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What are the advantages and disadvantages to completing a Masters program before applying to a Ph. D program?
I've been considering applying to graduate school of some form or another in Mathematics. During my undergraduate years, I did decently on my undergraduate coursework (mostly A-s, some As, a B) but not stellar, and it wasn't until I started taking graduate courses as a senior that I started buckling down and getting solid As or higher. I also had no research experience at this time.
I eventually want to apply to a Ph. D program in pure mathematics. Since I didn't really click until later in undergraduate years, so I was considering applying to 2-year masters programs in mathematics, and then based on my performance there, decide whether I'm fit to work towards a Ph. D.

My question is, what are the advantages and disadvantages to completing a master's program before applying to a separate Ph. D program?

I know masters degrees are sometimes considered terminal degrees. Would doing well in masters coursework be advantageous in applying to Ph. D programs later on as opposed to immediately after undergrad years? Does strong performance as a masters student make one a more attractive candidate, or do programs have less interest in applicants who already have a masters? Is it wiser to apply for a Ph. D directly? I'm sorry if this question is considered too much of a soft question. Thank you.

Welcome to Academia.SE, and you don't need to be so hesitant - these questions are exactly on-topic for this forum!

I can only speak for my (computer science) department.  Students who apply to our PhD program with MS degrees are held to a higher standard than applicants who apply as undergraduates.  What we look for in PhD applicants is strong evidence of research potential.  Most undergraduates don't have an opportunity to undertake a real research project, but MS students do have that opportunity, by definition.  It's much harder for MS applicants without publishable results to be admitted than an undergraduate in the same situation, all else being equal.  Grades are much less important (unless they suck, which yours don't).
On the other hand, the fact that your already decent grades improved when you started taking graduate classes is a huge point in your favor.  Be sure to get recommendation letters from your instructors in those courses, and hit them up for research opportunities.  I recommend applying to both MS and PhD programs; some departments will even let you apply for both simultaneously.
There's a similar effect in NSF's evaluations of graduate fellowship applications.  NSF splits the applicant pool into three piles based on the number of years of graduate education: still an undergrad, less than 12 months, and more than 12 months.  Expectations are higher for applicants in later piles.  In particular, publications are a de facto requirement for students in the more-than-one-year pile, even if their one year of graduate education was in a non-research masters program.

do the publications need to be in the same field? For instance, a completely hypothetical TCS student with publications in say mathematical biology. Are those useful?

@ArtemKaznatcheev — I think publications in any field is more useful than no publications at all; Sticking with any project long enough to ship it is a good sign.  But publications in distant fields might be less useful than publications in close fields.  (Speaking personally: I don't know what publication in mathematical biology "means".)

"but MS students do have that opportunity, by definition" - is this specific to the US or something like that?

@AliceRyhl Not particularly, no.

Many PhD programs require you to do a masters on your way to a PhD, so the point in many cases is moot. That being said,
Advantages:

You'll get a chance to see whether research is something you like before committing to the PhD process.
You'll complete most of the coursework, so when you get to the PhD work you'll be able to more quickly focus on research.

Disadvantages:

Depending on the masters, you may be spending money on your degree. Many PhD programs will fund your way (in exchange for you doing awesome research).
You'll be required to do a master thesis, which can be comprehensive, and you may come to view it as a waste to do it twice (one for masters, one for PhD).

Do not spend money on your MS degree.  At least in the sciences and engineering, if they don't want to pay for you, they don't really want you.

Don't want to be the grave digger of this old question, but I think one needs to add here that JeffE's comment is certainly not true for Central Europe - around here, paid master's programmes are almost unheard of.

@JeffE, does this hold true for coursework based master's degrees in math and/or stats? From looking online, it seems like most big-name/top/reputable programs don't offer funding to these kind of students.

@BonnieKlein No, it doesn't.  On the other hand, at least for computer science in the US, course-based master's degrees are not intended to be preparation for PhD programs.  If your eventual goal is a PhD, you want a research master's program, and you want to publish before you finish it.

Other than what eykanal mentioned, you might want to consider the following points:
Pros

If you have lackluster UG grades with little/no research experience (in terms of publications/term papers/internships), few top PhD programs would be even willing to look at your application, not matter what are your scores in the GREs. I assume your letters of recommendations (LORs) from faculty would be average at best as well, which would really, really hurt your admission chances. So, a Masters degree would help you rectify that - you can aggressively start pursuing research-based projects with the faculty, and work at a publishable thesis. This would both give you something added to your profile (a publication), and you can get much better LORs from your masters faculty - something that may get you into that top school where your dream adviser works!
You can get (some of) your Master's course credit transferred to your PhD program, so that you can start working on your thesis much early, and may even finish faster! However, this really varies from department to department, so make sure you inquire about this before applying!
If you are really, really sure of what field you want to research in, you can find the top people in your field (whom you'd want to be advised by during your PhD) - and start corresponding with them during your Masters, asking queries/having discussions about their most recent papers, and using them in your Masters thesis (assuming you'd be working in the same field). That way, when you finally apply, you would stand out in their mind from the other applicants, as someone who is genuinely interested in their research. Mind you, I'm not asking you to fake anything! Be sincere about your passion to work in the same research areas, and they just might be convinced to bat for you during applications review!

