text:
What are the academic career prospects for someone in their late 30's starting a PhD?
I'm in my late 30's and started a Ph.D. program and am wondering what my academic career prospects are. From my understanding, after the Ph.D., there are 2-3 years of postdoc, then 4-6 years of tenure-track before becoming a Prof. Is that correct?
My field is machine learning (or artificial intelligence) and I'm in the US.

Broadly speaking, can you tell us what field you are in?  In my experience this can vary pretty widely.

Updated the question with relevant information

Also Shamoon, similar to Jeff's response - what country is this you are referring to? There might be different expectaions/oppertunities relevant to your location

Updated with the country as well.

If you work hard and get extremely lucky on the job market, that's what your career could look like. In practice, you may need to spend 5+ years as a postdoc, and even then that's no guarantee of landing a tenure-track or permanent job.

@astronaut I don't believe that's true at all for data science and machine learning.  But maybe turn your response into an answer?

What are the academic career prospects for anyone!?

I think the answer here is that it depends on a lot of factors, but that you'll generally do better in the Machine Learning field than you would in many of the older, more established fields.
For starters, there's just not that many people out there with PhDs in Machine Learning.  I'm an economist, but I've spent a lot of time working around the edges of machine learning and data science.  Many of the faculty in that area have degrees in different but related fields.  Econ, stats, math, and computer science are common.
Machine learning is also an incredibly hot field right now.  Before I went back to academia I worked in applied research, and finding an experienced person with a "data scientist" title in their job history was a nightmare.  Private sector jobs are common, and the salaries are high, which pulls people away from academia.
So while being an older graduate hitting the job market may be a challenge in academia, I think the shortage of talent available in this field will offset it.  Especially if you have relevant work experience in data science, research, and/or machine learning from before now.
On a side note, unless your goal is specifically to do PhD research (i.e. are you interested in applying ML in teaching or research, or are you interested in working on the mathematical underpinnings?) in the field and earn tenure, you can accomplish a lot, even in academia, with a master's degree in this field.  Might be something to explore if you decide not to go the whole way.

Can you elaborate a bit on “you can accomplish a lot, even in academia, with a master’s degree”?

Just as university examples personally known to me, people with MAs are full-time lecturers, and program directors in this field.

Why is being an older graduate unquestionably a challenge in the academic job market?

I cannot speak for @Jeff, but I would say two practical impediments are older graduates being more likely to face two-body or other familial constraints, and general physical decline, particularly dealing with fatigue.  And that's ignoring the challenges of outright age discrimination on behalf of hiring committees.

It's good to hear others don't think age is an issue.  That hasn't matched my experience, but I edited it to say "may".

@Jeff I wasn't being rhetorical. I was asking why you think the job market would be worse for older graduates.

A slightly utopian answer, but I’ll wait for all the naysayers out there to correct me if they want to:
Your academic career prospects as a beginning graduate student in your late 30’s are the same as they would be for a beginning graduate student of any other age group.
If you are talented and work hard, you will succeed. Don’t overthink this.
In addition to that, your area is super trendy and I’m hearing about a lot of hiring activity currently going on in this and related areas (anything that falls under the label of data science). So your prospects seem generally good, both in academia and (perhaps even more so) in industry.
Good luck!

Minor quibble: If you are talented and you work hard...

It's a nice hypothesis, but it's not backed up by evidence and I would venture the guess that it's wrong.

Kinda sad that complying with the law and basic ethics would be considered utopian.

@ElizabethHenning I never mentioned law and ethics. But yes, in general I agree it would be better if I could post the same answer without feeling like I ought to qualify it as slightly utopian.

@WolfgangBangerth well, I personally know some successful academics who started their careers late. But you are correct that this is more based on personal opinion than on hard statistical data. Anyway, if you have evidence for your guess to the contrary, please share it.

@WolfgangBangerth I guess by “evidence” you mean something like “empirically, there aren't many late-starting PhDs who go on to become very successfull”. But may that not well be mere correlation? Surely, most talented researchers quickly go from undergraduate to PhD, so that would be why you don't find many of them amongst old PhDs. But this doesn't imply that any given one of those couldn't still become succesfull if they had their PhD delayed for a decade by force majeure.

Major quibble: If you are talented and you work hard and you're lucky and you have the right connections and your area of research is popular, you will succeed. Academia is extremely competitive, and there are far more people going after academia positions than there are academic positions. Believing that things will magically work out if you're talented and work hard is simply delusional, on the order of the just-world fallacy.

@DanRomik: I don't have any evidence either, just a gut feeling. Part of it may be that it's uncommon in STEM fields for people to go back to grad school after a few years elsewhere, and uncommon rarely leads to (statistically speaking) higher success rates -- some exceptions notwithstanding, of course. (It's different in other fields: In adult education and human resource development, nearly every professor had a career before academia.)

@anomaly everything you say applies equally to young researchers. Yes, academia is very competitive, everyone here knows that. But OP’s question, and my answer, was about the difference in the ability to succeed between younger and older researchers. So I stand by my remark. Your major quibble, while true, is not any more true in the context of OP’s question than it is in a generic context (and in fact it’s less true for machine learning PhDs, as I discuss in my answer), so doesn’t add much to the discussion IMHO.

@DanRomik: My objection is specifically to the comment that "If you are talented and work hard, you will succeed," which I don't think is useful advice to anyone, regardless of age, and doesn't fit the specific situation of the OP.  The career prospects for anyone in academia are bad. The career prospects for someone in industry in ML are quite good; but if the OP is interested in academia, it's possible--- though unlikely--- to jump from industry to academia in ML; in other fields, it's a total nonstarter.

@anomaly ok, as long as we’re clear that your position is that my advice is bad advice for anyone and not just for OP, I am happy. :-)

@DanRomik: Ha! :)

This is definitely utopian, and completely untrue in the real world.  If you start 15 years late, you've lost 15 years, and nothing will get those years back for you.  Instead of happening at a typical 40, tenure probably won't happen until 55.  The career prospects are absolutely different for someone starting late.  OP would be a fool to ignore those very real circumstances.  That's not to dissuade them, but it's disingenuous to pretend that it's like they can start their life over at 22 years old again.

@J... You could also have your career shortened  by cancer or numerous other events. This doesn't address the OP's question. Why would prospects be worse for an older graduate?

@ElizabethHenning Prospect = probability for future success.  If there is less future, the cumulative probability of successes goes down.  Consider OP having started their career at 22 versus 15 years later.  Do you believe on their 50th birthday that these two hypothetical futures have equal probability of achieving the same level of progress?  It doesn't even make sense.  Tenure at 40 is a reasonable goal for OP's 22 year-old self starting a new PhD.  Tenure at 40 is completely impossible for OP as it stands.  They likely won't even earn their PhD by that age.

@ElizabethHenning Again, this is not to say that this isn't the right decision for OP - it could be a brilliant move for them, but as before, it's disingenuous to ignore the fact that such a late start does have a serious impact on career progression.   It's something OP needs to consider carefully for themselves.

Your age is not the thing you should be worrying about. You only have one life and you should be working to live it as you find comfortable, pleasurable, useful, ...
The particular field you think you want to enter now should also be a secondary concern in terms of its "hotness". Whether it actually interests you and you feel it is worth pursuing is a much more important consideration. Your chosen field, whatever it is, will probably have a different "hotness index" when you finish than when you start.
You will be older in a few years whether you do the doctorate or not. If you don't, then where will you be in your life's plan. My former spouse finished a doctorate at about 40 and went on to a nice career. And, of course, a decision made now can be altered somewhere along the line as things, including your own needs, change.
Whether you need to spend time in a post-doc depends on a lot of things. Many people do now-a-days, but a lot of that is just the job market. If it takes you a few years to earn the doctorate then the market is highly likely to be different when you finish than when you start. Unfortunately you can't say whether it will be better or worse then, but that would be true if you were 20, now.
And being on the tenure track in the US (an assistant professor) is really being a professor. You just don't have quite the same job security as a tenured person, but the job is really just the same: Teaching, Research, Service in some proportion depending on the institution.
So, my best advice is to do what most appeals to your sense of self-worth.

Anecdotal evidence:

I started in my PhD program at age 40, and now have a permanent faculty position (teaching) in Electrical Engineering.
A friend was a little older than me when she started the program, and she is now an Assistant professor in computer science.

Here's what my friend and I found. As I aged, my raw ability to solve problems and memorize things has diminished. In exchange, I am really good at the following: prioritizing my time, presenting, writing, networking, taking initiative, and other important skills. Essentially, even though we're older, we still can have a good package, and other people know it.

I'd absolutely love to have a conversation with you if that's possible. Would that be okay?

