, yes. The point is for you to be aware of what is completely standard (hence, known to professionals) and what is more idiosyncratic to your particular write-up. This awareness is not so easy, and you need advice from ... an experienced professional, such as your advisor.

Your advisor is presumably intimately familiar with the area you are working on. As such, she should be able to read just a chapter and understand what is going on. If she can't, I'd agree that the chapter itself is badly written, and requires better structuring.

This question reminds me of a possibly relevant quotation from the preface of the book "Recursion-Theoretic Hierarchies" by Peter Hinman: "... that peculiar brand of obfuscation which results from an author's implicit assumption that the reader has perfectly understood and remembered every detail of what has preceded any given point."

The flow of thesis differs in preference from one supervisor to another. The specification provided by your supervisor doesn't seem unreasonable. In fact, I would endorse it myself.
It is natural for most readers to skip the introduction and just cut to the chase. Readers would be particularly interested in the implementation and results. Although that doesn't mean introduction isn't mandatory. You just have to minimise the dependency between the main matter and the introductory matter. The lesser you make the reader to turn back pages, the better would be the reading experience.


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Will it improve my PhD applications if I take a gap year to work on research?
I was a philosophy major who took a bunch of graduate-level classes in linguistics and I wanted to apply to PhD programs in linguistics (in the United States). I had a writing sample in the philosophy of language, and I found out later from other professors that PhD programs in linguistics are mostly only interested in BAs and MAs in linguistics (unless they have a very strong linguistics writing sample), regardless of what courses they took. So I ended up getting waitlisted to a couple of schools (one top-ranked) and rejected everywhere else, and turned down at both places I got waitlisted. I informally applied to a bunch of MAs in linguistics in May, just by sending emails, and I got accepted to many but without any kind of funding, so I wasn't able to go anywhere this year.
I have no plans or anything whatsoever this year, and to be honest, it's depressing and boring. I'm also unable to get a job.  I'm doing my best to do research and work on two new writing samples for linguistics, which I hope will make me seem like a more serious applicant.
I was just wondering: will this situation look bad on my application? Should I describe what I went through in my statement of purpose? I want to reapply to a school I got rejected from and another school I got waitlisted from. Would that be all right if I really improved my application?

I find it a little curious that you got wait-listed at a top-ranked school but not accepted anywhere.  (To be more precise, this would be strange in my field -- mathematics.  I don't know that it's the same in yours.)  How many programs did you apply to?

Can you apply for a MA in linguistics for this fall?

Pete: I guess you could say I had a weird application. I was very strong in some areas of the application (transcript, recommendation letters) and weak in the most important bit of the application (research). I guess the top program I got waitlisted from didn't care as much about research.
And I already (informally) applied for MA programs and got accepted. But no funding, so I can't go.

Your situation sounds similar to mine. After finishing my undergrad and not getting a PhD position, and since it was too late to apply for a full MSc, I moved to another country, enrolled just in the thesis and I worked on it for a year. After that, I got a lot of experience, a good recommendation, and a position. Now, I was lucky I could move and found a university that the only requirement for registering was finding a willing supervisor. So, I won't say necessarily that everything is lost, but it may be difficult depending on your situation.
I would advise against being fully independent researcher. You are fresh from undergrad, and with not so much experience in the field. If you work without adequate supervision chances are you will be reinventing the wheel, walking down paths that lead nowhere, or creating a beautiful yet useless theory. Your priority should be finding a professor that can guide you and provide some interesting problems to work on and feedback.
You should also keep an eye to applications in Europe: positions are opening and rolling all year round.

You are right, so I'm keeping in touch with my professors. I already have a research/paper topic ready and I'm going to start writing it soon. I've even done the experiments needed for the paper. Some of the professors say they're too busy to give comments on my research though, so it's not very heartening. Some of them say my research is really good though. Life is hard. I looked at schools in Europe and I can't afford to go to any of them I'm afraid.

@Nephenee what do you mean you can't afford going to Europe? A PhD is paid, and usually there is no tuition. (MA is different, though).

I was talking about an MA. I don't intend to get a PhD in Europe (if I even bother to try again).

@Nephenee may I ask why are you rejecting Europe?

David's answer looks very worthwhile thinking carefully about.
An additional option for you might be to enroll in a carefully selected program as a non-matriculated student in the U.S.  You would sign up for something like two credits of research.  This would not require you to go through the whole admissions process.
The key here is to find a professor who is willing to do this with you.  It's basically an "independent study" project.

