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PhD student, quit or not?
I'm half-way through the second year of my PhD in computer engineering in a top tier university in the US and I recently moved to a big city away from the main campus of
the institution to the research center because I switched advisors over the summer. I've been thinking about quitting my PhD for over 6 months now. Here is the story: during
my first year, I was a full teaching assistant but I was spending over 50 hours on research per week for the faculty who initially sponsored me when I was getting into
the PhD programme. During this time I came close to a conference and a letter submission but in the end they never went through because my advisor didn't feel like they were
completey ready yet(I'd like to point out here that based on my observation of submissions to the same venues I felt like my work was more than on par with what was being
offered. Then at the end of my first year(after summer), he said that he would not be able to support me full research funding so I went on looking for someone else. In the meantime
he told me that I could try getting an MSc instead.
I'd like to pause here to note that I already have an MSc from top institution in Europe in Electrical engineering with a focus on telecommunications.
Moving on, I was a little peeved off naturally. He waited all summer, leaving me no room to think before the start of the next semester. In that sunken place, filled with
desperation, I contemplated just quitting right away but at the same time half-heartedly looked into other potential advisors out of a mixture of vanity, determination and
pride. The problem was, most faculty wanted to recruit PhD students and make a long-term committment so the option of converting to an MSc for a second degree of the same
type seemed bleak. Concurrently, I was realizing that after living in northern europe during my initial MSc that the American style of living was something that took over you
instead of accenting your personality. Additionally, I had frequent talks with my parents who have been ever supportive. Naturally though, jumping over some of the tedious
details, I will say that they wanted me to stick it out with positive intentions for my future. So, as I was sending some faculty requests, one responded. He was a professor
in the research center of the university located in a big city rather than the campus-city of the main campus. Anyways, at that point, it seemed like I had somehow managed
to tether myself to a line of proceeding down this path with a second chance. At that point with no regard to my previous thoughts about my lack of synergy with the American
lifestyle, I just went along and agreed to an interview without making my intentions clear in the first place. During the interview, he went on about "how this was a long
5-6 year committment", "that I would be making sacrifices", etc... I just kept nodding emptily, more concerned with maintaining a cool and composed appearance, rather than
properly analyzing what he was really saying. He looked at my MSc record and told me that the graduate-level coursework I went through made me qualified for the position.
He said he would give me 2 days to contemplate and made me an offer for a research assistant. I'd like to emphasize that there was 4 days until the semester began because
until a week ago I was still doing research for my previous advisor who had declined to fund me. Anyway, thinking that it would be all good, and that it was a second chance
I accepted in a blur of two days, taking advice from potentially everyone in my inner circle (friends who are doing PhDs of their own, those who finished their MSs and went
onto find jobs, both in US and europe and of course my parents). After accepting, he told me that he would give 1-semester before making me move to the research center, so
I stayed in the smaller campus-city and familiarized myself with my new research topic and tried to complete my coursework. It was as if I was starting a PhD from scratch
(at least the research part), but "ok" I said, a second chance.
Now, coming to you live, 2 weeks after my move to the general DC area. I'm completely drained of motivation. I come into the office area, sit down try to read papers and
standards, still trying to pin a concrete idea for a research topic after a full semester of familiarizing with the area. After 20 minutes half-hearted sloppy skimming
I start having small panic attacks with the following ideas rushing through my mind:
- I'm 1.5 years into a PhD and have absolutely nothing CONCRETE to show for it (no publication, no industiral project work).
- I'm living in a hole in a hole in an expensive city, not able to afford proper nutrition, while some of friends who completed their MSc without a thesis are starting to
pull in 90000$ a year.
- I think about the life I left back in Europe (northern europe) and how the lifestlye here is crushing me into oblivion.
In order to appease myself, I start looking various potential jobs in northern europe that I find myself suitable for. When I discuss with my parents, they get flustered
(still with good intentions) and they say that I'm not giving this a fair chance and that it was my choice to come to US after MSc in Europe in the first place( this is true
but the reason was, due to the heavy influence of american pop culture, I wanted to experience it for myself and see it, unaware that it would spiral this much out of control.
I initially applied to internships, but of course getting an internship in US without a standing VISA is already impossible since the company won't really bother to
sponsor unless you're like exceptional, which I'm not.) Anyways, I look at job postings in europe, the cost of living in some cities, the average salary reports and try to
fantasize about what kind of a life I could have.
But at the same time, I come lab everyday at 9am and leave at 6pm with the hope that establishing at least some routine of sorts in the work environment will help with
my adjust period. Lately, however, I've been thinking that the research life, the lack of direction\certainty and a sense of result-orientedness is draining me. I still try
to cook up some superficial update for my professor, making myself look knowledgable beyond my standing, for the weekly meetings (to be quite honest, since the topic is a
very new topic in the community he himself isn't very familiar with it). This has naturally mislead him and he is thinking of giving me more responsibility. He said, he
would need my help with writing some proposals and he is including me in the tour of a very important 'something' (no details). All this happening while I'm spending my
"working hours" having over ten mini-breakdowns about my future in research. I keep thinking that with an MSc I could've landed a decent enough position in Europe and
risen on a career path with more practical technical certifications such as those of CISCO and AWS, instead of pursuing a path where there is no gaurantee it will end
good. In fact, based on my current track record and some light stalking of some other PhD students in the same field, I'm way below average with no publications whatsoever
to show for the past year. Deep down, deeeeeeeep deep down, I know I want to quit, go back to Europe and find a job. But I feel like its too late. I'm afraid that my
professor will be mad, he will somehow try to block me, since I wasted a full semester of his. On top of that, my parents invested some seed money of their own to set up
my new house here (with a full year's lease signed), they keep telling me to stick it out a little more. I feel like, however, the more I wait, the more time I lose, the more
difficult it will be to leave after.
After hearing this short story, any advice on what to do? How can I approach my advisor after having led him on for a full semester and also having signed a contract for the
next two semesters?

Can you make this readable and get rid of most of it?

Agree with Buffy, but moreover, I think you need to address what your long term career goals are. If you want to stay in research, then getting a PhD is probably a good idea, and you should focus on strategies on gaining motivation and choosing a topic. If you want to work with Cisco and AWS, then you should move forward with that and stop worrying about making people angry.

That being said, having to switch advisors and move across to the other side of a state is a major life event, so waiting to see how you feel in a little while might help.

@PerilHideDive What is your main motivation behind pursuing a PhD degree?

Based on the American culture comments, I think you should try to make use of the DC area and join a university club or intramural team, try to make some connections. I think your isolation from local contacts isn't helping your outlook on life..

Meanwhile, don't compromise on sleep, exercise and nutrition. The lack of it can cause permanent health issues.

@mkennedy it's mentioned in the post that it's an extension campus of a state university, so such activities are likely few or completely nonexistent.  Of course, there are many community groups one could get involved in.

This stands out: "He said, he would need my help with writing some proposals and he is including me in the tour of a very important 'something' (no details)." It seems a bit odd to me that he would be inviting you in writing proposals, especially after only a semester of work with that professor.  That may be a sign of future funding issues. I think your abilities are fine, for being in the second year of a program it sounds like where you're at in terms of research is pretty average.


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Is it acceptable in an academic interview to pretend like you derived something, or to explaining where it is from
Video in reference: https://youtu.be/dUwN6GI-0EQ after 4:05
In a Cambridge (model) interview, someone was asked to sketch a graph of sin(x)/x. The intention was clearly that they were not to have seen this function before. When watching, I immediately recognised this as sinc(x) (a function sometimes used in electrical engineering). They were then told not to evaluate this function at 0 because it's difficult, however I knew how this could be done. If I was in this position, would it be acceptable to pretend like I could derive everything I knew about this function already to impress the interviewer, or important to say that I have already seen the function before.

Generally best to tell the truth, as a baseline... (for most of us...)

Pretense is often caught. And what if you get it wrong anyway?

Also, how is it clear to you that they were not expected to have seen that function before? It is one of the iconic examples... Indeed, when I design exams or tests of any sort, I don't seriously expect people to solve serious puzzles in real time while I'm staring at them, but, rather, hope that they recall having seen the things before. So I'm entirely happiest to hear people respond "oh, yes, I've done this before. It goes as follows..." Perfect.