By and large, ageism in academia is less pronounced than in many nonacademic fields. In some fields like pure math and theoretical physics, arguably there is a bias that young minds do the best work, but even there demonstrated research success overcomes that bias, and I believe it is less in computer science to begin with.
However, age often correlates with greater family responsibilities and less geographic and schedule flexibility. The "two-body problem", navigating the job market, is challenging enough for a couple in their 20s, starting out a life together but (usually, not always) without additional dependents, and a decent tolerance for temporary distance relationships and sleeping on lumpy couches. It then gets more difficult when a move is required (e.g. postdoc to junior tenure track) just as the family unit wants to put down roots.
Since you're about 10 years older, think about how you and those close to you will react when your academic career requires you to move to a different corner of the country when you're, say, 42. Maybe that's not a problem, or maybe your specific qualifications will be enough in demand that you can be choosy, but worth considering how much this will constrain the optimal random walk through academia your career will take.


text:
What makes a good reference letter for a junior faculty position
I'm in the process of applying to junior faculty positions (e.g. Assistant Professor). This will be my first time I ever apply for an academic position.
My direct supervisor asked me to write a first draft for my own reference letter for this application. I know that this can be considered unethical but I cannot change it. I have never before written such a letter nor read one. The examples I found online are not very helpful.
What are the elements of a good reference letter?
What distinguishes an excellent reference letter from a good one?

What country/area and field is this?

Among other things, a good reference letter for a junior faculty position (in the US) is written by someone who has read good reference letters for junior faculty positions in your field, and in particular, is written by the person whose signature appears at the end.

Country matters a lot, see e.g. https://theprofessorisin.com/2016/09/07/how-to-write-a-recommendation-letter/

@JeffE I agree with you, however, one might not have that option. I can't really "force" my busy supervisor to write it from scratch after he asked me to draft it. I consider borderline unethical for me to be anywhere near that letter, but still preferable than to waste his time.

I agree that if @JeffE 's supervisor asked them to write their own letter, they probably consider this writing task as time consuming / annoying and they might not be in the best mood if they were pushed to write the letter - and the last thing one needs is a letter written by an annoyed supervisor

@FábioDias I'm struggling to wrap my head around the idea that doing something borderline unethical might be preferable to wasting someone's time.  But my real point isn't about the ethics of writing your own letter.  Rather, it's about the effectiveness of writing your own letter.  You might explain to your "busy" supervisor that writing your own letter could do serious damage to your career, simply because you don't know how to write a good letter.

@Kimball this is for a position in Europe, I am also from Europe.

Disclaimer: I have not served on a faculty hiring committee, so this answer is not based on first-hand experience. What is expected of a recommendation letter also greatly depends on the field, country, and whether the department is teaching-focused or research-focused and how "elite" it is.
Academic recommendation letters are quite different from non-academic reference letters.
A good academic recommendation letter should be detailed. Simply saying "spore234 was my student and they were the most smartest, and hardest working student ever" is not going to cut it. In particular, it should discuss your research, its significance, and what you contributed to each project. This is particularly important if your research is collaborative -- recommendation letters can elucidate what you contributed relative to your coauthors. It should also discuss teaching and service if applicable.
That is probably why your supervisor is asking you for a draft -- you are more familiar with your work than she/he is and can thus provide more detail. Hopefully your supervisor will heavily edit your draft (please encourage her/him to do so), but you can help provide details to include in it. Don't underestimate how little your supervisor may remember about what exactly you contributed to this or that project, or even what the project was. By drafting the letter, you are providing a reminder.
Furthermore, recommendation letters sometimes include a comparison to other students. E.g., "I have advised 10 PhD students during my career and spore234's research contributions would place her in the top two. Spore234 is comparable to my former student X, who has gone on to a successful career as a now-tenured faculty at the University of Y." This is still a subjective assessment, but it's a more precise way to express an opinion than simply spouting superlatives. (I would be hesitant to draft such a paragraph about myself, but perhaps you can let your supervisor fill in the blanks.)
Of course, a recommendation letter should also include the usual pleasantries, some detail about the recommender and how they know the subject, and some forward-looking discussion of future potential.

If this is in math I think you may have misunderstood your task.  Math recommendation letters are weird.  They start and end with a paragraph or two of a normal recommendation (comparisons, opinion) and in the middle there’s 1-2 pages of detailed description of the persons research.  This will have a little bit of judgement (“I think this is their strongest paper” or “this one of the best papers in the subfield in the last five years”) but mostly about the papers not the candidate.  This is kind of a problem because it means writing letters in math is more work, but a short letter from all but the most famous people will hurt the candidate (especially a short letter from an advisor).
What you should do is write the middle section with minimal judgement and let your advisor add the judgement.  That is write a kind of annotated bibliography of your work, maybe grouped by research program starting with the work you think is the best.  Include a little judgement comparing your own paper (“this is X’s most important work”). Then your advisor will add the first and last paragraphs and more judgement.
You can even ask your advisor (again, if it’s math) “I’d be more comfortable writing an annotated bibliography, would that be enough?”
At some level this even gets formalized.  When I went up for tenure I was asked to write an annotated bibliography to be sent to my outside letter writers to decrease their workload and increase the number who will actually agree to write.

You can google and find plenty examples and tips:
https://www.google.com/search?q=writing+recommendation+letter+faculty+position
In general, a good recommendation letter, regardless whether it is academic position or postdoctoral fellowship, should be supported by evidence as much as possible. Not just a hand-waving, that he is excellent and brilliant. But he is excellent because he published in such and such journals, trained such and such students, achieved such and such accomplishments etc etc. Try to support everything. Try to convince.
For academic position (your case) state explicitly why you fit for this position (e.g., your track record, mentoring / teaching experience).
Excellent vs. good is the difference of how enthusiastic the letter sounds. "He is one of the best in..." or "you will not find better candidate for this position" will likely make a letter  excellent. But as I wrote in item 2, the letter should not be a mere hand-waving. But given that the letter does provide good factual information, the more enthusiastic the letter is the better. Put it simple: if the person who recommends you is of very high opinion of you and what he/she describes is supported by the facts (e.g., publication record, mentoring, teaching), then the letter will more likely be excellent.

Good luck!

A recommendation letter that merely regurgitates your CV with some hyperbolic adjectives is not a good recommendation letter.

Excellent vs. good is the difference of how enthusiastic the letter sounds. No. Superlatives do not make a strong recommendation. Detail is more important.

The aspect of details has been emphasized in item 2. Obviously, item 4 is valid subject to fulfilling item 2. I updated my answer for clarity,

source: Stack Exchange

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

sort: votes


text:
How can I overcome feelings of unworthiness after finding mistakes in my research?
I'm currently a PhD student suffering from extreme anxiety after finding some mistakes in my scientific paper 7 months back. I've talked to my supervisor about it and he said that those were simple errors that would not affect my conclusions... Something that triggers for my anxiety is the fact that we issued a formal statement to correct them, hence this will be forever on my record. Furthermore, I discovered a ridiculous calculation error in the estimation of one of the parameters that I'm comparing in my paper that would change the looks of three points in my graph (which has around 30 points in total) -and this wasn't corrected in the statement because the estimation I used, even though originated from a silly mistake, can still be valid depending on how you consider the system. I suffer from constant fear of people thinking that I'm a dishonest researcher and that I fabricated data, because the data that I got from a mistake looks better than the "correct" one, even though the main parameter we show in this particular figure doesn't change in either case... I'm really against dishonesty of any kind, so this is a huge deal for me.
I know that my supervisor assured me that everything was ok and that he is happy with my performance regardless of those mistakes, however I can't help but think that my record is "stained" and that I'm a bad person that does not belong in academia. I was doing pretty well so far, but then my entire life fell apart after this. I feel like I lost the ability of feeling excited about my research... I think I've failed my life goals and my moral values.
Have someone gone through something comparable in academic life? How did you cope with the constant feeling of unworthiness?
Thanks in advance...
Edit: Differently from the question pointed out as duplicate, I would also like to know how researchers view my mistakes and how can I regain my confidence to carry on with my work..

Possible duplicate of "I've somehow convinced everyone that I'm actually good at this" - how to effectively deal with Imposter Syndrome

Related: https://academia.stackexchange.com/questions/110965/how-does-an-erratum-on-ones-own-paper-affect-ones-career-as-a-researcher

@user2390246 my question is more aimed towards how I feel with my mistakes and how other researchers view them. But the thread that you shared has some good insights regarding the feeling of not being good enough. Thanks for that.

Learn from these errors and move on... Your supervisor seems ok abut them, so just don't repeat them...  I had to re-grade 150+ exams due to an error I had in my marking scheme - what I called myself I can't type here... My supervisor : "Good, glad you sorted it, students will be fine, Thanks"

Also related: https://academia.stackexchange.com/questions/68707/how-common-is-it-for-submitted-papers-to-have-minor-errors

Also related: https://academia.stackexchange.com/questions/55479/how-to-overcome-discouragement-on-finding-major-error-in-work-just-before-paper

Related: https://academia.stackexchange.com/questions/83059/how-to-deal-with-fear-of-failure-as-a-phd-student

Basically, I would browse the errors-erratum and emotional-responses tags because you will see a lot of advice on these topics.

The type of language you are using says to me that you might also benefit from your university counseling services (if available). They are experienced in these type of (common, treatable) thoughts by grad students. I also think my answer to an unrelated question applies here: https://academia.stackexchange.com/questions/95747/how-do-i-know-that-i-have-truly-lost-interest-in-research-and-should-drop-out-of/95751#95751

@Dawn Many thanks for the topics. I'm already familiar to most of them, and although the advices there do helped me along these months of uncertainty, I did not find them correlating too close to my specific problem. You see, my worst fear is of being seen as corrupt because of the data issue I had... I did not find a topic to have a similar problem so far...