This is a possibility, but to me it seems unlikely that you'd find a professor willing to work with you as a non-degree seeking student. Independent study and research with students are often uncompensated activities for professors (don't carry teaching credit, etc) and so they are usually done only with degree students, in whom the institution has a greater "investment".

This sounds like the US equivalent of what I did, thanks for adding the right terms. I think they key to overcome @NateEldredge's objection is to show the professor that you can be more useful than drag; I think that is why my supervisor took me on: he wanted someone to work on a project, and thought I would take less time than doing it himself.

I suppose the place to begin looking would be the MA programs that gave informal acceptance (without funding).  ---  I forgot to say, this approach would probably involve moving to a new town and getting a part-time job to pay the rent.  A little scary, but doable!


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Can I change my recommendation letter provider?
I wrote a few weeks ago about a conundrum I had with a professor regarding my recommendation letter for graduate studies in UIUC. I'm very grateful for everyone's responses, but I still have not received an LOR from this professor. My advisor has asked me to speak to him again (my advisor has spoken on my behalf as well), but I'm beginning to wonder if it's worth it.
Things may not just be uncomfortable with this professor due to our previous interaction, but he also seems to be caught in some private matters, and has had to travel on short notice to his hometown. On top of that, UIUC is a competitive school, so should I just change my recommendation provider? Is it advisable to do so? The professor I have in mind is fantastic, and I've enjoyed her courses and stayed in touch with her, but her field is non-technical. I already have recommendations from great professors in my field, though, and wouldn't it reflect well on my application to be recommended by a professor outside my field as well?
Any advice is welcome. I'm not sure if I'm overthinking this, but I've never heard of anyone changing their recommendation provider AFTER the application has been submitted.

Contact the admissions department, explain that the professor is "caught in some private matters" and hasn't been able to do the letter as a result.  Ask to switch the reference to a different prof.
In my experience, you're much better off being certain that you don't miss the admissions timelines due to a delayed reference letter than the source of the letter mattering very much.  That being said, I'm not familiar with the specifics of UIUC, so my experience may not be relevant.

Thanks! I did just that. I have scrounged through this website, and having a non-technical professor, as long as you have strong technical recommendations, can show you're good at other things as well. So I'm hoping that's how it goes in my case! Plus, this other professor has things to say about my research and communication skills, so that should be very relevant, God-willing.


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Is there a place in academia for a physicist who reads mostly about math?
Background
I’m 25 years old and have recently started the second year in my PhD. I’m from Brazil, where most people start their PhDs at 24 and finish them at 28, so I’d say I’m following the classical schedule quite closely. I’ve graduated in physics and did my masters in a field of mathematical physics called quantum chaos. I’m currently working in the same field. I had my first article almost ready from my masters, but then found out another guy had already published something very similar.
When I identified the Problem
During my undergrad years I took courses on measure and integration and differential equations in the math department, having studied real analysis and linear algebra on my own. On several occasions I almost left physics to go to math.
During my master’s I had to take physics courses again, and they made me feel exactly the same way I felt when I was in undergrad: I didn’t understand what those people were talking about, basically because most of them were not interested in defining well enough what they were doing. People were talking about S matrices and Feynman diagrams, while I was extremely uncomfortable with the fact that no one had even defined what an inner product was; people were taking limits of series they didn’t prove were Cauchy in spaces they didn’t prove were closed and applying opperators they didn’t prove were continous to get results they didn’t prove were unique. I couldn’t figure out what the hell they were doing.
I turned myself to functional-analysis and spectral-theory books, studied a lot, and was able to make sense of some things they did, correct some logical mistakes, understand that some of those problems they were ignoring are actually very hard and at least grasp what they were doing.
I then resumed my usual undergrad behavior: I quit going to classes, studied the subject on my own and only met the class to deliver exercise lists. While most student’s lists had x pages, mine had 3 x: I needed to prove everything I was doing made sense, and this consumed a lot of time and effort, and was – probably – ignored by the teacher and useless to everyone but me. I then talked to some teachers and they said that studying the maths behind physics was very useful, but that I shouldn’t spend too much time on it, otherwise I wouldn’t be able to do research. In their words:

a physicist should know enough math to be able to do his research, and no more

I had a very hard time processing this, since 90 % of my time was devoted to study mathematics. I thought about leaving academia.
Attempted Solution
Leave physics and go to math. Do what I was reluctant to do in my undergrad. If I like math so much, why am I still working with physics? I spent almost six months thinking about this, unable to do my work, after all I was apparently a useless piece of gear in the non-Cauchy, non-continuous and non-unique mechanism of physics research.
But then I noticed even though I liked studying math from math books – that is, working on exercises and proving theorems –, I would be very unhappy if I had to prove theorems for a living. I only used mathematics to be able to clear my view regarding physics, and although it did allow my to see deep into many physics problems (“rigour clears the window through which intuition shines”), I think this clear, rigorous view might lead me to a bitter, unfruitful place inside academia: a place where I understand very well what is done, but cannot create new physics by myself.
I might just not have been born for research, only for studying. My advisor is not at all interested in math, although he does respect and see some advantages in having a student that is. My work with him is mathematically ill-defined and has a lot of programming (which I learned to like), but when I attempted to try to make it rigorous he only cared about the end conclusion and didn’t pay attention to the process. In a word, he doesn’t care about rigour, but allows it.
I would like to work exactly in the same field when I finish my PhD, but touching more profound problems which could only be accessed with the use of heavy maths – which I still cannot actually fathom.
Actual Question
Sometimes I feel terrible about my interest in mathematics, since it is not very well accepted between people in my field, besides being probably useless to create new knowledge. I would like to apply mathematics to physics from inside physics, that is, I like rigour to understand, but I don’t like rigour to explain (I don’t want to prove complex theorems, I want to see new problems in mathematical physics and expose – perhaps study – them). Is this possible? Is there a place for someone like me inside academia?

Just in case someone is thinking about suggesting migrating this to [physics.SE]: it's not on topic there.

The famous representation theorist Harish Chandra did a thesis in physics at Cambridge, under the direction of Paul Dirac.

The statement that mathematics is "probably useless to create new knowledge" is unbecoming of a physicist.

@DanFox I also found this statement absurd when I began studying physics... Somehow they made me believe it.

I have a somewhat similar background: I primarily studied physics but also did roughly a bachelor in mathematics (a “Vordiplom” to be precise). I never liked regular theoretical physics much because the mathematical background was never properly explained, if it was mentioned at all. I did my master’s-thesis equivalent and PhD in complex systems / chaos theory.
So far, my mathematical background was an enormous benefit to me. I published three papers which clearly wouldn’t have been possible without it, and in the rest of my work, it often helped me to understand things much quicker. The main impact of mathematics on my work is that it allows me to identify and formulate problems, draw connections, know the keywords to find the relevant literature and understand it. While I did prove things at times, this was only the icing on the cake – and I would consider most of my proofs not very challenging.
The main exception was the proof of a number-theoretical statement that I had already confirmed very well empirically. If I had not eventually found the proof, I would probably have consulted the next-best expert on number theory at my university. Still, I am more proud of finding the right statement to prove than of proving it.
Almost everything that I proved is published.
So, I really do not see a problem with your interests. There is almost certainly a workgroup that is interested in the same questions, though it does not seem to be the one you are in right now. However, if your supervisor accepts your mathematical inclination, they may also be able to connect you to the people who care about these issues to give you feedback.
Bringing a new background to your workgroup is an asset that is very likely to make you see new connections or identify and solve new problems, which can eventually lead to new physics. You may need a proof on the way, but I would not worry that this will consume most of your time. At the end of the day, even most mathematicians do not spend all day at their desks trying to prove something, but also have to understand existing concepts, find connections, and so on. And should you stumble upon something that you cannot prove, you can still collaborate with mathematicians or leave it as an open problem/conjecture.
Another perspective could be to simply establish a mathematical framework for what your workgroup does (which then may contain open questions for you or others to fill). Depending on the relevance and extent of what we are talking about, this may already be worthy of a PhD or even enough work for an entire research career.
Finally, some random asides:

You probably are at a stage of your career and a field, where few people care about whether you are actually a mathematician or a physicist.
Beware of the impostor syndrome. If your master’s thesis could be turned into a paper, that’s already a good start. That somebody else managed to publish it earlier, is bad luck for you, but still shows that you produced publishable work.
If you are doing a lot of programming work, it can be very helpful to understand more about the methods you are using. Moreover, you may find yourself developing new numerical methods – where a mathematical background is extremely helpful.

a physicist should know enough math to be able to do his research, and no more

While there is some truth to this for some areas of physics, most physicists do not actually know enough math to do their research, or they are limited in what they can research by the math they know. Most importantly, in the more mathematically inclined fields of physics, I disagree with this due to the reasons stated above.

I couldn't be more grateful for your answer. It really helped me think I'm not doing anything wrong. Comparing the mathematical physics done by Brazil and by, say, Poland, I can see that we are very far from doing real mathematical physics here... it just looks like the theoretical one that, as you said, many times makes little sense. Maybe this contributed to making me believe that to do physics knowing mathematics was not a good idea. I hope I can get rid of this thought and what you said was very motivational. Than you again.