You have seen sin x, so sin x / x is really simple without having seen it. Taylor formula is 1 - x^2/6 + x^4/5! etc. so it starts with y = 1 going down to 2/pi at pi/2, going down to 0 at pi, and then it looks like sin except it gets flatter and flatter, enveloped by +/- 1/x.

They were then told not to evaluate this function at 0 because it's difficult --- (mathematical wording nitpick) Well, unless you say more about the function than simply sin(x)/x, it can't be evaluated at x = 0 because it's not defined at x = 0. Of course, it has a removable singularity at x = 0 (i.e. limit exists at x = 0), so there's an obvious (to the presenter, at least) continuous extension to x = 0, and that continuous extension is defined at x = 0.

I really don't think the interviewer cares one way or another whether you've seen the problem before.  She just wants to know if you can solve it, and to hear how you go about it.
In the video, she does say "the function that I'm going to write down, you've probably not seen before"; but I interpret that as just a way to reassure the student that the problem should be possible to solve whether she has seen the function before or not.  It's so the student doesn't panic or get stuck trying to remember the function, rather than actually trying to solve the problem.
So I don't think there is any point in either pretending the problem is new to you, or in announcing that it's familiar.  Neither will significantly help or hurt you in itself.  If you know how to solve the problem, solve it and move on.
On the other hand, it probably wouldn't be helpful to just draw the graph from memory and say "here it is, done".  The interviewer is almost certainly more interested in having you demonstrate that you understand the concepts and methods used to solve the problem, than in seeing if you know the solution.  So you would be wise to work through the problem methodically, explaining what you are doing and how you know to do it.

NO. What you are describing is dishonest behavior. It is absolutely, categorically, not acceptable to behave dishonestly in an academic interview.
And if you think you can get away with it, I think you’re severely underestimating how easy it would be for the interviewer to notice your pretense.
Don’t do it. It’s a terrible idea.

This happened in my Cambridge interview. I think you are presupposing that it is necessary to either come clean or deceive. I don't think it would play out like that unless they explicitly ask "have you seen this before?" (which in my experience they wouldn't bother asking).  I would just answer all the questions you can to the best of your ability. They aren't going to say "You've seen it before and didn't say so, so you cheated".

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Peer review prior to beginning a study?
In scientific research there are a number of problems today:

Studies that aren't reproducible.
Studies and papers that are criticized for their methods, conclusions, or bias.
Industry-funded studies that are discounted due to accusation of conflict of interest.
Individuals and groups who are defensive of their work due to their personal and/or financial investment, and are inherently not open-minded toward critical feedback.
Even if researchers are open to critical feedback and scrutiny, it may still be infeasible to re-run a flawed study due to logistics, financial, and time limitations.

From my experience in engineering, arguably the most valuable ROI effort in a large project is getting early peer review before significant investment is made toward an approach.
If a group of peer reviewers had a chance to give their feedback on how a study was going to be performed, then the results are more likely to be valid, and the reviewers are more likely to accept whatever the results will be.
I am not a reseacher and am completely unfamiliar with the process of publishing a study or a paper.  However, the only peer review I have heard of is where only final results are reviewed.  I am curious:

Do journals, institutions, etc. have processes that require peer-review of initial proposals and procedures before a research study is allowed to commence?
If not, why not?

I suspect that such a process would have the potential to greatly increase the quality of studies, and prevent much wasted effort where studies are published that never gain acceptance (presumably due to quality problems but perhaps for non-technical reasons as well).  Curious to hear others' thoughts.

While much of this is opinion-based, there is a factual question buried in there (Q1). So I'm voting to leave open.

I'm searching for the question in here, and the only one that can be answered is that the appropriate level of 'peer review' for proposed experiments is taught during graduate school. (And, in the end, I don't think any experiment I set out to do was done exactly as I first imagined it - nature usually ended up being more complicated and interesting.)

where only final results are reviewed Just to be clear, methodology is part of the review process, and I have rejected papers for having poor methodology.

Principles of academic freedom usually leave it up to the individual researcher to decide what to study (within ethical limits).  They may certainly be judged (for promotion, tenure, raises, etc) based on whether their research is successful, but there's no "prior restraint" as it were.  So an institution usually won't require this sort of pre-review.  It is certainly wise for the researcher to seek advice regarding the feasibility of their planned study, but if they don't think it's worthwhile, or want to go ahead even if the reviewers think it's a bad idea, that is their prerogative (and their time wasted if it fails).
On the other hand, if they need money to do their work, there are certainly elaborate peer review processes for grant proposals.  It's considered fine for a researcher to risk wasting their own time with a poorly planned study, but not for them to risk someone else's money.
For studies with possible ethical concerns (e.g. human or animal subjects), there will be an ethics review required before the work begins.  This will mainly be aimed at whether the techniques are ethical instead of whether the overall study is likely to succeed, but one consideration may be whether the study's benefits outweigh potential risks to the subjects.

While only a minority of scientific work (I imagine mostly medical science?) is done under quite the conditions that you describe, there are two other things that help:

When funding organisations decide who to award grants to, the grant proposals are usually subject to peer review. I imagine that this is, in effect, quite similar to what you were thinking of.
IN some areas it's common for large projects to have a steering group of other academics and/or representatives from industry that the PI reports to every so often, and which will offer advice. It probably isn't peer review in quite the way that you were thinking, but it does serve many of the same functions.

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What are the chances of *Jim* to make it big in academia?
Jim, a fictitious character, scored a mediocre 3.48/4.00 in his undergrad (in Physics). It took him 6 years to complete the 4-year program. He is enrolled in a masters program but due to COVID, he missed the on-campus exams. So he has to sit for the exams next year. He is unemployed and feeling very low. Is it possible for him to make it big in academia and get research or teaching opportunities in future?

Yes, it is possible.

@Buffy, Thank you for commenting. Could you tell me what I can say to convince him that way?

@incredible sulk Show him this post

Keep working hard. For some emotional issues professional help is indicated, of course.

Although no direct answer, see https://academia.stackexchange.com/questions/87668/how-do-you-come-to-terms-with-the-fact-that-you-might-never-be-among-the-best-in?r=SearchResults and https://academia.stackexchange.com/questions/2219/how-should-i-deal-with-becoming-discouraged-as-a-graduate-student

This site tends to answer "you can do it!" to pretty much every question. And it's true, "Jim" could wake up and in his sleep have come up with a breakthrough in string theory, with Harvard knocking at his door. However, it's also important to face tough life choices realistically. Given what little information you shared, it is unlikely "Jim" will make it big in an academic environment where people with considerably superior qualifications frequently fail. I recommend "Jim" start investigating alternatives.

I was one of the votes to close. The answer to the direct question is obvious, but the underlying issue is too complex to get a good answer here. Many people suffer setbacks and overcome them.

@DanielHatton, Yea...I do understand what you are saying. Jim is depressed and I do not know how to give him hope.

@henning--reinstateMonica, Thank you for the amazing suggestions :)

@gnometorule, hmm...I also feel that way. He should move on.

It is possible but not probable. Also depends on what one means by "making it big." Nobel Prize? I mean, that is a vanishingly small percentage of even top graduates of top schools. Make full professor and have the esteem of some colleagues? More probable, but in today's world, where the tenure track is largely disappearing, still hard even for the most qualified.
The dirty secret of academia is that it creates many multiples more qualified people for the "good" positions than there are "good" positions. The academic labor market is severely misaligned, in terms of ratio of Ph.D.s produced to demanded. So everything else being equal (including qualification and achievement, and those are of course not equal!), most people in academia will not make it big even with the wind at their backs.
Like many areas, academia tends to look at credentials--not only where they are from in terms of prestige, but the manner in which they were acquired (how long it took, and so forth).
In addition, academia also relies very heavily on personal recommendations of advisers, and someone with these credentials (OK but not great GPA, long time to degree completion, missing exams, and so forth) would probably not do well in the evaluations necessary for advancement, like letters of rec, or being thought of when a job comes up that needs filling.
This fictional character would likely need to gain a foothold in some sort of more technical job, like working for a large collaborative project where he could do "grunt" work, demonstrate superior completion of that work, and then use that work up the ladder.