@Dawn Surprisingly, I never considered attending counselling sessions in my University... That is a very good idea.

You should look at the answers to the other questions and note that they are not accused of corruption by anyone who is well-trained and acquainted with the research process. Note that almost all papers have minor errors. Corruption is about motive and secrecy. If you want to feel 100pct secure, post the updated version on website or arxiv. Then you have hidden nothing.

I'm going to suggest you attack this on three fronts:
1) As you progress as a researcher, I think you will come to realize that minor errors in published research are actually quite common. I define minor errors as those that don't affect the conclusions of the paper. See this question/answers: How common is it for submitted papers to have minor errors?
2) Understand that corruption is actually about intent and secrecy. High profile cases of corruption and ruined careers only generally happen when the researcher or the study is famous and the problem involves purposefully lying. You can easily avoid this type of situation by putting a corrected version of the paper on your website. See this question/answers: How does an Erratum on one's own paper affect one's career as a researcher?
3) Get a handle on how you think about problems like this, which are relatively common in the life you have chosen. I would suggest that there is a long way between "reasonably cautious"/"feeling embarrassed" and "extreme anxiety"/"failed my life goals and my moral values"/"bad person that does not belong in academia." I am going to strongly suggest seeking out your university counseling services, if available. See my answer to this (only somewhat related) question: How do I know that I have truly lost interest in research and should drop out of a top CS PhD program?  Or similar: How to deal with fear of failure as a PhD student?

Sure, we all want to publish error-free papers, but mistakes happen sometime, and when mistakes happen, the best you can do is be proactive to get the correct information out there (and do better next time so you don't make the same mistakes again).
I know of one particular case in my area of research that sort of matches what you are experiencing. In 1997, Derek Shaeffer, who, at the time, was a PhD student at Stanford, published a paper with his advisor, Tom Lee, in the IEEE Journal of Solid-State Circuits. Then, due to some errors in the original paper, not one, but two correction papers were published to correct the mistakes of the original paper.
Things apparently turned out OK for Derek: he is now the Director of Engineering at Apple in Silicon Valley.

all_licenses: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


text:
Are journal back covers, inside covers (i.e. not front covers) worth the cost?
In two recent submissions, after acceptance the journal contacted me to see if I was interested in submitting an image for consideration as back cover, inside back cover, or inside front cover. The cover image would need to be produced by our side, but then we additionally would have to pay the journal a fee (~$1000) for the "cost of producing the cover."
While I know front covers are generally seen as a mark of prestige (at least in my field, physics/engineering), are these additional "cover-lite" opportunities worth the cost in increased citations, views, prestige, or other intangibles?
I should stress that the journals are established and well-regarded (i.e. not predatory journals). One is explicitly a for-profit owned by Wiley, the other is a society journal.

Similar question:  https://academia.stackexchange.com/questions/117149/pay-for-journal-cover-image

upvote since the edit

I would assume your question can not be answered without a personal perspective - what makes it "worth the cost"? Someone liking it? Two more people reading your paper? An invitation as invited speaker? 2 million [insert a currency of your choice] of additional funding per year?
To be a bit more serious: I would check how the pages are included in the digital version of the journal. Most readers do not read the journal but go to the website and pick specific articles. If the images are not shown, very little people will notice them.

i get that it's probably a floating bar based on the cost of the cover, but i think the most important point for me would be substantially (>1.5x) increased citation frequency? since absolute knowledge is probably impossible (what would have the citation frequency have been without the cover?), personal perspectives from other users would still be helpful as additional data points to help make a decision.


text:
Pharmacy graduate: What are my chances of obtaining a scholarship for physics graduate studies?
Background: I am a pharmacy graduate who spent several years in business, but I always had strong passion to physics and now I want to change my career to theoretical physics. I have done many studies on my own and took recently a good collection of non-degree intermediate and advanced physics undergraduate courses. I have also shown excellent performance in those courses.
Questions: Would any respectful university (let's say in the top 100) be willing to adopt a case like me and offer me a scholarship for a master degree in physics or would they all necessitate full undergraduate certification in Physics in order to be eligible for scholarship? Some professors advised I should apply for a master degree, while some others (given my old age of 42 years) recommended that I should go straight into a specialized PhD in theoretical physics. What route should I prefer?

@Atheist I'm not sure OP is looking for a specific recommendation rather than advice about whether it is realistic in their situation to apply generally; but OP should perhaps clarify as much.

Maybe I should remove the part about "please provide names" but still really I am confused about options whether I am pursuing the right track by chasing universities for graduate scholarships or is this a waste of time

@Atheist True! I removed that part.

@henning I also removed it but not sure who removed first

@Omega Yes, we stood on each others feet for a second. :)

@henning, never mind :)

I think the first question you need to ask is whether or not you'll be accepted to a graduate program in Physics, Masters or Doctoral. There are loads of people who have stellar undergraduate and even industry experience in Physics who may beat you for a spot.

Let me pose another very important question: even if you can get a PhD do you have any chance for a reasonable job at academia.. Liberal sciences may be more forgiving, but being a 45-50 yo candidate for a tenure track job in physical sciences can be a challenge.

Yes you're wasting your time [seeking a scholarship, not studying physics].

It's not a scholarship you're aiming for, it's a teaching assistantship.  Your chances for that might be better if you apply for a PhD rather than a master's.  Make sure you have all the coursework needed, and look at similar questions on this site.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/3.0/


text:
Is it bad to apply to one PhD program with the intent of leaving for another (more prestigious) one?
I'm in my senior year of undergrad. I messed up a little bit academically this semester - not seriously, but enough to be confident I wouldn't get into a top 20 math PhD program. So I wanted to work on improving my CV for a year or two and then apply to the top 20 PhD programs (kind of like this person). I was thinking of this year applying to 2nd-tier schools for either a Master's or PhD program, then if I'm excelling really well in my first semester, applying to 1st-tier math PhD programs at the end of that semester. The main question I have is whether I should apply to the Master's or the PhD programs at 2nd-tier schools.
At first it seemed like a no-brainer to apply to the PhD programs at the 2nd-tier schools in order to receive free tuition and a stipend (which usually don't come with Master's programs). But then I was worrying if it would be looked down upon by both the university I am at and the one I am applying to if I am "quitting" one funded PhD program in order to join another. I especially felt concerned after looking at this answer, which describes a PhD as a "long-term relationship... an expensive and rare opportunity." Should I avoid applying to one PhD program with the intent of leaving for another (more prestigious) one? If so, should I just apply to Master's programs at the 2nd-tier schools this year?

You say you can't get into a top-20 PhD program, but is it feasible for you to get into a top-20 masters program? Just a thought. 1st tier masters to 1st tier PhD seems like an easier move to me than 2nd tier anything to 1st tier PhD. (But I'm not in mathematics, so I don't really know.)

@ff524 Actully, industry jobs, while also doing independent research and application writing on the side, is a much more affordable way to improve ones application and get into a good PhD program. A masters degree from a top 20 Uni is usually around 50 - 100k. Given the author's question, affordability might be an issue, so I think we should help provide the OP some affordable/unconventional options. I should probably elevate this in my asnwer, as it is a bit burried below my moral point, which I think is much more minor.

Do any top-20 math departments even offer master's degrees in pure math?

This isn't really conclusive enough to count as an answer but I would like to add to those below: 1. This can often be viewed as "poaching" and is frowned upon. I would also point out that nobody really cares about your classroom grades in a PhD, they're more a weeding process than anything, and what anybody really cares about is your research work and who your mentor is and what school you came from. So while it's possible, it is rare and not necessarily something you should/can plan for.

@ff524 Very few (if any?) top PhD programs in math offer an official terminal masters degree. Some of these programs have very high failure rates on qualifying exams (upwards of 50%). The reason often offered [unofficially] is their goal is to admit more students than they can fund to completion and then only keep the best [kicking out those who don't do well on very hard exams and giving them an MS]. Is it hence unfair to take advantage of this system, if they are taking advantage of their students, by intending to kick many of them out? Its unclear whether mid-tier math programs do this

@r2d3 it's been 2+ years....so, what did you do??

Practical standpoint: You do not know for certain you will be accepted after reapplying to the more prestigious program. I'd only go to the second tier school if you would be happy staying there until completion of the PhD. Going out into industry can equally look good on an application. Stay connected to the literature and study a bit each day while working in some research related job. This can often create a very strong application in the future (probably tells a much more interesting story in a personal statement than a masters from a second tier school).
Dan111 says that schools frown upon students leaving (of course this is true, just as a company would frown on you quitting to join another company). However, I think he is overstating the degree to which schools will block you from doing this. Many schools do in fact let you leave with a masters degree after 1-2 years of PhD work (usually after a qualifying or advancement to candidacy exam). Now of course some don't. This is something you should check. It's usually buried somewhere in the departments website (they don't exactly want to advertise it, because as Dan111 said they don’t want to encourage it). A good place to look for it is in the "degree requirements" or "qualifying exams" or "degree timeline" etc. sections. There is actually a good reason for the school to include this information. Strong (but risk adverse) students like to know that if they try their hardest but find out that the PhD just isn’t for them like to know that there is a fall back such that they don’t lose too much opportunity cost.
Moral standpoint: There will be a lot of disagreement here. Many academics will say this is morally wrong. Their argument usually goes something like "You owe it to the school that accepted you to finish there because they are funding you and subsidizing your tuition." However, in my opinion this is not a completely fair way of looking at it. Based on this logic, a professor who initially got hired at a second tier University, who  planned on using this university as a stepping stone, and then published many prestigious papers due to this hard work and motivation, should also not leave the University that first hired them. The first university made a similar investment in that professor, that the University would make in a student, (arguably a much more costly investment). Students should do what's right for them, and an advisor at a lower tier university should help their student make the decision that is in the student's best interest (this will probably, more often than not, be staying, but when this isn't the case, a good advisor lets their student go).