To add to this answer, I know a few physicists with very strong mathematical background, who have made very important contributions to various fields of physics, that would have been otherwise impossible for them without that background. So if OP already reads math, it would help them a ton finding a theoretical physicist adviser who is good at physics and appreciates the math.

So far, you've been reacting.  You sign up for a course, maybe it's required, maybe it's not.  You're given a homework assignment.  The hand waving approach in the lectures bothers you and you spend a lot of time building up the mathematical background, and you fill in the blanks.  If you successfully managed to keep your instructors happy enough to give you good grades while you were engaged in this intensive self-study, good for you!
At some point in the not too distant future, you are going to want to start taking the initiative to give shape to your studies.  Here are some ways to do that:

Search for papers that really, really intrigue you.  One of these
might give you an idea for a direction you'd like to go; at the very
least, such a paper can give you a mental image of what a
math-friendly physics project can look like.
Find out how you feel about other aspects of physics.  You mentioned that you enjoy working out the mathematical underpinnings
of the assignments you're given, and you enjoy programming.  But I
wonder if you have figured out how you feel about working in a lab,
designing experiments, carrying them out, analyzing experimental
results, writing programs to analyze experimental results, choosing
and installing new equipment, designing a new or modified
experimental apparatus, communicating with the engineer and the
machine shop technician, testing a new experimental set-up
("commissioning")....  This is good information to have about
yourself.

Please don't forget that you are studying in the Third World, not that one should look down on science in the Third World, but just to reassure you that it is forgivable that your instructors might do more hand waving and less rigor than is at least sometimes found more commonly in the developed world.
My spouse is an experimental physicist, who uses math very, very frequently, and sometimes writes a theoretical paper, using mathematics to explain, as you have been doing so far, but also to create, as you are dreaming of doing.
Note 1: At some point you may want to correspond with an author of a paper you've identified in your search.  Science as become incredibly international.
Note 2: I wasn't sure from your post, whether you might sometimes have a bit of trouble keeping your eye on the big picture (getting the assignments done, without getting so sucked into the mathematical underpinnings that you might have trouble making your deadlines).  If so, take a look at Is there a place in academia for someone who compulsively solves every problem on their own?, which is a rather extreme example of what I was describing.  If not -- have fun in your explorations!

In my undergrad I had 4 advanced physics labs and worked with experimental physics in my first project. I liked doing experiments, but I hate analysing data. I really tried working a bit with experiments, but I think I'm more comfortable with the abstract aspect of physics. Right now I'm trying to get a collaboration with an experimental group going. They look interested... let's see if it gets somewhere.

Also, I don't compulsively solve problems. I just solve what I need such that my vision is clear. My grades are pretty high, but I sense that if I used some conclusions without proving them I would get the same grades with much less work... the thing is that I'm already convinced that maybe this extra work might lead somewhere, thanks to the answers received. I can only thank you for your suggestions and answer :)

@QuantumBrick - Good! I did have the impression you were probably holding the reins pretty comfortably.  Forget I mentioned it.

Do not worry about leaving the field, there is plenty of work to be done in physics using a more mathematical approach. From my opinion, finding and applying new mathematical techniques in physics help us advance - great advances in physics in the past have come by using new ideas and concepts from mathematics. Take the famous example of general relativity, or new modern theories of gravitation. Without mathematical techniques it would be impossible to find new ways to describe the universe. Developing and introducing new mathematical concepts in physics could potentially redefine modern physics. Hence, pass the 8a/8a+ grade and go beyond!


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Forgetting what you have published
I was discussing this topic with an older professor of mine who had published more than 90 papers and couple of books in his field. The papers are highly specialized and half of them are with different co-authors from the same or a different field.
Since he has so many papers, I asked him if he was able to remember and / or explain all of his published papers to a random guy or student on the street if he's asked to do so. His answer was, of course, 'not really'. Since his papers were highly specialized and he tends to change his research interests over time, his memory of the papers tends to fade. He'd still be able to remember and explain the methodology and results of any of the published research, but not in detail or without first re-reading them.
My question is, how much is expected from a scientist to remember from his papers? If you get asked to explain some of your papers, what of the following would you do:

Just explain what's in the abstract (if you remember), or
Tell them to just read the paper themselves, because 'everything is there'

I would expect a person to explain as much as he remembers, leave, get his notes / diaries / lab journals, and email you the details. This said, I'm not in the stage of having published too much, so I won't post this as an answer.