Honest and spot on!

The probability of any individual winning the Nobel Prize in their field, rounded off to a few decimal places is probably 0. A better measure is producing a few doctoral students who, themselves, do the same.

Thank you very much. I really appreciate it :)

Sure. But even that is a proportion that approaches 0 asymptotically. And is producing such students "making it big"? OP would need to tell us what the definition is.

Except you can't work up the ladder.  Spend a few years in a technical job and everyone thinks of you as a technician and not a research leader.

@Nate, He only talked about getting research and teaching opportunities. I think that's what he meant by 'making it big'

Can Jim "get research or teaching opportunities ...?"
(Answer for the US) YES, at least to teaching.  Two- and four-year colleges hire Ph.D. physicists for teaching.
Research opportunities will depend on Jim's Ph.D., not on his earlier academic performance.

Thank you for answering. This is really helpful.

But his ability to get into a Ph.D. program (just the first step) will probably be predicated on undergrad and master's degree performance (assuming the master's degree mentioned above was terminal or otherwise not-on-the-Ph.D. path). (N.B. Most Ph.D. students get a non-terminal master's somewhere around the 2nd or 3rd year, as an indicator of completion of exams or prospectus defense.)

Lots of 2 and 4 year colleges are closing their physics programs and have just one poorly paid part-time faculty member in physics.  Full time teaching jobs are very competitive and hard to get.

This answer is wrong.  @AlexanderWoo is right, except that quite a few colleges never had physics programs so they can't close them.

Hi @AnonymousPhysicist, Do you think Jim has any chance to survive and thrive in academia?

In my opinion, Jim's chances are no different from any other randomly selected person.

@AlexanderWoo  I was amazed when you said that.  I looked at a couple of 4-year colleges (Ohio Wesleyan, Oberlin) and found that they both offer physics majors.  I looked at a 2-year college (Ohio State University at Marion) and found physics courses offered (including labs and in-person exams): students can start at Marion, then transfer to OSU Columbus for the last 2 years.

@GEdgar - Yours is a biased sample.  Oberlin is easily in the top 2% of 4-year colleges, and Ohio Wesleyan well in the top half.  The OSU branch campuses are all comparatively well-resourced.


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Strategies to plan research and make the maximum out of it
My masters advisor handed me a bunch of papers and an old dissertation. After week 1, I have hardly managed to read one paper. He asked me to focus on a specific part of the project and I have read the relevant paper but I have not been able to read others. Many weeks have gone past and I feel like I am already a disappointment to him.
I seem to either concentrate on reading papers or doing specific tasks related to the project (e.g. try to understand specific details and implement the knowledge to infer something). I feel for the project to be something fruitful I would need to read a lot of papers, keeping record of the ideas that I came across while reading which can be used in the project, and also reference them while writing my dissertation.
How can I manage time better to read papers and other project related work given that I don't have any coursework or other commitments? How can I keep record of reading to fulfill the aforementioned needs?

Why is it taking you more than a week to read a paper? Is there something in the paper you are stuck on? If so, what is it that is getting you stuck? Are you trying to understand every possible aspect and corner of the paper and following citations down rabbit holes, or just trying to get a general idea first? Are you doing other things besides reading the paper? Hard to give suggestions if it isn't clear what the issues are.

Have you tried https://academia.stackexchange.com/search?q=How+to+read+paper ?

Also, what does your advisor say?

@BryanKrause: In my area of mathematics, I wouldn't expect a grad student to be able to read and understand a significant paper in less than a month.  Doing peer review for a moderate length paper takes me 30-40 hours of work.

@Alexander Sure, that's why I asked the follow up questions. Reading a paper to get some idea of the general idea and field might not require that level of depth, OP may need only to determine whether the paper is worth reading further.

Since scientific and math writers are writing for experts, and in fact specialists, it can be very difficult to read papers as you are getting started. Specialists share a mindset that implies that they can leave a lot unsaid. The author of a paper is likely very familiar with all of the papers cited, and you are not. This makes it especially difficult.
To understand a given paper it may be necessary to review many of the referenced papers first. At least the abstracts of those papers. It might be necessary to become familiar with some terminology that you aren't used to. Wikipedia can be a big help in many fields, actually.
But if you are starting out as a masters student then your education up to now has been mostly as a generalist, not a specialist. Don't get overly discouraged, but it takes a lot of work to build up your knowledge base to the point that you can understand a paper.
Dissertations are usually a bit easier, since candidates are expected to be a bit more complete than is true for published articles that depend on earlier work.
It is probably easier now than when I needed to spend hours in the math library, searching for referenced papers and then the papers referenced in those, etc, until I got some idea about what was being said. Now you can find a lot of those older papers online. The understanding hasn't gotten easier, of course.
But eventually, you grasp the specialized language and also the way of thinking of experts in your field. Lots of hours.
If you can ask questions of your advisor or others you can shorten the understanding process quite a bit.
As you read, take a lot of notes. Write down key ideas, of course, but also write down questions you still have. Then try to answer those questions either with more reading or by asking of others. If you find an answer in written work, it is good to write down the citation. You may want it later.
An effective researcher will also write down questions that aren't answered in the paper being read. This gives you an opportunity to extend the work.
Think of the knowledge you need as a tree that you need to explore. You need to go both wide and deep to acquire the understanding.


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How to take notes during lecture properly?
I am struggling with note taking during lectures for a long time. I find that if I only listen to the lecture I am able to understand the concepts properly. But the downside is that I often forget some important details. On the other hand, when I concentrate on taking notes, often I just end up writing a lot of things without paying much attention to the concepts. I have been trying to improve my note taking skills by watching video lectures from OCW or YouTube. My lecture notes look more like lecture transcripts. I pause and rewind the video and end up writing a lot. I can't figure out how to improve. I would really appreciate if anyone could have any suggestion.
PS. I take notes with pen and paper and I haven't tried note taking on a computer.

When I was a student and a professor explained the passage from one equation to another, maybe giving explanations for half an hour, on my notes (not very many, admittedly) between the two equations I'd only write the word then. When studying later on, I'd have usually wondered: "then what?!". But the process of reconstructing what was in-between those two equations was quite educational :-)

I never really took notes, just wrote down some questions or spontaneous ideas for side-projects. The only time I took notes was when we had to (at high school, as instructed by some teachers), which usually was pretty counterproductive... Therefore, I'd ask myself whether note-taking really does something good for you, or restrict it to the few things that you need to look at again, where you need to ask for clearification or which you can use in some other way

re-writing what's in your textbook is completely pointless.

I'd say it should be a mix of writing down what the lecturer is saying and listening to what they are saying, don't just frantically scribble down everything if you are not listening carefully.

I answered a similar question at CSEducators a few years ago.
I agree that taking notes with pencil/pen and paper is superior to doing it by typing into a laptop (see the reference). But to be truly effective you need to do more than just take the notes. I suggest that you re-read and annotate them as soon as possible after a lecture, adding questions as well as notes/corrections. The second pass will help firm up the ideas. This is best done immediately, but certainly within a few hours if classes are taken back to back.
Another trick is to capture, from the notes, the most important ideas given in the lecture. The instructor will possibly point them out, but most of us would go in to a lecture wanting to especially make one or two points. It is good if you capture them.
But a single pass over anything is unlikely to lead to deep learning. And utilizing the information (exercises) is even better for firming up the ideas.
As to taking transcripts of video lectures, the same can apply. When you finish such a video, re-read and annotate the notes, marking or extracting the key ideas and making sure you understand what is being presented.
For situations in which you have access to the lecturer, write out any questions you still have and try to ask them at the start of the next lecture, or using some other communication channel.

There is a joke that the "purpose" of a lecture is to get the teacher's notes into the student's notes without going through the mind of either. Don't let that become a reality.
I once took a "course" in which that was literally true. Two of us had an independent study with a professor who gave us the task of literally copying his written notes (no lectures) but gave no real opportunity for questions, exercises or feedback. It was among my worst educational experiences ever.