Your example with the professor who leaves the second tier university seems like a false equivalence to me. I don't think most people consider it problematic to leave a PhD program if your circumstances change, or if you realize after starting that a PhD is not for you, etc. The moral problem is accepting an offer and leading the department to believe that you plan to finish a PhD there when you actually do not intend to - depending on how sure you are at the time of acceptance that you're going to leave, it can be deceitful.

@ff524 I think I am being misunderstood, the example here is that the OP is going to work really hard and elevate themself, with the intention to apply to a more prestigous school. It is exactly the same as a professor working very hard at a tier 2 school with the intention of getting a job at better school. It is equally decietfull, yet many still wouldn't call this wrong. I editted the example to make it more clear that the professor is intentionally working to this end. Thank you for pointing out the lack of clarity.

WetLabStudent, I think both you and @ff524 have good points. The analogy can be very good or not so good, depending on the similarity in the chances of the professor, respectively student, to get a job/admission at the better school within a couple of years. In the professor's example, I find it a bit far-fetched to say the prof has an "intention" of getting a job at a better school. The extent to which "intention" can exert much control over the outcome here is pretty limited. That's probably also true (statistically speaking) of the student's case, although maybe not for the OP's case.

... So, to summarize, I think both the prof and student examples (but the student a bit more IMO) inhabit a murky gray ethical area where an action is being contemplated that will only probabilistically involve unethical consequences, with a likelihood that is hard to estimate. Considering the fact that all incoming PhD students cannot know with certainty that they will want to complete their PhD's, arguably the current example is not so different. But "arguably" is the key word here - I am sure a fair number of people will view this as unethical, and probably with some good reason.

Their argument usually goes something like "You owe it to the school that accepted you to finish there because they are funding you and subsidizing your tuition." — No, you don't; students do not have a moral obligation to finish their degrees.  But all but the saintliest student will hide their intention to transfer up when they apply, which means they would be accepted under false pretenses.  It's the prior intention to transfer that causes the problem, not the transfer itself.

Just to add a point that hasn't been emphasized yet:
A major aid to getting accepted into a lot of programs (after initially getting 'your foot in the door' with transcripts or GRE scores) is having strong recommendation letters.
If you moved to a new program (be it masters or phd) for a year, you will likely run into some major issues with letters. First of all, your goal of using the position as a demonstration of improvement will almost certainly not be reflected in a recommendation letter from a new advisor or instructor. Less than a year is just not enough time  to allow them to see you accomplish enough to write a convincingly strong letter. Not to mention, they will still barely know you.
Secondly, you'd essentially be burning bridges at your stepping stone program by leaving under those pretenses (especially if you're 'snubbing' a phd program like you've described) . As a result,  you will likely struggle finding someone to write you a strong letter or offering to write you a letter at all. Additionally, the research/academic  community is smaller than you think, and burning bridges can have a strong adverse affect on your career (read: people talk and upsetting the wrong folks can get you blacklisted).
Thirdly , if you avoided these above issues by just seeking letter writers from your undergrad or unrelated institutions, it will raise red flags to new programs. Avoiding a rec letter from your current institution would actually raise questions about your efficacy in your new institution, thus  negating the appearance of improvement you're looking  for  (at least as reflected in a rec letter).
Most of this applies to the bailing on a phd program scenario, but depending on the masters program you might fare equally poorly by quitting on them. No one, including large University programs, likes to be used.
Overall, I'd say your abandon ship idea is a poor one. No one will see  enough of your abilities your first year to allow you to demonstrate improvement (bc remember, you apply to new programs after less than 6 months in your new school!). In the end, apply to some masters programs with the intent to finish them and get ready for the long-haul decade-long trip to the start of your career! Though, apply to one or two of the PhD programs you're interested in, call up someone in the department at those schools and get them to know you (as  a person and not just a name on a paper) and wish for the best!

A lot of these low-ranking programs admit people to PhD programs in order to staff their large lecture courses with TAs. This is often the primary reason the university supports you, especially in the humanities. They are well aware of your dim academic job prospects with a a degree from their institution. Chances are you did not get rejected from a top-ranked school because of grades, but because your application materials did not suggest you had a firm sense of direction in your research. If you discover after a year in a low-ranked program what it is you want to do and can compose much better materials, then reach out to the people that wrote you the letters the first time around and see if they would support your effort in reapplying to top programs. Do not feel guilty. This your career at stake and you don't want to be flushed out a low-ranked program after years of hard work and excessive TAing only to find that no universities want to hire graduates from your program.

I want to emphasize a point that was made in some comments and as a secondary point in some answers. The question asks about going to a "2nd tier" program for one semester, then applying immediately to a "top 20" math PhD program.  Ignoring any ethical concerns:
Attending a master's or PhD program for one semester does not seem likely to strengthen your vita very much when you apply to top PhD programs.
Top 20 math PhD programs are extremely selective. While it might be possible to overcome a poor undergraduate record and earn admission to these programs, it is likely to take more than one semester of classes. By the time you apply, in the fall of your first year at the new program, the professors there will have known you for about 4 months. There is not really enough time to earn the kind of recommendation letter you are looking for, if you want to not only attend a top 20 program but do so after a poor undergraduate record. Moreover, you will have, at best, one set of grades from the new program (from that fall semester).
It seems to me that, if you want to end up at a top-20 PhD program, a more viable plan may be apply to the best master's program that you can get into - perhaps even at a top-20 program, if they accept students directly into a master's program - and then finish the masters and be absolutely excellent while you do it. That will give you a longer record of success at the graduate level, and time to develop very strong letters of recommendation.

A prof with enough clout to be leaving for a top tier university from a second tier one, gives the latter something for the time they hired them: good work, grants, reputation. It is clear that, when they hire him, they may or may not retain him.
A PhD, on the other hand, is still a position where, in general, there is some lead-in period, and the main results are expected only towards the end; starting with an intention to break off is clearly unethical in terms of the investment by university and supervised. Furthermore, it is limited in time (to 3 or 4 years, depending), so the student can be reasonably expected to commit for this limited period with the intention to complete. Failure to complete can be a markdown for universities, so it's a doubly penalising situation for the uni.
The only real argument when a PhD transfer should happen is if the student decides that the topic or the supervision didn't work out for them. This can happen, and, in this case, a transfer is legitimate. But it should be the exception, and not the original intention.

A PhD student that will successfully transfer to a top 10 University will have certainly given back to the first university through publications and reputation. I highly doubt that a PhD student from a lower university could transfer to say Harvard, without doing exceptional work at the lower level university.

@WetLabStudent I find rather unlikely that a student after 1 year will leave a bunch of brilliant results published, instead of just a big pile of mess.

Applying for a Master's Degree makes sense.  Applying for a Ph.D. degree with the intention of switching does not.
My only advice that differs much from what others have said would be when you apply for Master's, apply to some first tier schools.  There is much less risk involved with accepting a Master's student that doesn't work out than a Ph.D. student, so you might find some surprising offers.  However, see my answer HERE about Master's program quality.

I know of many people who "intended" to drop the PhD for a masters when applying and then infact did complete the PhD! Sure if you are 100% sure you will drop [or switch programs], that is dishonest. However, what percent certainty that you will switch makes it ethical, I think that is unclear.

all_licenses: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/3.0/


text:
Communication with a student pursuing the bachelor's thesis
As a part-time lecturer, this is the first time that I have been assigned to drive a bachelor's thesis.
I try to convey to them my interest in their project. And, I also recommend them to be in contact with me.
A student asked me for my personal phone number, and I gave it back.
We have exchanged a few WhatsApp messages, always, fully work-related. Nevertheless, I have serious doubts about if it is professional enough to use this means of communication. And if I should avoid this in the future.

I would really advise against this in general.

Giving your personal phone number to a Bachelor's Thesis student will allow the student to contact you at inconvenient hours or during your free time. This is the main reason why people do not give their private phone numbers at work (neither to students nor to their boss).
If you are fine with this, there is probably not going to be any other major consequence. The student is not going to think less of you (on the contrary, they will appreciate it), and others (colleagues, boss...) will probably be indifferent. In the end, it is your choice how you want to communicate with your students.

Agreed. You get to choose how you communicate with students. If WhatsApp is convenient for you, by all means use it. However, you do not need to give a student your number, ever, even if they ask for it. One suggestion to follow up on the point made by @wimi, before you give a student your number you should be clear with them what level of availability they should expect. I would tell them that you will not answer texts or messages outside of working hours.

I agree too. On an unrelated note: I hope you are being properly compensated for this work if it's outside what is usually expected of a part time lecturer at your school.