Con

On the other hand, if you do not fare well in Masters program, most admission committees (ad-coms) would take it as a red flag - as it would bolster the less-than-stellar impression your undergrads created, and hence they might deem you not fit for PhD at all. This might be the case with even the ad-coms that might've been willing to give you the benefit of the doubt when only presented with your undergrad records - so, tread carefully if you happen to embark on a Masters, as your performance there would undergo even greater scrutiny!

Thanks for your insights shan23. The con you mention is also a personal red flag for myself. I figure if I can't perform well in a master's program, that's better than applying and then washing out of a Ph.D program.

The con may be a pro in disguise.  If you do not fare well in your Masters program, especially in your thesis research, that may legitimately indicate that you are not really suited for research.  Better to learn this about yourself earlier than later.

@JeffE how about this qualification : "that may legitimately indicate that you are not really suited for academic research." Academia is a unique beast.

Fair point, @Amy.  (But then your definition of "academia" has to include my colleagues with PhDs in industry who publish in the same venues as academics.)

@JeffE Of course, but there are lots of opportunities to do fulfilling research that don't involve holding a PhD. I see a lot of people in academia forget this, so I just wanted to add my voice!

@Amy I apologize if this is a bit late. "but there are lots of opportunities to do fulfilling research that don't involve holding a PhD" Can you please tell me where does this happen? As far as I know, companies are involved with r & D rather.

So I'm a first year math PhD student. I did not get my masters before entering university, but I don't think that had a big role either for or against me. I didn't end up applying to any masters programs actually, and I had two major reasons:

the primary reason for me was money. None of the programs that I was interested in funded masters math programs. I'm sure that there are such programs, but school is expensive. And I'm poor. So it goes.
the secondary reason was inspiration. I'm going to do original research, right? That's the goal. And I'm impatient ad ready for it (at least in spirit). It happens to be the case that we spend our first year here doing a lot of work, quals, etc. It's the second year where things kick into gear, and I'm already straining for it. (However, if I already knew everything, I would have already passed my quals, so it's not unfair treatment or anything).

If I were to give you my personal recommendation, knowing that you wanted to get a math PhD eventually, then I would say apply to both if you are in doubt. What's the worst that can happen? If you are a strong enough candidate to go straight to PhD, then great. Why not, right? And if not, then a little graduate coursework can't hurt your application.
I would also like to mention that, at least in my program, there is no transferral of credits. You come in, pass qualifying exams, and write a dissertation. The transferral of credits would come in the form of you already knowing enough to pass the quals immediately (I did not know them all, for instance - some people knew more and some less). In all likelihood, you'd still burn at least a semester, more likely a year, just like all of us do. So a masters would likely lengthen your studies (at least at my uni).
On the other hand, it is possible that you don't have a big idea of what area of math, or what field of math in particular, you want to work in. This would be a big issue, perhaps. I knew I wanted to do number theory, and I was interested in the work of some of the number theorists at Brown. But a combinatorialist, graph theorist, or many other people would be hopelessly alone here (there is little love for combinatorics here). I suspect this sort of problem could be true in many schools. But if you know what you want to do, then this is no issue.
To end, I wanted to note that it's fine to test the waters, i.e. to see if you're fit for a math PhD, in a math PhD program. I've known people who have gotten a masters a year or two in, decided that was enough, and left the program. I suspect this isn't uncommon (although it would be uncommon where I am), and you'd get paid to do it.

Thanks mixedmath! I'm interested in algebraic things, (algebraic number theory, commutative algebra, algebraic geometry) but most of my experience with these subjects came from the graduate courses I took. I feel like I don't really know what real research in those areas entails. When you applied to graduate programs, how familiar were you already with the research field for number theory? I'm curious because in the case of writing a statement of purpose, I'm unsure of how knowledgeable one should be already.