Also note that learning requires reinforcement. The review of the notes, with annotations, provides the start of that. See The Art of Changing the Brain by James E Zull for some of the science behind that. A search of this site for "Zull" will turn up some further mentions of these ideas.

Here are a few practical suggestions from a former student who also only took notes with pen and paper.

You can't write everything down from a lecture, to attempt to do so is counterproductive.
Unless you are an incredibly fast writer, there is no way you are going to be able to simultaneously write everything down that is said and understand/learn what is being said. Based on your post, it sounds like you have already encountered this conundrum.

Because you can't write everything down, you need to filter the incoming information stream for core concepts or important ideas/insights
When I took notes, I was constantly monitoring what was being said and trying to pick out what the key ideas and important points were, and then only writing those down.  This sort of forces you to learn/comprehend on the spot, because you can't figure out what is a key concept vs just an example unless you actually understand what is being communicated to you.
The main idea here is to differentiate between what you think will be important to know/remember later and what is closer to "trivial" information (anecdote/filler material/example).
For example, if a professor introduces a new equation that is related to the theme of the lecture, write it down.  If he then talks about how that equation was developed in the 1800s by some scientist or briefly shows another equation that seems unrelated, don't worry too much about not writing that down.  The chance this information ends up being important later is much lower.

This method actually follows the flow of most lectures fairly well
Most lectures generally follow the pattern of core concept, further details, examples and background, core concept, ...
If you follow my strategy, you will identify and write down the core concept immediately.  You then have some time to digest the core concept while also half listening to the details and examples that inevitably follow.  If something jumps out from that section you can also write it down, but if not, now you have more time to chew over the main ideas in the background while continuing to listen to what is being said.
This essentially ensures you are focusing on what is critical for keeping up with the lecture (and by extension learning).  If you get all of the core concepts but miss a few details along the way, will you still be able to keep up? Yes.  If you record lots of the details but then miss or are fuzzy on some of the core concepts, will you be able to keep up? Probably not.
Your ability to comprehend and record information is both a fixed and limited resource during a lecture, so spend it on what matters.

What if I have trouble figuring out what matters and what doesn't?
This is a skill you develop over time and also something that often develops over the course of a class as you begin to learn the material and understand how it all fits together.  That being said, there are a few practical tips I can offer.

Is this something I can easily look up later (either in your book or online)?
If it is not, then consider writing it down.
A good example of this might be a mathematical proof.  If you know your course textbook doesn't contain very many proofs, and the professor is starting to give one on what seems like an important equation, then you should consider writing it down.  This might be one of those situations where you have to decide to sacrifice understanding for the sake of recording information.  Often for me this went something like, "I am just going to focus on writing this down as fast as possible without errors. I won't be able to understand it because I am so focused on writing it, but that's ok. I know I have it written down here and I will come back and actually review/learn it later if it ends up being important."
If, on the other hand, you know your book often contains proofs for important equations, or you will be getting a copy of the lecture notes later, I would recommend not trying to write it down. Focus all of your energy on trying to understand it instead, and maybe just write down "proof given" in your notebook to record that it was discussed.  This gives you an opportunity to understand how the proof was constructed and potentially develop and ask questions if something is not clear. You can always consult your book/lecture notes later if you really need to review.

Think "meta"
A big part of being able to filter information well is not just thinking in terms of the current lecture, but how the information provided fits into the bigger picture (of the week, the unit, the course, your degree, ect.).  Try to ask yourself, "Why am I learning this?  Why would this be important for me to know?"
Often people will recommend you read/skim the material before hand to help you get a better sense of what the key points are.  If you have time to then go ahead, but being in an intense program myself I found I never had time to do this.
What worked better for me was to just review the syllabus and skim over the table of contents/chapter headings to get a rough roadmap of the course. This helps you know what topics are going to be covered and roughly how they all fit together.
For example, if I'm taking an algorithms course and a whole week is going to be spent on learning how to measure algorithm performance, I am going to pay careful attention and make sure I really understand the concepts because they are likely foundational and going to come up a lot during the rest of the course.  If we are covering a particular algorithm one week, however, and there are some technical details I can't quite get, I might not worry too much about needing to fully understand that information.  Especially if I already know we are going to cover 20 other algorithms as part of the course, there is no way I will be able to remember that level of detail for all 20 of them, so it is a poor use of my limited resources to try.

Filtering is learning
Simply being able to take in information, understand it, and then pass judgment on it's relevance is an act of learning in and of itself. In this sense, learning how to take good notes is also learning how to learn.  Once I became good at taking notes, I found I needed to do very little review outside of lecture because I had already grasped a lot of the material simply by ingesting it.
I bring this point up mostly because I don't want you to be discouraged. Learning to learn is hard, but it will pay big dividends in all of your future coursework. Don't be afraid that you are struggling now, because that is a normal and expected part of the process. If you really lean into that struggle and keep going at it until you improve, it will pay off big for the rest of your time as a student.
Essentially, I encourage you to view taking good notes (and learning how to learn) as an additional class you are enrolled in every semester. Things are going to start out hard and uncertain, but if you continue to put time and effort into your "course" you will improve and things will begin to make a lot more sense.

A few final suggestions.  If you are really worried about missing information, see if you can record each lecture on your phone or laptop.  Rules around this likely vary by institution, but it probably involves asking each professor for permission. I don't think this should be a long-term solution for you, but it might help in the short-term if it removes some of the pressure to feel like you must write everything down.
Finally, as I alluded to before, view note-taking as more of a learning method and less as an archive of everything the professor said.  I often took a ton of notes while reading and during lectures but then rarely reviewed any of them.  In retrospect this was because the act of ingesting, processing, and then writing the information I was receiving was really how I was learning. The fact it produced information on paper that I could review later was really more of a byproduct  rather than the primary benefit.
EDIT: One important thing I forgot to mention is that shorthand is your friend.  You shouldn't be writing in full sentences (and frequently not even full words). Jot down the minimal amount of characters necessary for you to remember what was said.
Instead of
Isaac Newton published the universal law of gravitation in 1687

Write
Newton pub univ law grav 1687

If Newton is mentioned frequently in the lecture or course, you could further abbreviate to Newt or even N/ as long as you think you will remember what N/ means if you were to review your notes later.
Other shorthand notation such as w/ for which, what, and when, bc for because, eg for example, et cetera are also useful. It might not seem like much, but for a slow writer like me the small time saves from shorthand really add up over the course of a lecture and are instrumental in my ability to keep pace.
You want to do anything you can to minimize the amount of time your brain is distracted from processing the key concepts being presented, so try to shorten/condense what you need to write as much as possible.

Thanks so much for writing such an outstanding, elaborate answer. I am taking these points very seriously and I will try to implement them to the best I can. Thank you once again!

I'm going to give you a very tactical recommendation.  This is hard to keep up with, but is the premier way to engage with material in lectures is to PRE-WORK the content.

For math/science/applied:  Pre-read the chapter.  Work any examples in the chapter.  On paper, in your notebook.  Work the homework problems.  All of them.  Check your answers to the extent possible.  Rework (from scratch) any problems missed.  Use your notebook to do this work.

In the BACK of the notebook, write down any questions you have, with space to fill in an answer.  Quite often, you'll actually figure it out yourself. Then fill it in. But in the cases, you didn't, these become questions to ask in class (or if too minute, will allow a very quick, targeted, efficient questioning of the instructor in office hours or even just ad hoc few minutes after class.)  Note, that it is NOT just the answers to the questions that educate you.  But the WORK you did to develop them and then record the answers.

When you are in lecture, the entire lecture will be a refresher.  Write down what you feel is important.  The good thing is even if you do take long notes (not needed), because you know the material already, it will be very quick/easy to write down the content (more so than if fresh).  Put little star icons on the pages with class notes (segregate by page, but will be in the "rolling forward" part of the notebook) for lecture notes.  This allows you to differentiate them from HW practice.  If anything new/important (as opposed to just a practice problem or derivation you already understand) is covered, than box or give it some little star or the like on the margin.  Again, note that it is not just the nuance content itself that is educating you, but the act of thinking about it and registering it as such.*  Also, given your level of understanding of the topic, lecture notes will NOT be a key to look at in the future.  Your key content is the textbook and drill problems, when doing exam prep.