I would recommend that you avoid this in the future. At my institution it's officially highly frowned upon -- in fact, the school strongly leans on us to only have contact through the official school email accounts, so that if disputes arise (harassment claims?) they can track down and look at all the contacts.
To me, the main thing is that it potentially impinges on your personal and free time which must be defended at all costs to avoid burnout. Make sure you're tracking your actual time spent on tasks carefully so that doesn't spiral out of control. I recommend that you give clear contact expectations to any students you have contact with (e.g., "I usually respond to email within one business day.").

If you're in the US, it might also be a FERPA violation because written communication with the student is part of the student's educational records.


text:
Ethics of the mention of Nazi weaponry for a computational physics task
A colleague of mine and me are organizing a 3-day preparation course for undergrad students to prepare them for their upcoming lecture about computational physics (the course in about 1.5 months).
This course takes place at a German university.
The third day of this course will involve a "do-it-yourself-day" where the students can choose between different projects to do.
We are in the process of creating these projects.
Usually, we are creating them independently of each other and uploading them to our course-site and inform each other we added a new project. Sometimes we'll also talk about them to discuss specific tasks etc.
So I made a project to calculate the trajectory of an artillery from the WWII.
It's perfect for an academic task because it has a high velocity and goes high into the atmosphere so the students must do the calculation with air friction and height effects like decreasing temperature and pressure.
I almost completed this project to be ready to be uploaded but my colleague has moral concerns since its a weapon and was used by the Nazis.
I don't have that many concerns since its a purely academic approach to this and it's not like we are calculating how much damage it can do. Also, the approaches used to solve this task are not so unlike the approach to get a space shuttle again safe to Earth (which is much more complicated though since I didn't choose it) for example.
Q: Are his concerns justified and should I abandon this project?
(I'd also be glad to new proposals, it should be fast and go high to use friction and height effect.)

Can you not alter the project to describe some generic rocket, rather than a specific weapon?

I'm of mind that it's ridiculous to have "moral" concerns over a historical projectile just because it was used by the bad guys. What is the actual morality that he is concerned with? Are you planning on using your results to build yourself a bigger and badder weapon? Morality doesn't lie with the math/physics itself but with what you do with it.

Where would this stop? So anything used by nazis (including airplanes, trucks, bullets etc) should not be even mentioned anywhere?

Is there any reason why you want to use that one particular projectile and not, say, a modern one?

You have to know about the works of the bad guys, even if you want to avoid any fighting. Work that into the intruductory text for the assignment.

So i accepted the answer below and my colleague and I came to a consensus to alter the task to make it more generic. But thanks to everyone here. Im glad to know I didn't do something unbelievably wrong. @PsySp I saw something similar in the past so I adopted it. I don't really know something about weapons, especially modern ones so I just rolled with it.

Much of radiation oncology, medical imaging, medical physics/dosimetry, etc is based on the extrapolated effects of radiation on humans after Hiroshima/Nagisaki bombings.  The bombs are a moral grey area to say the least, but no one suggests we cease all radiation therapy/ medical imaging.

@Hobbes: True, but irrelevant, since this is not academic research.  This is an assignment in computational physics -- i.e., the students are not going to learn anything practical about designing weapons: it's just a setting for a physics problem.

@JulienKluge I think you did well by removing the mention to a specific armament piece since it is unnecessary to describe the problem and could make some people, especially in Germany, uncomfortable. The answer you accepted only addresses the ethical in that issue, and I agree with most of it, but the dominant component here seem to be social/cultural.

It is not morality, it is about considerate about potentially sensitive topics. In Japan, you don't make example calculations about the Hiroshima bomb, in Israel you don't make diy gas chambers, in Germany don't make nazi jokes or similar, just to avoid awkward situations.

@PeteL.Clark, I'll rephrase, we still hand out assignments on radiation physics/ dosimetry that have their foundation in the bombings.  Students learn how radiation can heal/hurt and how to build devices to heal/hurt with radiation.

@Hobbes: true and more relevant, but still not an argument in favor of this particular case: in your example, the actual academic knowledge was gained from the real world events.  In this case, the real world aspect is an illustration of much more general scientific principles.  The OP writes "It's perfect for an academic task because it has a high velocity and goes high into the atmosphere so the students must do the calculation with air friction and height effects like decreasing temperature and pressure." OK, but there are a lot of things besides Nazi artillery that meet those criteria!

Indeed the OP makes this clear when he writes: "I'd also be glad to new proposals, it should be fast and go high to use friction and height effect."  Finally, in a comment above, the OP writes: " I don't really know something about weapons, especially modern ones," making clear that there is no specific technical knowledge being conveyed.

No, his concerns are not valid and you should not abandon the project, which has scientific value as well as a small amount of historical added value that I think is of independent interest. There is nothing about the representations of Nazis or Nazi history in this project that would make it any different from mentioning the Nazis anywhere else, e.g., in a movie or work of literature, or in the Wikipedia article you linked to about Nazi weaponry for that matter. So your colleague's logic would imply that one must never discuss anything related to the Nazis, which is clearly absurd and false. Of course, an important piece of context is that you are in Germany, which leads me to speculate that your colleague has indeed been conditioned by his upbringing to shy away from discussions of Nazism. Perhaps he had family members who were involved in the war and his parents discouraged him from discussing Nazi history, or he absorbed this sentiment at school or through the media; who knows? But it is pretty clear that his sensitivity about these things has reached rather exaggerated and irrational levels.
Incidentally, warfare in general and World War II in particular have driven a large amount of development of new scientific and technological ideas. Personally I find it fascinating to read about this interaction between science and world affairs, including reading about scientific work the "bad guys" did, and fail to see how merely studying historical events can carry any moral or ethical meaning or can be anything other than a good thing.

On the historical note: one of my favourites is the German tank problem: estimating the number of tanks based on the serial numbers of the destroyed or captured tanks.

Yes, the context matters, but in a different way than you suggest. Rather than being "conditioned by his upbringing to shy away from discussions of Nazism" the colleague might also have learned to be suspicious about -- or learned to take into account that others could be suspicious about -- a certain fascination with nazi memorabilia and the military, which in Germany can signal a revisionist attitude.

@henning good point.

Now that I’m reading this a long time later, I must admit that I find the arguments raised by people objecting to my analysis, especially @PeteL.Clark, pretty compelling. I still think that what I wrote is logically correct, but I can also see that there is a cultural component to this that I didn’t sufficiently take into account at the time. So my revised opinion is that it is best to avoid using Nazi weaponry as the basis for a physics project in a German university, unless there are really compelling reasons that make that particular piece of weaponry uniquely relevant to the discussion.

German citizen here. My feeling is that your example is not at all outrageous or morally problematic per se; but it might lead to some raised eyebrows in the given setting (a German university) and for quite understandable reasons.
You use a German WW II weapon simply to illustrate some computational problem. That is, you don't make any evaluative statement about nazism, German WW II aggression or even warfare and weapons in general. Neither is your problem about making weapons more effective, which could then be seen as an implicit value judgement.
It is also, fortunately, no longer "taboo" to discuss the nazi past. German political culture has overcome the lead-heavy immediate post-war period, in which the memory of the atrocities that Germans had committed was actively repressed together with everything that reminded of them. To be sure, there is a (perhaps large) minority that prefers to rationalize, relativize or even idealize the nazi regime and its crimes. Some of these guys have a strange fascination for WW II memorabilia and nazi paraphernalia. Here it can be hard to draw the line between hobby historians and hobby revisionists.
So as your student I would wonder: Of all the examples that you could have chosen, why this particular one? If the course was about military history or WW II, the choice of example would make immediate sense. But since it isn't, your example seems quite arbitrary. (Wouldn't other projectiles or objects have similar physical properties?) This would probably lead me to conclude that the example is "just and example", but I couldn't quite help to speculate a bit about your motivation and perhaps your historical-political attitude. Less so, however, if you are not a German.

"So as your student I would wonder: Of all the examples that you could have chosen, why this particular one?" This is in my view (which is also from a German perspective) the key sentence in this answer.

@henning: Thanks for this answer.  It amplifies on the perspective I presented in some comments, but as it comes from a German citizen, is much more trustworthy and valuable.

@PeteL.Clark Sure. You plow example is a very good point.

@Schmuddi, I was wondering the same thing, but then I read the description of the weapon. https://en.wikipedia.org/wiki/Schwerer_Gustav  "It was the largest-calibre rifled weapon ever used in combat, the heaviest mobile artillery piece ever built in terms of overall weight, and fired the heaviest shells of any artillery piece." Also, the bit of history about being designed to destroy the Maginot line, but that it wasn't deployed in time, is also interesting. For the record, I'm not gun nut, nor am I a history buff, but I still found this very interesting.

"So as your student I would wonder: Of all the examples that you could have chosen, why this particular one?" This reminds me of the joke (which I read recently in the excellent autobiography "Adventures of a Mathematician by Stanislaw Ulam) about the Jewish mother who gave her son two ties for his birthday. The next time she saw him he was wearing one of them, so she asked in frustration "what, you didn't like the other tie?"