This is speaking only from my experience in Public Health and Epidemiology, so its slightly more general, but hopefully it will be helpful. Some of these have already been mentioned by other posters.
Advantages:

You have the potential to establish your "research chops", or shore up your grades. If you don't think you have a strong application coming directly out of undergrad, this is probably a plus.
If you move programs between your MS and your PhD, you get to see two schools. That's good for both perspective on research (rather than only being exposed to "The University X way of doing things"), and it means an extra set of contacts, though admittedly your network from the Masters university will probably end up being somewhat weaker.
You get the "feel" for your potential research topic. Which means that if you don't like it, you can switch. Getting an MS and a PhD in two different but related topics (like say Pure Math and Applied Math/Operations Research/CS, etc.) is pretty run-of-the-mill. Switching PhD programs mid-stream is a much less pleasant experience.
In contrast to some of the answers here, in my field at least I'd argue that undergraduate applicants are judged more harshly than their MS-weilding colleagues. Several major programs simply do not accept folks directly from undergrad into their PhD programs, and several others say they do, but in practice without someone pulling for you or an act of God they're not going to do so.

Disadvantages

It will probably add time. If you're coming straight from undergraduate, a university's combined MS/PhD track (wherein essentially you get an MS by way of your PhD coursework + a thesis) is likely the "least time" path to a doctorate. While you'll be able to transfer some of your credits from your Masters into a PhD program, some will almost certainly not transfer, and the university may have a core set of courses that they'll want you to take over again. For example, in my program, I'd say having a Masters trims about a year from your time in the PhD program. But most Masters degrees take 2 years...
You have to move again. The flip side to getting to see two places worth of stuff is you're going to find yourself hopping across the country not once by twice.
There are potentially some cultural problems. Some places view Masters students (not necessarily incorrectly) as transient, so its hard to command a professor's attention as someone worth investing tons of time into, compared to a doctoral student who is going to be around for 5, 6 or more years. This is especially true for professors outside your thesis advisor and maybe the professor who taught a class you did particularly well in.
Money. In contrast to @JeffE's assertion (which is absolutely true for doctoral programs) my field doesn't necessarily fund Masters degrees that aren't part of a combined MS/PhD track. It's hard to get faculty to use their limited RA positions on Masters students instead of doctoral students, and because in the field there's actually a very small number of undergraduate programs, there are few TAships available to people who haven't passed through at least some of the coursework. Because the MPH is also heavily used in my field as a terminal/practitioners degree, it's treated somewhat like a professional school - you pay for your degree.

I cannot speak for Mathematics but for Computer Science the importance of getting Maters degree first is multi-fold which of many have been stated above but one which I feel is also very important. Sometimes in the middle of the PhD program you might feel like taking a break for couple of years and consider doing a job either for relaxing or to get a hands on experience in the industry. Having your Masters degree then will help you find a better job than with undergraduate or god forbid you quit your PhD, you will have Masters degree in your hand.

In some fields (this is true in my own experience for some humanities and social science disciplines), there are departments whose terminal MA programs are recognized as being "feeders" for more competitive Ph.D programs. So applicants who go through those are not necessarily at a disadvantage—possibly the reverse, especially if one's undergraduate grades or training are lacking in some respect. You will need to find out, though, what is true of the field you are working in, and of course which MA programs, if any, have this reputation.


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Could it be beneficial for me to not disclose my gender/ethnicity in an REU application?
I am an undergraduate in the US applying to REUs in mathematics. Every REU I am applying to through MathPrograms has a section where you can choose to fill out your gender/race, along with a message of the form

The U.S. Department of Education requires [university X] to report on the racial or ethnical composition of its student enrollment. Information on individual students is held in strict confidence. Self-identification is entirely voluntary.

It is not a secret that REUs want to encourage higher participation of minority groups, and indeed the web pages of some programs say things like, "Members of underrepresented groups are especially encouraged to apply."
I am a white male from a suburban area. Clearly this is not going to boost my application, so my question is, could there be much benefit in choosing "decline to answer" on these questions?

"I am a white male from a suburban area. Clearly this is not going to boost my application" - [citation needed]

While the type of job is different, the answer to Should I disclose gender, race, disabilities etc. in tenure track job applications? seems to address your question as well.

@ff524 That post was helpful; I'm just going to follow the general consensus there and fill out the information. Thanks

For job applications, demographic information like this is usually kept separate from the rest of the application, and is not used in making the decision.  Is the same true for REU applications?

Depending on demographics and field, not listing your ethnicity may result in you being put in a much tougher pool of applicants

Just to be clear: being a white male does help your application significantly through unconscious bias. Some programs will be better at being conscious of and counteracting unconscious bias, but not all are. There are many studies where a predominantly white male name on a resume/application resulted in more acceptances than a female or ethnic name on the same exact resume/application.