I thought the whole point of writing it down was so we didn't have to rely on our demonstrably terrible human memory!

@corsiKa the fact that the paper is written doesn't mean that a discussion with the author cannot be helpful -- to understand faster,  or gain some insight about what is not in there (ideas that failed,  and why,  for instance ). That's one of the reasons people give talks.

Intelligence is knowing where to find the answers, even if it is in your own previous work.

@corsiKa Reminds me of Henry Jones (senior)

It's pretty much similar to the phenomenon that the programmers don't usually understand their own code right away after even 6 months.

People usually do not ask: "explain this paper" they will read a paper and may ask a more specific question about a part they did not understand.
The professor may or may not be able to answer. If he wants to, he can look up the paper or the answer to the questions asked. His experience and knowledge will probably help him to find the answer faster than the person who asked the question. If he does not want to, or cannot answer the question because he forgot, does not have time, or for any other reason, the person asking is simply out of luck: they will have to ask someone else or do research themselves to find the answers they are looking for.
Nobody can remember all the details about 90 highly specialised scientific papers, especially if they involved lots of work by different authors that may have been done decades ago. Professors and other scientists are human beings: they forget things and make mistakes just like everyone else. This is not a problem.

Perhaps it is idealistic on my part, but papers that require explanation should be published.  What are we supposed to do when the authors die?

@emory Spend centuries trying to find the proof he chose not to disclose in the margin, obviously.

One of the main reasons for writing a paper is that you no longer need to remember what's in it, because you can go back and read the paper.

Is that really one of the main reasons for writing a paper for some people?  It's certainly a benefit, and a reason to write notes, but it's never been a reason me to actually write a paper for publication.  (I have however wanted to write up something quickly before I forget.)

@Kimball: It's certainly an important reason for me.  I mean, it obviously isn't why I go to the trouble of polishing it and getting it published, but whenever I figure something out I get worried that I will forget it if I don't write it down.

@AndyPutman And if we merely write it down without publishing we may not be able to find it, or we will find some erroneous draft version.

Heck, I can’t remember half the stuff I wrote in my PhD thesis. I’m probably the only person reading it semi-regularly, to look up how/why I did specific things.

@KeithMcClary: I don't think that's true for most people.  I'm not exactly the most organized person in the world, but my papers are organized in such a way as to make me able to easily find the most recent version of any of them (and I can't imagine someone who is able to function in academia for a long period of time who hasn't found a system that works for them).  I publish my papers for a variety of other reasons -- peer review, getting raises/grants, making sure my work is permanently archived in libraries and available to future scholars, etc.

One of the reasons I write papers is so that I don't lose insights that I worked hard to discover!  I certainly cannot reproduce from memory the technical details of my papers except for the most recent ones (though I generally can remember the basic gist of them).
I actually write a huge number of notes to myself that I never publish or distribute.  I put a lot of work into figuring out other people's work from my own point of view, and if I didn't write it down that effort would be wasted.
I periodically get emails with questions about my older papers, and I generally have to spend a bit of time re-reading them before I can give an intelligent answer.  I've also had the following common experience many times.  Someone (say, one of my graduate students) asks me a question.  I'll get excited and we'll talk for a while without answering it.  A few hours later, I remember that I once wrote a paper answering it!


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Will turn down a graduate (Master's) program have effect on my application for the same program?
I have asked a similar question.
Is it bad to apply for the same Master's degree program in consecutive years?

If I failed the first year, will it be a negative factor for my
  application the next year (say if I could been admitted originally,
  but because I failed the last application the year before so I am not
  accepted)?

But what if it is the other way around. I turn down the admission to do a gap year thing and reapply the same program the next year. Will my rejection in the first year be bad for my application for the same program the next year?

You previously asked about deferred admission ( http://academia.stackexchange.com/questions/82125/is-defer-enrollment-normal-or-acceptable-by-graduate-programs-what-are-the-acce ), and this is exactly the kind of situation that deferred admission is designed to deal with.