@DanRomik Ha, nice joke! I agree this suspicion is irrational or exaggerated to some extent, but I guess culture often works that way. Hence my conclusion that I "couldn't help to speculate", although per se the nazi weapon example is not immoral.

I don't see anything immoral about it. What if the weapon was used by Americans? It's an aspect of history and if the weapon has an interesting application in your course, why not use it?
Personal feelings aside, if you're worried about stepping on your colleague's toes, you could just describe it as a generic projectile and not mention its historical significance so you can still use it in your course material. I don't know the logistics of your project, but why be specific about the weapon?

As a teacher I try and stay away from controversial topics unless it is related to a learning outcome. There is no way to teach about evolution and geology without running counter to creationism/intelligent design. In your case, one could argue that using a historically accurate weapon enhances learning about the trajectory of a projectile. The issue then becomes what is the least controversial weapon to use as an example without impacting your ability to deliver the learning objective.
In Germany, any WWII weapon is going to be controversial. If you choose a weapon used by the Allied powers, you are using something that was used to attack their country. Choosing an Axis powers weapon has the obvious issue of being perceived as "pro Nazi". Without knowing much about historical weaponry or physics, maybe a weapon that wasn't used in WWII would work (there are an awful lot of non WWII era Howitzers).

In Germany, any WWII weapon is going to be controversial. That statement is itself controversial. If it is "controversial" to mention a historical fact in a completely neutral context having to do with a math problem, then pretty much anything at all is "controversial".

Wiping out a "shameful" part of the history is also a controversial decision (similar to censorship, cf. Ministry of Truth).

@DmitrySavostyanov I didn't propose to wipe anything out. I do however believe in censoring myself in the workplace.

@DanRomik I am not sure I would go that far, but sure. The point of my answer was that to the extent that I can I make the same point, with the same level of clarity, in the same amount of time, I choose the option that I think is likely to be the least offensive.

@StrongBad ok, but there is a real cost to bending over backwards not to offend people. For example, an abstract math project about an unnamed piece of artillery is a lot less interesting than the same project involving a real-life, historical piece of World War II weaponry. Because of OP and his colleague's fear about offending people, they are going to water down the content of their course to the point that it will be less compelling. As a result, someone who might have been captivated by the real-world usefulness of math might be less engaged and choose a non-math career instead. ...

... And all of that would happen because of an irrational fear that any mention of the Nazis is "controversial".

@DanRomik No! I am not saying don't use a real example. I am suggesting that the FH70 might be a better example since it is post WII, but still German, assuming it doesn't fundamentally change the physics.

I think there is something quite defensible in this answer that is not being expressed in the best possible away.  @Dan Romik is right that shying away from controversy is antithetical to academic sensibilities.  However, it is also not in the spirit of academia to court controversy for its own sake.  Could there really be any pedagogical loss in using an FH70 rather than a Nazi-era weapon?  I don't see how....

...Moreover, when you say "Nazi Germany" then of course you are going to set off certain thoughts and emotions in the listener.  If Nazi Germany is what you're studying or has any inherent connection to what you're studying: definitely you need to say it anyway and push past these thoughts and emotions.  But if there's no connection: isn't it a bit distracting?

Finally, I want to point out that "This course takes place at a German university."  I think that is of some significance, in a way that for a (say) American to understand requires some reflection and imagination.  The equivalent for a US audience would be something like a problem optimizing the design of a human-pulled plow on an antebellum plantation: that's a lot of baggage to put on a physics problem.

@PeteL.Clark I think your slavery analogy is seriously flawed. To my knowledge, there isn't any interesting mathematics associated with slavery. Moreover, the Nazi-era weaponry being discussed is nothing more than a piece of weaponry used in warfare. Discussing the science behind it is no more offensive because of the fact that it was developed by the Nazis than it would be if it were developed by any other "benevolent" warfaring regime. By contrast, a hypothetical slavery-related technology would be offensive because of the slavery connection, since there are no "benevolent" forms of slavery.

@Pete your comment defending StrongBad's answer is very eloquent. Nonetheless, I cannot agree that it makes sense to replace the Nazi weaponry by something else to avoid "controversy", since I don't agree that there is any controversy here. Is the Wikipedia article linked by OP "controversial"? No, it is simply an article about a topic in the history of weapons technology. Similarly, OP's project described in the question is neither "courting controversy for its own sake" as you said, nor would abandoning it be a form of "shying away from controversy" (except of a purely imaginary kind).

"If you choose a weapon used by the Allied powers, you are using something that was used to attack their country." - for the record, as a present-day German, I wholeheartedly reject the notion that Nazi Germany is "my country". The regime known as Nazi Germany would be as much an enemy of nowadays' Federal Republic of Germany as it was to the Allied Powers.

@Dan: Let me just say that I didn't use the word "offensive," and I don't think that discussing science/engineering issues related to Nazi Germany is offensive or immoral in any way.  But it is potentially distracting, which is a negative to be weighed against the positives.  If there is any clear pedagogical positive to be gained from using these weapons specifically, it would be justifiable to do this (and good to explain why).  By the way: a small percentage of students will not be thrilled to be studying weaponry of any kind as a physics project.

It's a good applied physics example, but I don't get driving the WW2 weapon IN GERMANY.  The Germans have a hard time with the Nazi past.  Not happy with having been the bad guys.  But also not happy about having it rubbed in their faces all the time.
Obviously you picked the German weapon because you thought it was relevant. But you don't understand some of the issues in that country.  So you're actually being sort of clueless when you think you are being relevant.
I assume that you main target is to teach the topic.  Not to get snarled up in other kerfuffles.  So give it a rest.  Your colleague is being smart here to warn you.


text:
Is it okay to resend an email to a journal asking for the status of a submitted manuscript?
This question is related to the question asked here: Is it okay to inquire about the status of a paper when the online submission system shows no update three months after submission?.
Around 4 months ago, I submitted a paper to a Math journal for peer-review through an online submission system. The same day I received in my e-mail an acknowledgement message saying that the paper had been received.
The status of the paper on the online submission system is still "Manuscript submitted", and the paper has not been assigned to an editor yet.
One month ago, I sent a polite email asking for the status of the paper, but I got no response.
Should I send a second email in the regular way (that is to say, not using the journal's online system)?
Is it possible that things go slower during this time of the year (due to holidays or something)?

I don't really see a difference here to your first question. You waited about 3 month without a response. @MadJack that might not be too relevant here as it is not even in review. The review process could take a while, the assignment of an editor is usually much faster. I don't know exact times for Mathematics, but everything longer than about 1 month shouldn't be normal.

@TheAlmightyBob Good point. I'll remove the link.

Definitely send emails until you get a response.  I think you are one of many victims of the relatively new -- not yet so functional -- online submission systems that permeate our field.

Yes, you should definitely send another polite email. You could also write directly to the editor, since your situation sounds fairly unreasonable. You deserve some sort of response to your submission. I would consider withdrawing the paper and submitting it elsewhere if you don't get a response.


text:
Should I choose the same editor for two papers?
If I submit two papers in the same area at the same time to the same journal, and the journal allows me to choose from a list of editors, should I choose the same editor or different editors? What are the pros and cons of each way?

If the two papers are closely related -- e.g. if one of them cites the other in an important way -- then it seems logical to try to have them processed together, even by the same referee.  In that case the same editor makes things more efficient.  If the papers are not closely related: do you really need to submit both to the same journal at the same time?  Though I can't think of a critical reason for this, most people like to spread things around more than this.

@PeteL.Clark Re your last sentence: That's certainly true in math, but I believe in many fields there may only be a couple of suitable journals for a given article.  Because of this, the answer may depend on the field (if the papers are not interrelated).

I've have multiple papers under review at the same time in the same journal for various reasons (e.g., special issues, highly preferred venue, standard community venue).

When the papers were linked, we made sure to request the same editor---otherwise, you're just making life more difficult for the editors because the editors of the two papers will have to coordinate in any case.
When the papers were not linked (and I've had utterly unrelated papers simultaneously under review, since they came from different collaborations), we selected an appropriate editor to request independently, which might or might not turn out to be the same.

The key principle here is to remember that your selection of an editor is only your personal recommendation to the journal.  Just like a statement preferred reviewers, the journal has no particular compulsion to abide by your selection. If they think a different editorial distribution makes sense, they will assign it that way instead.
Thus: don't handicap a paper unnecessarily by recommending a suboptimal choice of editor.


text:
Is it ethical to post (part of) my research question on the internet?
I do research in math. A lot of times, I get stuck. I wonder if it's considered ethical to post questions on which I get stuck on internet sites, for example Math Overflow or Math Stackexchange.
If the question is just a small step or something already well-known, it is probably a waste of time to reinvent the wheel myself (and I don't get credit for doing so.) On the other hand, if it turns out to be a crucial step, then I could potentially be dishonest if someone on the internet solves it and I claim it's my own work. Sometimes it's not easy to tell beforehand which case the question will fall into.

It seems to me the only unethical thing would be claiming you did it when you didn't. If it's actually hard, I doubt anyone on MO is going to just dash off an answer, but they might be able to point you at relevant work. This seems fundamentally not very different from a literature search.