Note, classes in history, lit, art, etc. will be a little less drill oriented.  And the professor may do a bit more enrichment, discussion, etc. outside the text.  However, even in this case, you should have read the reading AHEAD of time.  At a minimum, this will make you familiar with the basic content.  And able to come up with insights like what is ADDITIVE to the content versus what is in the text.  Another insight might be differences in rationale or interpretation or emphasis.**  Even in a pure discussion class, pre-work can make a difference.  I took a 10 person at a round table history class (with a real historian and top majors types)...we had two discussions a week of comparative history.  For the TUE, we had done a 2-page compare/contrast essay ahead of time.  For the THU, not.  And you can bet your sweet ass which day had a better discussion/argument amongst the students!

Similarly, of course, classes with case methods and Q&A (think John Houseman in The Paper Chase, or perhaps Harvard MBAs) are much better, the MORE you have pre-studied the material.  And it's not just not looking stupid when called on (though sure, that's a feature) but getting more out of the session.

*Humans are NOT computers (sorry comp sci folks) that just need a clear instruction set.  Instead, we are more like animals (literally we ARE animals) that need training and repetition so that the learning is engrained in longer term memory and working ability.  This is "pedagogy" as opposed to "content".
**For instance in history, there is a common issue of "historiography" (scare quotes intentional, this is basically people interpreting history in terms of whatever left/right, dreamy/practical, original/not-sin views they have).

What is the purpose of a course lecture for you? Do you see it as a resource to improve your understanding of the topics being presented based on what you have already read about them. Or do you approach it mostly as your first (and perhaps first in-depth) exposure to the course topics? You will more likely be caught in the quandary that you express for the latter case rather than the former. The less prepared you are with some knowledge of the topics in advance, the more you will fill a strong pull to one of two approaches. You will be pulled to listen intently to learn the topics for the first time, thereby having less time to take notes. Alternatively, you will be pulled to take copious notes to read later, thereby having less time to digest (learn) the topics as they are being presented.
One starting point to improve how you take notes during a course lecture is to read about the topics in advance of attending the course lecture. Indeed, take notes as you are doing your reading. Mark places from the textbook or course resources for the upcoming lecture where you recognize that you would like to learn more during the lecture itself.
The additional advantage to preparing in advance on what you know should be in the lecture is that you will be able to capture full context of any surprises. You might always anticipate that you will see something that you have not seen yet even in the best preparation. How comforting to be able to reflect on the new information in real time because your mind is not occupied still trying to make the best sense of where the new information originated or should fit in everything up to that point.
A useful advantage here is to have the course lecture notes in advance. If this is your situation, here are some additional questions that you might answer to find ways to improve how you take notes during the lecture: How intently have you reviewed the lecture slides in advance of attending the lecture? Have you matched the content on the lecture slides to the topics in the textbook in advance of attending the lecture? Have you marked the places on the lecture slides where you will ask for help during the lecture?
What is the purpose of having the notes after you take them? Do you use them as your only resource for study? Do you use them as supplements to the other resources on the topics? You will be pulled to the quandary when you see lecture notes as the only study resource. When you develop habits to review the lecture notes in parallel with other resources from the course, you will be less anxious at the outset about the need to take copious lecture notes during the lecture itself. You will learn how to fill in the gaps from the lecture notes with the information from the other resources.
Finally, what do you do if you discover that your lecture notes have gaps in them? Do you skip over those gaps hoping for future insights? Do you try to fill in the gaps using the other resources for the course? Or even … Do you schedule a meeting with the instructor to ask for help on the missing information?
A useful advantage here is to have recordings of the course lectures. If this is your situation, you can certainly review the videos to see if you can fill in the gaps. What do you do if the lecture does not fill in the gaps? Again … Do you schedule a meeting with the instructor to ask for help on the missing information?
In summary, to improve how you take notes during a course lecture, determine the reasons why you are taking them. Do so at the front end: What preparations do you make before you attend a course lecture? Do so at the back end: What do you want to do with your lecture notes once you have them?
Finally, taking notes is only equivalent to making an inventory of information. Developing the expertise to review notes and put them in their fullest context to themselves and the other resources around them is where the real learning starts. Whether this is done with notecards or with the latest and greatest electronic gadgets, the goal is the same. For further insights, search for readings on personal knowledge management systems. A recent hot-topic approach in this field is the Zettlekasten method.

Very often (in my own experience most of the time), the lecture contains the first and only presentation of some material in a class. Even in classes that had textbooks, my professors would often present related material that was absent from the text. It wasn't even possible to anticipate what would be taught necessarily.

@AlexReinking As I also do. We might agree that, with advanced preparation on the material that is not new, the ability to capture fresh material improves. Also, we might expect that the instructor would not simply leave the lecture as the sole source of that fresh material. Doing so is an injustice to the responsibilities to teach effectively. It still argues that one is better prepared for what should be there in order to be able to capture the surprises.

Hi Professor @JeffreyJWeimer, Thank you so much for taking the time to write such an elaborate answer. I really appreciate it and I am very grateful. I am currently taking a course on Genetics and Evolution from Coursera where there are lecture slides available ahead of time and I am doing pre-lecture preparation as you suggested. At my university (I am from the Indian subcontinent), there is no scope for preparing ahead of time as we usually don't get any reading assignments and our instructors usually bring their notes to the lecture hall and write them on the white board word-by-word.

Hi @AlexReinking, Thanks for sharing your experience.

In case you do not get any reading assignments in advance, you can still benefit by having a report of the schedule for the lecture topics. Correlate the schedule of topics to the chapters or content for the course. Read what seems relevant even without having explicit instructions. The worst that can happen when you do is that you learn more than what you are required to learn. The worst that can happen when you don't is that you continue to fall behind.

@JeffreyJWeimer, Thank you professor for the suggestion. We do not get lecture schedules (we know at what time the lecture will be held but we don't know what would be covered). Since the notes usually don't change/ haven't changed for a long time, we collect lecture notes from someone who have previously taken the course. Everyone's lecture notes look very similar as we only try to write what's written on the white board. In the finals or midterms, we are mostly evaluated on our capacity to memorize those notes.

@JeffreyJWeimer, I have tried bringing a copy of old lecture notes in the lecture. Instructors usually don't allow someone to do that (I was scolded for it!).

I personally adapt the method found in this talk by Marty Lobdell. The dilemma of writing to little or to much is solved by - doing both!

during the lecture, you quickly and superficially jot down keywords/concepts from the lecture, with no regard to utility even a day after the lecture
right after the lecture, take a new sheet of paper and now summarize the lecture using the keywords you wrote down, such that the note is usable later

Advantages are:

You can focus on what's being talked about during the lecture. It can help you from dozing off because you have to listen in order to write usable notes
You process the entire lecture again afterwards, expressing it it in your own words, which aids and tests your understanding, and shows you where it's still lacking
It's easier to judge what's actually important after you saw the entire class, so the notes get better for later reference

The disadvantage is, of course, that it's more time intensive - it my experience it usually pays off though in the long run, as it reduces the time you have to study later.

Thanks for the write up! I watched Marty Lobdell's talk a couple of days ago. Really an eyeopener.


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How to effectively read thesis and research articles in molecular genetics/ systems biology?
I am new to research. My thesis supervisor gave me a few articles and a thesis to read. I started reading the thesis from the beginning to the end and I feel like I am going nowhere. My research topic is molecular genetics/ systems biology. Considering the fact that I only have a BSc degree in Physics, how should I read these? I feel like it will take me ages to finish just one article.

Don't get bogged down too much by all the small biological details, you can often understand much of the paper without getting stuck on these.

You have a supervisor... Ask your supervisor!