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Is it appropriate for me to get a recommendation letter from a teacher whom I TA for, but whose class I have not taken in 3 years?
I am a teaching assistant for a biology teacher. When I took biology 3 years ago, she was my teacher. There is another teacher who she works EXTREMELY closely with, and there is essentially no differentiation between the two teachers regarding what I help out with, and I am close with both of them.
Is it appropriate for me to get a letter of recommendation from one of them even though I took the class as a freshman and am now a junior teaching assistant? For any other freshman teachers, I would not consider getting a letter of recommendation; however, I have gone far above and beyond the normal duties of a teaching assistant -- namely designing and implementing labs, grading, and even teaching the class as a substitute (there was an official proxy but I did the teaching). Humbly, I am quite appreciated, trusted and I have no doubt that I would receive quite a stunning recommendation letter. I would love to have a recommendation from one of the two marvellous teachers that I TA for, but I cannot decide which one -- the one whom the position is designated to? I feel there is potential for the other to be offended, and I would much prefer that that didn't happen. A selfish part of me wants the 'better' writer to write my letter, although I don't know who that is and I would prefer not to think of it that way (though a part of me suspects that is it the teacher to whom my position is not officially designated).
Just to clarify, I am in high school, and the recommendation letter is for undergrad/combined university programs.
Is it appropriate for me to get a letter of recommendation from one of these teachers? If so, how should I choose?
Edit: one of the teachers is also the advisor for a club that I am president of.

Undergraduate admissions are off-topic here. I'm not sure what a 'combined' program is nor how their admission process differs, but I imagine that class performance will play a greater role than for graduate admissions, which are really primarily concerned with research ability (which is a quite different skill). So the usual answers you would get here may not apply in your case.

yes, anyone who has supervised your work is suitable to be a recommender. You should solicit recommends who can give you the best recommendation and also whose professional status is most impressive.

Pick the writer who can best attest to your performance and ability to work in a graduate setting. Being a student is one factor, being able to assist in teaching in another.
You have the best knowledge as to who will be better for you.

Mm yes, thank you; however, is it academically acceptable for me to receive a letter from one of these teachers at all? I ask because I know that universities and applications place favor on recent teachers.

I don't believe there are restrictions except for writers who are family and friends. Although there is a preference for professors, employers would work as well.

Thank you. Consider this +1, I don't have enough rep yet.

@Equinox place the tick to accept the answer - does not need rep...

Correct, I am waiting to see if anybody else answers with contrary opinions -- an accepted answer will often deter others. I am quite an active user of SE and SEO, although my posts are numbered.


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Is it fine to send a message to the author of a paper if I don't understand something and want to clarify it?
I'm a Ph.D. student and I have been studying one paper and had some doubt in one point. More specifically the author defines a concept in a way which is a little bit different from other texts I've read before and I'm failing to understand why it is the same thing. I believe I would benefit from understanding this correctly.
More specifically to the situation, the paper has been posted on arXiv and is really some lecture notes which were latter transformed into a book. The author also says to email any questions or corrections to his email in the first page.

Considering this situation (that it is really some lecture notes later transformed into a book and that the author says to email any questions to his email) is it considered ok to ask it?

More generally, if it is really some paper published in some journal, and if there is nothing written saying that "any questions should be sent to that email", is it still ok to ask of the author in case of any doubts?

My main issue is that I fear if the author might consider my doubt something "too basic". Is that really a problem?

I have heard once that in India "doubt" menas "question". Are you from.India and do you mean "question"?

No, I'm not from India. It is a doubt really. As I said, something I'm having a hard time to understand and considered asking the author about it. I want to know if it is considered fine in general to ask the author if I have some doubt or if in general this is not fine and we should find a way to handle it ourselves.

In any case, I'd recommend that you not refer to your question as a "doubt". It just doesn't suggest what you'd want, as, in U.S., Canadian, and much western european English, it strongly suggests distrust or disbelief in the author, as opposed to asking for help in understanding. That is, even if you privately "doubt" the correctness of an argument/proof, it is vastly more polite to ask a question as informational, and NOT expressing a "doubt". A "doubt" is lack of confidence... skepticism... distrust.

My take on this is that you should first make sure that you put in sufficient effort to understand what they have written (which means consulting the literature, your colleagues working in the same field or scientific advisor). Having satisfied this you should definitely contact them.

"confusion" might be a better word to use instead of "doubt".

In brazilian portuguese, both "doubt" and "question" also translates to "question", most of the time.

If there is one thing that I learned working with Indian, Pakistani, French, Spanish, Italian, .... colleagues and students it's that "doubt" is used as a neural "I don't understand this" in a whole lot of languages. It initially sounded strange to me too, but I have come to understand that they never seem to mean literally "I doubt this information".

@paulgarrett The cultural connotation of "doubt" in a academic context is completely different in India. Students often refer to any questions they might have regarding any topic as "doubts". In fact, many Indian cram schools/colleges have "doubt removal sessions", which are basically equivalent to office hours. Very interesting to see that the same word suggests distrust in another country! Just shows how easy it is to misunderstand words from another culture even if the language is same.