@zeldredge: There are definitely things that are "actually hard" that nevertheless the right MO contributor might be able to dash off.  But this is not inherently problematic: if you get signficant help on MO, you should acknowledge just as you would if it came from elsewhere.  If the help is significant enough, the appropriate response may be to offer coauthorship.  So one should not ask for help if that eventuality is not a desirable one.  But in most cases: why not?

Reinventing the wheel could be a major development if you do it in a way no one else has.  That being said, all mathematicians waste their time pointlessly reinventing wheels, or doing other stupid things that we might be too embarrassed to actually own up to.  That's most of the research process, I'd say.  The papers that get written are just the tiny fraction of work that wasn't garbage.  Getting through that faster is exactly why we talk to each other, or coauthor papers, or talk to people on the internet (a subcase of talking to each other).

@PeteL.Clark What if user A publishes a problem and user B from MO solves it and publishes it as a single author (author B) publication?  If B does not include A in the publication, it is wrong because B got to know about the problem because of A. If B includes A in the paper, it can still be wrong because A did not contribute enough to the solution.
My best guess would be that B should think and make A coauthor or mention in acknowledgment according to the amount of work A has done. But what is the guarantee that B is a righteous person?

Posting questions is ethical, the issue is with appropriate credit and potential collaboration. I would say that  most answers will be directions to published work that covers your question, if the question is about problems already solved. In this case, you just have to reference the books or papers that you used.
If it turns out to be an open question, it probably won't be answered in a simple post on internet sites. In this case, in the best scenario, you could find people that will collaborate with you in a more permanent way, till you both solve the issue and, eventually, publish a paper.

Of course, that part of the question which turns out to have been previously solved doesn't count as part of your new research. But that would be equally true if you found it in a book or journal.

Though in the first case, it may be nice to also give an acknowledgement to the people who pointed you to the right references.

If the question you post to math.stackexchange involves your personal education, and specifically you are seeking help to overcome an error you are encountering applying a specific method to a specific problem, then there is no need to acknowledge or give attribution.
If, instead, you post questions that are directly related to your research question and essential to your research progress, then you have an ethical obligation to provide notice and attribution in the body of your published research.  This could be done in footnotes/endnotes associated with those specific steps, or in an Acknowledgements section.  For example, in a footnote you might say:

"This solution [formulation/approximation/step...] comes from 'ysk', a member of the math.stackexchange online community, in response to my posted question (https://math.stackexchange.com/myquestion/answered). I am grateful for his/her assistance."

EDIT: added URL to footnote. However, since some communities are not publicly available and those that are may not have permanent URLs for posts, this may or may not be appropriate for published academic articles.
While some people might consider this to be ethical "overkill", I believe that it is better to err in the direction of giving more credit to others rather than less.  Anything that appears in our paper that is not yours originally deserves to be credited to the original author.  Mostly this is done through citations, but there are times when other methods are needed.

I agree that it is not unethical to ask for help in online communities, but that it would be unethical not to properly attribute the information. There are related threads on this site (this and that). They explain how to cite a MathOverflow post.

@henning I have updated my answer to include the (optional) URL to the question and answers.  I have explained why this is optional.

No, the URL is not optional.


text:
Authorship for insightful suggestion during a talk?
I gave a talk a few months ago, and one member of the audience made a particularly insightful suggestion. My advisor and I are still working on this topic, and it seems like our research is heading in a direction where his suggestion may end up being incorporated into our work in a fairly significant way. We haven't spoken to him about this work since, but how should we deal with this? Should he be an author, or only mentioned in the acknowledgments?

What does your adviser think? Just suggesting an idea probably warrants a mention in the acknowledgements. If you want, you can always contact them to see if they would like to collaborate more on the paper.

You should at least acknowledge the person who made the suggestion.
I would also ask this person if they would be interested in working with you to coauthor the paper.  If the person who made the suggestion is very senior or doesn't work in your area, then they'll likely be happy with the acknowledgement.
However, a suggestion like this, without any further involvement in the writing of the paper isn't by itself sufficient to merit coauthorship under guidelines such as the ICMJE guidelines for authorship.

At present, I don't think merely having a helpful suggestion, even if it launches a fairly significant line of inquiry, merits a paper authorship. They haven't, after all, actually worked on the paper.
This kind of thing is exactly what the acknowledgements section is for. And in several cases, I have thanked colleagues for contributions that were the result of something like this - a helpful comment, a directed question, a conversation over drinks, etc.
It may however be worth reaching out to them to see if they would like to work on the paper with you, if it is not yet fully finished. After all, they were extremely helpful once, they may very well be so again.


text:
How to pitch a research idea to a professor as an undergraduate?
I have an idea which I'd like to work on with a professor at my university. In my initial email would it be arrogant to ask if he's interested in working with me on this particular topic (he's published some papers on closely related topics), or should I just say that I'm interested in generally doing research with him? I really do want to work on this particular idea but also don't want to come across as trying to tell him what to do.

Make sure you include PDFs of your CV and academic transcript in your initial email. Many professors will always want to see them before deciding whether to work with someone. I know I do.

Having recognized your handle from an earlier question, it's also worth noting that you've worked on research projects before.

A small point about language: in the U.S., in mathematics, it might be more tactful and less presumptious (also) to not ask about "work with me", but "advise me on" [the project you propose]. At least to my perception (=old guy) this leaves many more options for the precise relationship. E.g., experienced people can often and easily give helpful advice without really actively participating. At the same time, depending..., they might find interest in doing so. Or, at the same time, they might see that it's better to let you do it yourself... etc.

I think that most professors like to hear about ideas that their students have to work with them.
I would simply send him an email telling him that you have an idea that you want to work on, and that you think he might be interested in.
Probably best if you talk about it face to face as most professors are too busy to read long emails.
Some thing like this:

Dear Prof X
I am contacting you as I recently had an idea for a research project
  on topic x.
I really enjoyed working with/learning from you on x [something he
  did, e.g., a class], and I am very interested in x [something he
  researches].
With that considered I was wondering if you would be interested in
  working with me on this project?
If you would like to know more, I would love to have a meeting at a
  time that is convenient for you.
Kindest regards,
[Your name]

Would you recommend at some level having a research proposal of sorts outlined? At least started, so the process isn't simply "I want to work with you on this idea," but "I actually have a proposed direction for the project." Probably a no-no to send this on the first email, but in communication at some point.

Good question. I think that having a literature review done would be a plus, but that any attempt to set how the project will proceed (which might be interpreted as one reason why you provided the proposal) could backfire. Additionally, the effort of writing the proposal could be futile, I notice that professors usually will take charge of undergraduate projects, both due to person preference for control and as they tend to genuinely know more about how to do the research

I would say instead of "if you are interested in working with me..." "I would need your counsel working with x". This way you enforce his/her position as a researcher

Yes, that is a nice suggestion. I would probably amend it again to say "I feel that I would really benefit from your help (or advice (as per paul's answer above) when working on x.

I'd have thought the only possible response to the email you suggest would be, "I've no idea if I'd be interested in working with you on your project -- you haven't even told me what it is!" There's no point inviting somebody to join a project if you've not given them any details. Better to just ask if they'd like to meet to discuss it and invite them to join you if they seem interested after that meeting.


text:
Applying to a new position after a few months?
Last summer, my current funding ended and I had to look for a new position. I managed to find a lectureship at a university. Unfortunately it is one which is more focused on undergratuates rather than on research. At the time, it was either that position or face potential unemployment.
I recently became aware of a position that would be the ideal one, however it really is a long shot. I recently published a paper in a world-leading conference in my field (and on the domain of the lectureship) which I believe improved my academic profile considerably, if compared to when I was looking for jobs last summer. The problem is that I'd have to ask my previous referees to send another letter and I guess that wouldn't reflect too nicely on me, especially considering the possibility that I could not even be shortlisted.
Considering the situation, should I seize the opportunity and think about the consequences later? What would you think as a referee if someone who was hired somewhere asked you for another reference some months later? I normally wouldn't do this but I believe that it's not in my best interests to stay in a university which is not research oriented for too long.

Are you sure that just one publication (even in a world-leading conference) will have that much of an impact on your academic profile?

The solution to your predicament lies, as I see it, completely in how you approach your reference writers.
I would approach them from the point of view that a great opportunity has presented itself to you in a very untimely fashion given that, "I already asked you to write a reference for me a short time ago. I hate to ask you to do this yet again, and I'll completely understand if you decline." That sort of thing.
Hopefully you saved a copy of their prior recommendations so they can use them as an easy guide. Offer to help them if they are pressed for time.
A great opportunity should not be ignored simply because someone might have to do a little bit of work for someone they've believed in very recently.
This just happened to me recently. A friend asked me to be a reference for him. He got hired. Two months later, another, better opportunity came up. He asked me again to be a reference. I didn't hesitate to say "yes".
A reference is nothing more than asking someone to attest to whether or not somebody can do a job adequately. There is nothing unethical about someone wanting to move to a better position. Good opportunities don't grow on trees.


text:
What should a student look for in an undergraduate thesis topic/supervisor?
I am an undergraduate student (in maths) looking for a topic and supervisor for my thesis.
What criteria should I use to judge whether a project/supervisor combination will make for a good thesis and productive experience? Especially in the context of preparing for graduate school. (I thought about asking separate questions for projects and supervisors, but they seem to be so closely linked that it makes more sense to have them together)
Conversely, what are red flags/pitfalls I should look out for and how do I avoid them?