I'm sure you will receive lots of advice on how to read efficiently. Some of it will be useful for you, some won't - many of these tips will only really work when you know what you are looking for or are sufficiently familiar with the way things are presented in a particular field that you can see the important points immediately.
However, I would advise you, that as a new starter in the field, to a certain extent, you'll just need to accept that it is going to take you a long time.  I can now read a reasonably size paper in an average of an hour, but a paper could easily take me a day when I was where you are now (approx. the same field), and I had a biology degree. You will get quicker as you get more practiced, I promise.
When coming from a new field, the hardest thing will be deciding on how much of the background it is necessary to understand, particularly in relation to methods - you do not have to go away are read up on every method you come across, sometimes you can just accept that it is saying what the authors claim, with really having to understand the detailed reasons why. Other times it is important to know what is going on. Learning which is which will help you cut down on unnecessary googling of terms/methods etc.

Thanks Ian. I am trying my best.


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Should I withdraw from a graduate math class to make more time for a promising research project?
I am a junior graduating May 2021 with a double major in physics in math, and I will be applying to commutative algebra (math) graduate programs this upcoming fall. I was recently offered an unexpected but very promising commutative algebra research project, but because the research is time sensitive and needs to be completed by May, I would need to withdraw from my graduate complex analysis course to complete it. I am wondering if it would be worth taking the 'W' on my transcript in order to gain a (very likely) publication. I've been mulling the decision over for over a week now and am desperately seeking some advice. Here is some background:

I am enrolled in 5 graduate courses (4 math, 1 CS) and a thesis writing class.
I have participated in math research and presented it at conferences, but am not currently published.
I have completed 4 graduate math classes in the past.

I tried cutting other commitments to avoid withdrawing from a class, but discovered that I just don't have enough time for my classes and research. Basically, I'm trying to gauge whether one more graduate math class or one more research project (albeit with a 'W' on my transcript) will make me appear more competitive to graduate admissions boards. Complex analysis is currently my largest time commitment – I am not confident that I can withdraw from anything else and still make enough time for research.

There’s absolutely no question: a paper is far better than one more graduate course. Assuming you do manage to publish it, it’s a fine reason to get a ‘W’.

@knzhou Thanks a bunch, that's what I suspected, but needed reassurance. There is, of course, inherent risk involved with publishing, but that's a risk I'm willing to take. Thank you!

What does your thesis advisor say?  Their advice is likely to be better informed than ours.

Be careful taking advice from non-mathematicians (like knzhou).    Undergraduate research plays far less of a role in math PhD admissions than in the other sciences.  This kind of question cannot be answered in the abstract, so you need to talk it over with a mentor who knows your situation in detail and also knows a lot about math grad school admissions.

@NoahSnyder My advisor's have given me waffling advice, and have said that either option is fine. When I mentioned that I was leaning towards withdrawing, one of my advisors recommended withdrawing and explaining the reasons for the withdrawal in my applications. I haven't received feedback on how a 'W', particularly one in complex analysis, will affect me.

@AndyPutman Thank you for the advice Dr. Putnam, I will talk it over again with my advisors in that case.

I'm very confused about where the May deadline comes from.  Is this for a CS conference?

As an aside, the possibility of unexpected opportunities arising outside of class is a good reason why your high courseload would usually be considered inadvisable.

@NoahSnyder I was offered the project by a post doc whose position ends in May. He is unwilling to mentor me remotely, hence the deadline. I could, however, potentially find another mentor.

Well, it's certainly far too late to help the OP, but if future readers are wondering about the relative value of undergrad research vs grad level courses, here are some things to keep in mind.

Research and writing always take MUCH longer than you think. It's essentially impossible to start a research project in February and have the final draft of your paper in May. Math research doesn't work well with hard deadlines.

When someone "offers" you a research project, it's easy to get swept up thinking this is a great idea and everything will fall perfectly into place. That never happens. Instead, obstacles arise the deeper you go into the research project and take more time to address than you expected.

You can pretty much always put aside a research project and pick it up later when there is more time.

In terms of admission, there is not a strong expectation from PhD programs that undergrads in math will have published research. However, success in graduate-level courses (and the resulting letters of recommendation) matter a lot.

Though it's too late, my recommendation would be to stick with the courses. A three month delay on a research project in math is very minor, and makes a lot of sense so that students can stick with their courses (the primary focus of undergraduate studies). If the post doc really wants to work together, you can do that by email during the summer or in some future year. You cannot, however, take an idea the postdoc gave you and then bring it to some other mentor, without the postdoc's permission. The best case scenario would be if the student and postdoc identified some professor (perhaps the postdoc's mentor) who could supervise the student in carrying out the research plan laid out by the postdoc, and then all three could be on a paper together.

Thanks for the answer David! I was splitting hairs back in 2020 and didn't have a ton of perspective as an undergraduate. Though I did end up dropping the class and the "research project" turned out to be reasonably successful, in general I think sticking with the coursework is more valuable, at least in mathematics. Looking back, I wish I had placed a greater emphasis on truly understanding foundational concepts rather than rushing ahead for the sake of "appearing more competitive" in graduate admissions -- I'd be further along in my Ph.D. now had I done that back then.


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How much does choice of PhD typically matter for a future career in academia?
I have obtained multiple bachelor's degrees and a master's degree. I'm very motivated to pursue an academic career, for which obtaining a PhD seems like a necessity. However, I find it hard to decide on what kind of PhD positions I should be applying to. I often feel like a subject would be interesting enough to work on for multiple years and fits my master's degree quite well, but I really want to be moving in a different direction (specifically, I have two bachelor's, in mathematics and in computer science, and a master's in AI; after my master's I sadly have to conclude that I prefer topics on the border of computer science and mathematics rather than most of what's considered AI nowadays).
I'm having very little success in pursuing those PhD positions that look the most interesting to me. I feel like I would have an easier time if I broadened my search to include any subject I think I could keep up for 4 years, but I worry that this would 'lock me in' to this area of research.
Are my feelings justified given the way things work in academia and would it be justified to say that wanting to pursue an academic career I should not be applying to anything that straightforwardly doesn't fit that career path? Should I be happy to get into any PhD program at all, and accept that my options are rather limited? Or am I worrying needlessly, and would it not be at all unrealistic to make major lateral moves within my academic career, towards mathematics?

Be very selective about your choice of advisor, as much as you can, and then about your choice of field.
I say this because you sound like you are more interested in chasing the research frontier, rather than settling down with a stable technique and deciding how to apply it. At the frontier entire fields emerge and evaporate on the timescale of a PhD. The field you go for when you graduate might not even exist when you enrol, making it impossible for you to study a PhD in it!
That's why you should optimise for your advisor. Their friendship and guidance will be the highlight (or lowlight) of your PhD. A good advisor will mentor you in productivity, wellbeing, networking, multitasking, working with students and admin, finding jobs and grants, and putting your distinctive touch on your research style. They can open doors for you and give you objective feedback. And if you find yourself in a good and healthy research group, you will immediately have a network of future collaborators to give you a leg up.
That's pivotal in choosing where to do your PhD, and you should work as hard as you can to find a good advisor. If it means picking a field you're a little less excited about, so be it.

A metaphor: The dinosaurs were highly specialized and the "fit" for their world was superb. Hence, they grew very large and even more specialized. Then, one day, the world dramatically changed and ...
If you choose today, to specialize for the hottest possible topic today, knowing that your career will only begin in several years, say about seven, then you may find that the world has dramatically changed in the interim. People may be looking in other directions, but also, in the interim period, many (many) other people have joined that hot topic and you may find the zone completely flooded. "We'd love to hire you but we don't expect any openings for several years. Sorry."
This happened to me, actually, and I found a very difficult entry into academia, even in mathematics as a whole, because of economic conditions that changed academia and the possibility of hiring new faculty at any level. The world changed over the course of about two years from a hot hot zone to an empty wasteland (In my case, it was the loss of science funding after the US landed on the moon - a loss no one predicted.)
At some point you will need to specialize to get a doctorate, but I suggest that you don't do that too early, or, at least, that you keep open a lot of options. And, stay open to other options as they arise. And, all the better if the skills you get, even while specializing, are applicable in a wider domain.
At the moment, the STEM fields are better bets than the humanities. Both Math and CS are good choices. That can be expected (predicted) to continue. But, AI may be in a passing phase for its "heat index". Only a very small part of AI as a whole is in the news now. That might pass. The important problems there might get solved in the next few years with lots of people looking at them. Or not. It might open more. It might close. The issues with such things as ChatGPT could, perhaps, renew interest in the humanities. For myself, I'm not looking forward to the day when news is generated by amoral, brain-dead robots, whether you call them intelligent or not.
I find it wiser, for most people, to choose a path that they will enjoy following even if it doesn't necessarily lead to fame and riches at the end. If you love math, then do math, though it may lead you to a job that isn't what it might have been "if only...". But the person I describe here may not be you. Good luck then. I hope you make it.
If you try to make choices that lead to a situation that is all (Full Professor at Harvard or MIT) or nothing, then you might get lucky (and it will take luck beyond your control) or  end with nothing. Many people can build a fulfilling life teaching math or CS at a liberal arts college, and it is more likely that there will continue to be demand for that than for specific sorts of high-octane research in a narrow field.
Prediction is hard. Especially about the future.