I have had mixed experiences with this, some authors will answer any questions you have about one of the papers as long as you don't ask too many and others are extremely unhelpful.

Yeah, "doubt" is one of those words that seems to have a completely different meaning in India and nearby countries, from the rest of the English-speaking world.  Like "alphabet".  It's certainly something to be aware of, to avoid misunderstandings.

By all means ask. A person who goes through the trouble of writing up lecture notes, is almost certainly a person who would be happy to answer.
As someone who receives a lot of questions from PhD students myself, here are a couple of pointers for how to phrase your question. This could be obvious to you, but I know for sure that it is not obvious for everybody.

If you have a local supervisor, it makes sense to ask them first - maybe it is a trivial question.
Read the paper first, and use the notation from that paper when you can.
Cut to the chase as quickly as possible. Don't explain their paper back to them in the mail, they know what they wrote.

I would maybe caution on taking the last point too broadly. Explaining the entire paper is different than sufficient context for explaining the question.  If I wrote some 50 page lecture notes 10 years ago, and someone just emails me saying 'I am wondering if you can explain why variable x is unique in a set' , without enough context or page numbers, etc.

When I ask questions, I sometimes "explain the paper back to them" because I might have misunderstood something that they can then point out. Would you say that is in some ways not to be encouraged?

@lucidbrot: I think you should ask your real question early, at least a TL:DR version of it, then go into more detail.  If the question is nonsensical for some reason, they'll know what misunderstanding to look for when reading through your thought process / detailed description.  That's the same advice I'd give for asking a good Stack Overflow question.  You still want to keep that later part concise, especially in a personal email where there's more of an expectation to read what you wrote, not just skim like in a public Q&A format like SO.

The author says to email them, so email them. You’re overthinking this. You would be using their publicly listed email address for exactly its intended purpose.
In general, people who prefer not to contacted by PhD students who have questions about their work will find a way to make that known or to avoid receiving such questions. Leave it to those people (who don’t really exist, by the way) to worry about such things for themselves.

I agree with all the other posters. (Go ahead, ask!) Two additional points:

You might not get a response; sometimes, non-urgent emails get lost in the shuffle. (Especially now, with the sudden shift to online teaching.) If this happens, try not to worry about it.
I'd avoid the word "doubt". It suggests (to me, anyway) that you believe there's a mistake in what the author wrote. Even if you do suspect this, it's still polite to write from the point of view that the misunderstanding is likely on your end. In the past, I've saved myself some embarrassment by doing this!

Actually I was unaware that "doubt" could in some way imply that (I'm not a native english speaker). In fact it is quite the contrary, I'm sure the misunderstanding is on my end. Thanks for pointing this out !

@Aegon I think the usual word for what you mean is "uncertainty". That is, you are uncertain about your own thoughts, while "doubt" tends to imply you might suspect that they are incorrect.

@Dronz To my ear (I'm American), "uncertainty" also carries a mild connotation of "I suspect that you're wrong".

@academic Yes, especially if the subject is the other person's work or rightness. It seems to me to depend on whether it's clearly written that the uncertainty (or doubt) is about the asker's own full understanding.

@Aegon: Apparently "doubt" often gets used as a synonym for "question" by Indian English speakers, like "I have a doubt (about ...)".  Some consider this a dialect, others just a common mistake.  In "regular" English it looks either wrong (when the meaning is still clear), or worse like you're doubting the correctness of a statement.  I only know this from someone on meta.stackoverflow pointing this out, after years of having seen SO questions that use that phrasing, sometimes even in questions that were otherwise written in fairly good English.

@academic. The nearest synonym appears to be query.

Book authors are not some kind of demi-gods whom you cannot look in the eye.
If someone writes a book, pushes some code on GitHub, write a blog post or whatever is public - you can contact them.

Some of them will be delighted and they will answer with joy.
Some of them will be happy but do not have the time to answer. They may send a short note, or answer later, or not answer.
Some of them may feel that your question is stupid and that you should learn something before asking questions. Well, there are assholes in all populations.

If you write a nice note (everyone likes to receive nice notes) and keep it to the point, normal people will reply.
When I was a kid I wrote a letter to the President and I got a reply. A few months ago I wrote a letter to the mayor of my small city and I am still waiting for them to "find time" to reply. You never know the odds.