The first thing would be to check the publications record for the supervisor and the research group, to see the dynamics of the research, if they publish in good journals with high impact factor, and how often, if they have grants, etc.
The most important thing and probably the best would be to see if you really like the field and the niche the group is specialized upon. The second thing would be to see if there is a match between you and them, based on the psychological connection between your personality and the supervisor charisma.

@MikeyMike, "impact factor" does not have the significance in mathematics that it seems to have in other fields. Nor are there "research groups". For that matter, grant funding is not as critical in math, since grad students are most often supported as teaching assistants, and teaching experience is very important (at least in the U.S.) for subsequent employability, since teaching is usually a significant part (if not the most high-status...) of an academic mathematician's responsibilities.

I am in math, and have some experience with undergrad research (from both sides), and there are lots of different ways you could have a good experience with undergrad research.  What would be good for you will depend a lot on your individual situation (mathematical maturity, background, independence, etc) and your goals (do you want to get a paper out of it? just get some research experience? learn something new? help your case for grad schools?).

For getting into a good grad school, what's most important is how well prepared you are in terms of background and how much potential you show.  This is evidenced by your transcript and recommendation letters.  Doing novel research or writing a paper is much less important (unless it's much more impressive than typical undergrad math research).  (Note: many undergrad theses in math are just an exposition of an important topic.  Some of these are very good.)  So in terms of grad school, the most important thing out of this project will probably be (1) what you learn, and (2) the impression you make on your supervisor, who should write you a recommendation.
For being able to get a paper out of it, research is never certain, but it's important that the project is well thought out beforehand.  More open-ended projects may sound interesting, and teach you a lot, but may not be conducive to having a finished project in the time available.  I generally find ones that involve some calcutions/computation have a higher rate of "success," in the sense you should at least be able to do the calculations, whereas projects that require you to develop some theory may just leave you completely stumped.  (Though some types of theoretical projects where you can follow the method of another paper closely also have high rates of success.  Conversely, try to stay away from projects of the form "look for pattern in this data.")  Hopefully you can get a sense of how well thought out the project is from the description; also knowing how successful the supervisor was with previous students may suggest this person gives high-percentage or low-percentage success problems (but if you're more concerned about grad school, where the students went for grad school is more important than if they published papers).
For learning things (which helps with grad school), a project where you have to learn some theory (even if just to do computations) is better.
Both to make progress and to learn things, an accessible advisor (say is willing to meet you once a week or so) is better.

Apart from that, I would say put some value in your general impression from talking to the potential supervisor.  If you have a chance to talk to former students of the supervisor, that could also be useful.

Ok practical advise. Not purely focused at Math. Depending on the subfield a lot of this might be irrelevant (or alt very relevant)

Avoid: Look out for re-occuring thesis topics within your school. Cherck last-years list of topics (and prior years), if the same topic is mentioned avoid it. If when you meet the supervisor he says "you'll carry on from the work of last years undergrad student". This is a bad sign.

If a topic is offered again, this means that previous students have not been able to complete it satisfactory. Which may be a sign that the topic itself is flawed. Maybe it is really really hard. Maybe it requires particular equipment that is prone to break down. Working on a "legacy project" is always harder (ask any software dev).

Look for: supervisor who has been around the school for a long time, and is fairly senior staff. What you are looking for is Realpolitik, and having supervised many undergrad thesis before. Undergrad thesis tend to be full of bizarre and unusual requirements; because they often occupy a weird space in the curriculum; e.g. being considered officially a "coursework" unit or other odd things.

So you want from your supervisor an understanding of these rules; and how to loop hole them; or the capacity to pressure the higher powers to ignore them.

Avoid: topics that are not compatible with the requirements of the marking guide. Be aware of what the marking requirement of the thesis are, and chose project to suit. Part of the aforementioned undergraduate thesis are weird is that they might not be assessed on what they look like they are; completing the projects goals perfectly might yield poor marks.

For example, my undergrad area was Engineering. There were a lot of "Design and Build" topics offered. Where you would design something then build it. However the marking guide is taken from the Science faculty. So it is not about designing something to do a task. It is about designing a experiment to test a hypothesis. There are no marks for building at all; even though it is the hardest part. Be on the look out for things.

Look for: for opportunities to make multiple contacts. For applying for Post-grad you need multiple recommendation letters. One will certainly come from your undergrad thesis supervisor. But if you got to work with someone else significant in the university, then that is a great second reference. For example one of my friends had to do a lot of electron microscope work. So he also got a great contacts with (and training from) all the people in the Microscopy center. I think his second reference came from the head of that lab.
Avoid: things that cost money. While there might be a university provided budget for your thesis; extracting money from a university can be like squeezing water from a stone. There may be a bunch of paperwork, and it may take months. However, this can be cancelled out, if the supervisor has great realpolitik -- and can thus pullout money easily.
Look for: chances to grab useful training. I mentioned my friend who did tones of microscope work. That goes on a resume. Working on super-computers, or large clusters; another rareish marketable skill.

When you begin your PhD your may have to justify that you have certain skilled. Having used them in your undergrad thesis is a solid demonstration.

in addition to the hard skills mentioned above. You also want to search for someone who posses soft skills. Skills such as organization, communication, patience, coaching/teaching skills, are abilities to die for in a supervisor.
Students always look for the superstar supervisor who has all the publications and funding but lacks the tact to help a student to grow. You spend years of your life under an unbearable person for what?
Off course, if you can find someone who is a top scholar and a great teacher it's the best


text:
Why is online course enrollment limited to specific times when a course is offered?
Online course providers like edX and coursera offer free courses, but you can only take/enroll the courses at specific times of the year (not any time). Why is that? If you just want to learn something (not for a degree in accredited institutions), it would be much easier if you could do it online anytime.

Actually for both of them some courses are fully autonomous "anytime" courses, while others are restricted to being offered at particular times.  So far as I can tell, the time-restricted courses derive two benefits from being time-restricted:

It creates a "cohort" of students learning similar things and doing similar assignments at the same time, who can then help one another in the associated forums.
Resources needed to support the course (e.g., TA monitoring, course material updates) can track the progress of the students through the course, increasing the return on resources and minimizing disruption to students.

There are also self-paced courses out there, e.g. MIT OpenCourseWare (OCW), or the still-relevant traditional technology known as "books" (ask your library for details). Of course, with these, you miss out on the specific advantages of MOOCs that jakebeal describes.

You kind find two type of courses.

Self-paced: When you select this type of courses you can enroll and take these courses any time of the year.
But the live courses will enable you to enroll only twice or thrice a year. This is because this type of courses will be conducted for large amount of students at the same time. That's known as MOOC-Massive open online course.

I have removed the link since it doesn't seem to provide any value to the post and makes it seem like spam. If you want to add the link back in, please expand on it and explain why it is relevant. That way if the link ever dies, the value of your answer will not decrease.

What does this add to the previous answer by jakebeal?


text:
Food for comprehensive or qualifying exam?
So it's pretty much an unwritten rule at least in biology departments in the USA that when a student is defending his or her thesis/dissertation that they provide some sort of food or refreshments. There has been at least coffee and pastries provided by the student for their committee and audience at every defense I've ever attended.
My question is, how often do students do this for qualifying or comprehensive exams? Since they are private I have never attended one to know... Would committee members expect at least some coffee?

My question is, how often do students do this for qualifying or comprehensive exams?

At my previous department (in ECE, if it matters), students do for qualifiers/prelims what they do for their defense, the only difference being that you scale down the total quantity of refreshments that you provide/purchase a bit if the exam is not open to the public.

Would committee members expect at least some coffee?

I don't know about "expect," but it's nice to have some on hand: at all of my exams, all of my committee members went straight for the coffee upon arrival to the exam.
Edited to add — The oral portion of the qualifying exam at my previous department consisted of a presentation which was meant to showcase any research highlights the student had achieved up to that point and future directions. If your qualifying/comprehensive exam is like that described by @CameronWilliams below in the comments, then bringing refreshments may not make any sense, i.e. your mileage may vary.

This is an interesting dichotomy with mathematics. In math, comprehensive exams tend to be standard exams that are taken en mass. Some universities also have an oral comprehensive exam that is many-on-one (or don't even have a written one at all) but I haven't heard of anyone providing refreshments for it since it is (usually) a formality.

@CameronWilliams Thanks; answer edited a bit.

I think this question is based on a misconception: in my experience here in the US, it is not the student who arranges for food to be present at a defense, but the advisor and/or the department, under the standard conventions for a talk.  As such, it would also be the advisor and/or department that would arrange it for earlier exams if appropriate.
So: if you are a student considering this question, don't worry about it; it's not your responsibility.  If you are a faculty member, ask the senior faculty in your department what their custom is.

I suspect that varies by location.  My wife certainly arranged for food at her defense (and was expected to).

@jakebeal, what you're describing I believe is appropriate for departmental seminar talks and such.

@Joe Maybe we've got another case of "Academia varies a lot" here...

@ChrisWhite Where I did my graduate work, Ph.D. defenses were always public and generally quite well-attended.  Essentially, it was the colloquium you speak of with the extra frisson of tension inherent in the possibility that something might go very wrong.