Ideally, I would tell you to follow your passion.
Instead, I suggest that you follow your passion while also looking at what you might do when you are done.
More realistically, I would submit applications to applied fields that interest me.
I give this advice for two reasons.
First, academic jobs are hard to get.
This will give you a good backup career outside of academia.
Second, there is less competition because people have other career options outside of academia.
Thus, all the graduates from your program will not be competing for a limited number of positions.
For example, pick engineering over (pure) physics; statistics/data science/applied mathematics over pure math; fisheries science over biology; or clinical psychology over academic psychology.
Look at where the alumni from the programs you are looking at end up.
They are the best predictors of your options when you graduate from a program.

There already has been quite a bit of advice, but as an addendum to all of the other posts about the primary importance being your choice of advisor, I would say to consider what you plan on doing post-PhD. and make sure your decisions map onto something that will contribute towards that. Namely, I would consider:

Do you want to work in industry?
If you stay in academia, do you want to be more teaching-oriented or research-oriented (and from 100% in one direction and 100% in the other, what do you feel would be the best balance)?
If you stay in academia, would you want to work in a CS department or a math department?

As others mentioned, some advisors will be better at some of these than the others. If you want to be research-focused and go to an R1, you should get a rockstar advisor with a track record of getting students into R1s. If you want to be more teaching-oriented, you should have an advisor who isn't clingy and lets you do some education research on the side (and select an institution that lets PhD students teach courses). And if you want to go to industry, you should get an advisor who will be happy to let you go to industry internships each summer (and ideally a track record of students going on to industry).
However, all else being equal (ie: having two advisors who both are good for your goals without anything strong pushing you towards one or the other), I would in general suggest going for the CS degree. In general, CS is "easier" to move into industry, and also easier to get an academic job (whether it is at an R1, a PUI, or any other type of institution).
However, it is generally rare for CS degrees to be in a math department, while the other direction isn't that uncommon. So if for whatever reason you are set out on being in a math department, then the tiebreaker might go to the math option. But otherwise, the tiebreaker should be towards CS.

You are making a good point and you are asking the right questions. However, instead of answering them for you, I'd rather provide some insight based on my personal experience that I think are in line with your concerns because, after all, you are facing a very important decision and in the end, you will have to make a decision yourself for which you will be the one who will face the (hopefully pleasant) consequences.
Knowing that you have already made your mind to pursue a career in academia, I can assume that you already know that research can be hard and also,  I assume that you are already familiar with all the things that could be or are wrong/unpleasant in/with academia. To name a few, I could point out to the publish or perish atmosphere, the limited number of opportunities, high-level of competition and etc. So, in order to make your decision, I would recommend to keep these factors in mind as well. Because, starting a PhD is going to be just the beginning of the journey, and for most part of the journey, you will be on your own. Therefore, because of this, I'd suggest  to keep the following two points in mind too, among others:

Select a field/subject that you truly enjoy thinking about and working on. As I said, doing research, both during and after finishing your PhD, is going to be hard. There will be so many long hours of feeling lost, getting bad results, frustrations and making little, if any, progress. And to make things worse, for the majority of times, there will be little help from anyone else. This is mostly because, doing research means working on a problem that has not been solved before. So naturally, there are not many people who even may have heard about it. Even if you are lucky to be with a very supportive supervisor, the chances are that they will not be of great help when it comes to solving the problem except providing moral support and pointing you to some of their previous research that may be of relevance to your work. Therefore, research can be hard as it is even if you love your topic but it will become easily unbearable if you do not.
Select a field/subject that you know you can be prolific at. This point comes after the previous one but nevertheless, it is very important because, to be successful in the academia, you will need to be prolific. As I mentioned earlier, in the academia the opportunities are limited and it is still suffering from the publish or perish culture. Therefore, even if you enjoy your research a lot but do not produce results (the kind of results that academia deems acceptable), you will have a difficult time finding post-doc positions, securing a tenure-track position and receiving grants.


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Altering the data (gaussian filtering) when writing a paper
I have some results that I unfortunately had to gaussian filter due to noise. This is to simplify post-processing later on, like first derivative.
I have asked around and I've been told that if it is honestly mentioned in the paper, this is not a problem. I still have some questions:

Because of the filtering applied I would like to do a conclusion on this data without looking at the numerical values but at the trends because they are mostly non-affected by the filtering. When plotting should I then omit the x and y number 'ticks' to stress that numerical values do not make sense? (I feel like putting them would be cheating, because they are somewhat still good in my case)

Should I still show the original data in the paper?

When you publish data that you use to make an argument, it is crucial to describe how the data was obtained. This would usually also include any preprocessing or smoothing, even if it is only applied for data in plots.
Your suggestion regarding also showing unaltered data is a good idea: For regression or box plots scattering the original data over the model can be insightful.
Also, this can be very problem-dependent so I would advise to check out how researchers in your field usually handle the same kind of data and problem.

Somewhat field dependent, but in many subjects it's best practice to provide the raw data (barring ethical/legal obstructions) along with a clearly written computer script that takes the raw data as input and produces the filtered data as output.


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Using data and equations from published work
I am currently writing my thesis and in my literature review, I (multiple times) used data and equations from previously published work to create figures and tables. In the case of figures, some of them are close to the original (same (approximate) data, same equations) but are clearly different in their form with added details.
I always explicitly cite the paper's full name and the (first) authors when I use the data. But, I've heard from some colleagues that I could get in trouble for not getting copyright permissions. Some other colleagues are less worried and claim that I should not get in trouble as long as I don't completely copy (screenshot and paste) the figures.
I know that the question has been asked quite a lot here but every post seems to contradict the others, could someone clarify?

You are probably ok with the equations, though it is a bit subtle. As stated here (https://math.meta.stackexchange.com/questions/1853/copyright-of-mathematical-formulas), ideas aren't copyrightable, only creative expression. And if an idea has only one expression then even that expression isn't copyrightable. And mathematical formulae capture ideas in a standardized format.
Note that the purpose of copyright and other IP laws is to extend scholarship, not limit it, while permitting creators to benefit from the creation. That is why copyright and patent have limited terms and expire. So, ideas can be used by anyone, even when they are found in copyrighted material. And, "fair use" implies that you can use and restate unique representations of those ideas as there may be no other way to express them.
In any case, the use of ideas isn't limited by copyright.
You need to cite the source of ideas, of course, but you know that already.
The data is a different issue, but if you use it, rather than republishing it, you should, again, be fine. Cite the source, of course.

Thanks for the answer @Buffy!


text:
Can this be considered as self-plagiarism?
I started working on a paper using method A, aiming to reach conclusion B. However, method A proved to be not so great and did not yield the expected results. That's fine, and as a result, the paper's focus shifted to a comparison of method A with a much more recent method A*. Unfortunately, this change meant we couldn't reach conclusion B. Instead, the paper became more technical and consists of a comparison with some partial conclusions.
I then started another paper using only method A*, where the accuracy of the method is less of a concern. I wrote this paper reaching conclusion B and beyond. Method A is not mentioned in this paper, BUT:

The methods used are fairly similar in their conception (different techniques, same branches), but diverge later on to reach conclusion B.
Some aspects of the papers are similar (same graphs for both papers but using different methods, ~2 out of 10 graphs).