What, not demi-gods? I, myself, have many of the characteristics of Budai. Overweight, wanders aimlessly, eccentric lifestyle... Hrrumph. But you are allowed to look me in the eye, yes, and ask me questions. ;-)

Well, when I was in Academia some 20+ years ago, one of the reasons I quit was that feudal system described in an illustration probably from a peer-review journal because it is so accurate

Yes it is fine to send such an email. If it is polite and/or phrased in the form of a question you might be more likely to get a reply than otherwise. Errors happen. The authors generally want them corrected.
But it is also possible that you have misunderstood something, of course.
It is also a way to establish a relationship for the future, provided that your questions and comments are useful.

My main issue is that I fear if the author might consider my doubt something "too basic". Is that really a problem?

Virtually everyone I've met has not felt "too basic" questions are not worth answering. Think about your own work and the questions you might get from your children/nieces/nephews/parents. They're likely to be too basic. They might not even be well-posed. But chances are you're happy to answer them simply because it's flattering that others are interested in your work.
So don't worry about asking - but be sure to make a serious attempt to understand whatever they're saying before asking a second time, to avoid giving the impression that you're asking them to solve your research question for you.

As someone early-career (about to be a postdoc) who has a few first-author papers, I would be delighted if someone emailed me about them!
Except a predatory journal... I hate predatory journals... but anything else, even an email from a 3rd grader asking what a p-value is, would make me very happy because it means someone read my paper!
The only scenario where I could possibly imagine this being annoying is something that happened to me at a conference, not by email. Someone who did not understand the analysis I was using as well as he thought he did came up to my poster at a poster session and started asking questions trying to "prove" me wrong. And even though I corrected the premise of his questions multiple times and tried to clarify things for him, he just kept going until he finally decided he had "won" the argument, told me I had no basis for my conclusions, and left before I could respond. So don't do that... people asking ignorant questions with a tone of "I want to prove you wrong" gets annoying fast!
I have also had a few different times when I wrote to authors of papers who were more senior and had a lot more publications than I do. I'd say probably about 80% of the time I get a positive response (even when I asked a fairly basic question because I'm not in the same subfield/specialty as the author), and the other 20% of the time I get no response (that just happens sometimes when you email professors - they have too much email). I have never had anyone get upset with me for writing to them or tell me that my question was dumb.

'Dear Dr. Gasbag,'
I am pursing a PhD in the field of offensive odors and recently had the pleasure of reading your interesting 1978 paper, "On The Origins of Stomach Gas." I am sure you are very busy with your research, but I wonder if I might call or correspond with you to briefly discuss some aspects of your work and to gain clarity on a few points in your paper.
Warmest regards,
Joe Shmuckatelly
Rikers Island University
College of Kusai
(808)000-0000

A call seems a bit much if it can be handled via a simple clarification. Maybe if it turns out to be a deeper issue, then a call would be in order.


text:
Can I start such a contact with one researcher that does not know me in one online conference?
I have a major in Mathematics and a masters in Physics and am currently starting my PhD in Physics. Since I've started my masters I am very interested in one particular research field. The main developments in this field have been carried out by a group lead by a very respected researcher. Moreover the book he wrote about the subject together with the papers of his group are what made me be interested in the field.
For my PhD I wanted to work with this field. My supervisor works in related stuff and he spent one year in the US doing his own research, but in a group that was actively discussing the subject I'm interested in, so that he got interested as well. In that case he accepted to supervise me. We are right now deciding on what to take as a concrete objective.
In that sense I had one particular idea that my supervisor really enjoyed and said it could really be the way to go. We are discussing now the particular details.
Now, I'm participating on one online conference and that physicist who leads the group which is making the most significant contributions to the field is participating. Moreover people say that he is approachable and there is one particular moment every day in the conference on which people are encouraged to talk to one another.
In that setting, I have been considering starting an interaction with that professor and ask him his view on the general idea of my proposal. In fact, in one of his papers there is one very short footnote briefly saying that one could perhaps do something related to what I have in mind, but his group followed a distinct direction.
Now while I think that trying to talk to him could be beneficial I fear whether or not I can do it and how to approach it in this online environment.
For starters he doesn't know me and we don't have any common acquaintances. Isn't it a bit of too much asking him privately in one online conference an opinion about an idea I had for my PhD project?
In that sense my question here is: can I try starting such an interaction? And if so how is the correct way to approach it given that he doesn't know me?

It doesn't matter who you are or who they are.  It is generally appropriate to ask people to speak with you.

It's certainly reasonable to ask him, say, if anything else has been done on this.  Whether it's better to do this during an online conference discussion or via email I think depends on how the online conference discussion is set up and what exactly you have to say.  If it's an online chat room with a lot of people in it, I'd probably start with an email.