Overall, the aim and conception of the papers are vastly different (one is a technical comparison, and the other aims to be impactful for experimentalists), but I am still concerned that it might be flagged as self-plagiarism on some points.
EDIT: also something important: this meant that I had to "hold" some information that could be put in the first paper for the second one.
I have a feeling that this situation might be more common than I initially thought. What is expected in this case? I would prefer not to merge the two papers since it would add confusion and break the narrative of both of them.

Was the first paper published? Has the second paper been published already?

Assuming that the first paper has been published and the second is in preparation, it is simple enough to cite the first paper in the second, saying that the new methodology is a variation/extension of the older one is sufficient to avoid charges of plagiarism and self plagiarism.
Make the full context clear and there are no issues.
If the second paper has already been published then you might try to request an update from the editor. Even a note on their website might be a successful dodge. But, yes, using something of your own without citation is a form of self plagiarism. It potentially denies readers of the full context of ideas and their origin.
If the first paper is still in preparation then there are more possibilities.

None of the papers have been published, the first one is going to be submitted very soon, the second one is still in the work. Simply citing in this case is enough then?

Yes, citation is how you avoid all sorts of plagiarism. Make the source of ideas clear to the reader.


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Is certified translation of diploma an absolute necessary?
I will apply for a Ph.D. position, and the university is asking for an English version of my transcript record and diploma.
My diploma/transcripts records are in French and the cost of a certified translation is enormous.
Is it possible to send non-certified translations? I would, of course, precise that they can ask for a certified one if necessary

Have you tried asking the university?  I feel like the answer to your question will be far too specific to an institution to answer here.

Had to deal with French officialdom once... they spent an hour arguing that the stamp should be in the bottom right corner, not the top right. I asked if it changed the information :) and they gave up in the end...

Is it a European university?

If you look the other way round, you may find that the university may accept what is sometimes (often) accepted in France, a declaration on your honor (déclaration sur l'honneur). You basically translate yourself, and state that the content is accurate.

In my experience two different institutions in two different countries "did the job" themselves. In one case I provided a translation and declared it conform to the original, too. Europe in all cases.

Yes this is an european university, I think I will try the solution of @Buffy and then ask my previous supervisors to check if my translation is correct and sign it

Just because this brought up good memories of French co-workers: precise is not an English verb ;)

If you want a translator or proofreader, I'd be happy to help. I have done such for  SwissCube (EPFL-ESA) projects and more.

My home university (Spain) provides English versions of diploma and transcript record for a tiny administrative cost. I would be surprised if this is not a common thing universities do.

Why are the costs enormous?  Is your diploma huge?  I wouldn't expect to pay more than perhaps €200.  Clarify with the uni if they need just the main part or also all the supplements.

@gerrit It's 59 € per page and I have 13 pages (transcript of record) + the two diploma, the cost is around 700 €, I know it can sounds normal for some people but I'm not able to spend that amount of money now

That is a lot, did they confirm they need the full transcript of records translated as well?  For me the diploma itself was enough, but Eriks Klotins answer is correct too (for my current job, I needed a German translation of a diploma available in Swedish or English).

Only they can answer the question as it is their rules that apply. But I think you propose a good solution. Send them a "faithful" translation that you can prepare at little cost. Offer to send a certified copy if necessary, but mention that the cost of such a translation is high.
But you might also be able to have your university provide an English language translation or even to assure the recipient that your translation is accurate.

I'll second the recommendation to connect to your university - it may be much simpler for them to issue an official document in English (most likely you're not the first person in their history with such a need, they may have a clear process for this) than to translate the documents you have.

When I applied for Cambridge University, I translated my diploma and transcripts to English. I asked the international office of my home university to certify that my translation is correct, which they did. Cambridge University accepted the documents.

My university in Italy had a special office which provided official translations of diplomas. The quality of the translation was appalling, but it was free and "official", so good enough for phD application requirements (I provided a different document with the explanation of all unclear details)

You are entitled to receive your degree certificate in English directly from your university.

Graduates in all countries taking part in the Bologna Process have the right to receive the Diploma Supplement automatically, free of charge and in any major European language.

Source: https://ec.europa.eu/education/diploma-supplement_en

This works.well, but often comes too late. Both of my graduations (where I received the diploma + supplement) came several months after I started first my PhD, later the postdoc. But the uni had no problem to create an English letter stating I have finished my degree.

Each program has its own rules and requirements, so the only way to know is to ask them what is required exactly. It could be the case that a certified translation is only needed at a later stage, or not at all.
If your degree is from a French University and relatively recent, you should be able to request a Diploma Supplement which carries information in English about your degree. This could satisfy some requirements better than a non-certified translation (but again, you should ask).

My experience is that if a certified translation is required, it will be stated explicitly.  In other words, asking for a translation is not the same as asking for a certified translation.

If you're on good terms with someone in the admin in the French university, you could

do you own translation; follow the format of the French documents.
take the translations to the admin person, and ask them to put an "official stamp" on your translations.
Have them also stamp a few blank pages, in case you need them later.

Don't ask me how I know this.
(My experience is that French universities have lots of stamps, and that US universities (if that's where you're applying) are just looking for something that appears official.)

authors: Vladimir F Героям слава


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Evaluating potential supervisors on the basis of past graduate student results
I am lucky CS senior undergrad who has received offers from a number of good departments in the USA. I am currently going through the usual factors for evaluating departments and supervisors. In the process, I've noticed a common trend in advice: most of the advice that I've gotten has not mentioned looking at where most of the students end up (e.g. quality of the thesis, do they get post-docs, coding jobs, industry research jobs, etc). Most advice (that I have read) emphasizes, not unproductively, the adviser-student relationship and the supervisor's research interests. This observation has led me to several questions:

Is it appropriate to ask potential supervisors what most of their students end up doing and why? Is there some other way to talk about this with potential supervisors?
How much should this factor into one's decision? Obviously, a lot of what happens to me is up to me and luck, but also obviously my supervisor plays some role in this beyond helping directly with my research.
Is there an easy way to figure out this information? Anything better than googling lots of names?
Are there more qualitative ways of looking at this question besides just looking at bare results? (Given the relative scarcity of positions over time and the amount of luck involved, I am amenable to the argument that simple stats are useless here.)

Some students are better than others, are you evaluating the supervisors ability to pick or to manage?

It is better to ask the professor what you could expect to wind up doing based on the assumption of good performance and their own experience.

It's perfectly acceptable to ask a supervisor what their former students are doing now, and I think the majority of supervisors would be more than happy to discuss it. They might even give you email addresses of their old students -- I myself have been contacted many times by prospective students of my supervisor and am always happy to answer their questions.
How much you factor the information you gain into your decision is really up to you, and depends a lot on your own motivations for doing a PhD and what you want to get out of it. For example, if you want to go into industry afterwards but a supervisor tells you that all of her former students are still in academia, would that influence you away from studying under her? Or if the majority of a supervisor's students are now in industry, how do you know whether they had to leave academia because they couldn't get a postdoc or because they really wanted an industry job instead?

I worry that giving out information about former students may break some rules. It is better if the prof contacts the old students with a request to contact the requestor (after permission, of course). Cleaner.

If you are entering a doctoral program in the US direct from a bachelors, this is easier than you think. Your actual doctoral research is still a few years away since the early part of the program will be coursework leading to comprehensive (qualifying) exams. You will have a chance to meet and interact with a number of professors before you need to choose your actual dissertation advisor, though you may have a less formal academic advisor along the way.
So, you will have several chances to sit down in the office of some potential advisor and talk about both research options and where you might wind up if you work hard. They will probably be more willing to discuss other students with you if they can do it anonymously. And they can, themselves, ask former students to contact you so you can explore further.
But, because of the time lag, you will also have the option to discuss various professors with their students, to see how they are getting along. That can be equally important to know before you sign up with someone. Many questions on this site deal with poor advisor relationships.
But this assumes that you are applying to a place with a fairly large faculty and plenty of options. It is a bit harder if you think you need the information just to choose between institutions.
I suspect that most institutions would be willing to provide you with a list of recent graduates and their dissertation titles, though perhaps not with contact information. Privacy and all. But that information and google can get you more information. Many professors list their completed students along with dissertation titles on their own web sites, as I do.
And note that this applies to the US and probably not so much elsewhere.