It's typical in these situations to collect this data independently of the selection process, so it's unlikely that the people doing the selection will have the data.  Of course, it's likely that your name and current institution will say a lot about you that could influence the selection process.

In fact, for math REUs demographic data on applicants is available to people making decisions.  This is not like the HR data kept separate for job applications.

A 2015 study demonstrates that women that men and women faculty members from biology, engineering, and psychology departments prefer female applicants 2:1 over identically qualified males with matching lifestyles:

Men and women faculty members from all four fields preferred female
applicants 2:1 over identically qualified males with matching
lifestyles (single, married, divorced), with the exception of male
economists, who showed no gender preference. Comparing different
lifestyles revealed that women preferred divorced mothers to married
fathers and that men preferred mothers who took parental leaves to
mothers who did not. Our findings, supported by real-world academic
hiring data, suggest advantages for women launching academic science
careers.

We also know that African Americans and Hispanics are typically favored over European Americans and Asian Americans in college admissions:

In court papers, Arlington, Virginia-based Students for Fair
Admissions said an Asian-American male applicant with a 25 percent
chance of admission would have a 35 percent chance if he was white, 75
percent if he were Hispanic and a 95 percent chance if he were black.

Also, there are numerous campaigns worldwide to increase the number of women in STEM, offering scholarships and other opportunities to women that are not offered to men. There are even cases known, where only women are allowed to apply for a specific academic positions, like this Assistant Professor Position for the Vienna University of Technology or these three senior positions at the university of Melbourne. Similar initiatives exist for "minorities" as well.
For these reasons, I would be inclined to not mention race and gender on my applications to REUs in mathematics.

None of this data is relevant to the question, which is whether you can expect any kind of advantage by not stating.

How did Students for Fair Admissions come by those numbers? That seems like a difficult thing to quantify from outside of the admissions office.

@AzorAhai : From the NYT : Harvard consistently rated Asian-American applicants lower than others on traits like “positive personality,” likability, courage, kindness and being “widely respected,” according to an analysis of more than 160,000 student records filed Friday by a group representing Asian-American students in a lawsuit against the university.

@JohnSlegers Yeah, I read that article when it came out, but it doesn't mention those specific quantifications.

@AzorAhai :  Why so sceptial? 60% of all students who score at least a 750 on the SAT is of Asian descent & only 2% is Black (source). Meanwhile, Aftican-Americans make up
14.6% of students admitted to Harvard and Asian-Americans only 22.2% (source). It seems pretty obvious to me that institutionalized discrimination (aka "Affirmative Action") is the main cause of this discrepancy.

@JohnSlegers Because I'm curious how they quantified it.

@AzorAhai : I guess you'll need to contact Students for Fair Admissions for more details.

There’s no advantage whatsoever to not declaring.  The NSF REU program does have as an official goal increasing representation of underrepresented groups (see official language below), but someone who doesn’t mark anything isn’t helping you meet that goal in a way you can put in a report to the NSF.  There’s just no difference whatsoever between marking white and not saying anything at all.

NSF is particularly interested in increasing the numbers of women, underrepresented minorities, and persons with disabilities in research. REU projects are strongly encouraged to involve students who are members of these groups.

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What is the difference between falsifying data and just being wrong?
I had to take a standard ethics seminar at my research lab (everyone in my lab must take the seminar).  As one would expect, I learned that the charges associated with falsifying data are serious.
Whether you falsify data or make a stupid mistake, the end result is that the published work is wrong.  But the charges of falsifying data are much more serious than the charges associated with human error.
My motivation for making this post is as follows.  Researchers must be allowed some leniency on accuracy, otherwise one would not progress at a reasonable pace.  Nobody is right 100% of the time. Some of the best papers and discoveries have inaccuracies (some are in fact 100% wrong).  However, if your data is innacurate, and the allegation is that you falsified the data, your career takes a major hit.
Question
What are the specific differences between falsifying results and making a human error?  How does one decipher  between erroneous results (due to human error, or negligence, or incompetence, or an early career mistake, etc) and falsified/fabricated results?  How does one prove results are falsified?  Conversely, how would a researcher prove his/her innocence?

This has the rather malodorous scent of "how do I game the system?".

Never attribute to malice that which can be easily explained by stupidity.

Related: What should raise red flags to detect fabricated data, How can editors and reviewers detect data manipulation?

Could you please clarify whether you are asking "what is the difference between the two things from the POV of the one doing them", or "what is the observable difference between the two things from the POV of one looking at the results"?

The clear difference is intent.
Human error occurs when people make mistakes accidentally. For instance, in my first paper, I submitted a graph that was physically implausible because of an error in a code I had written, without realizing it at the time.
However, if I knew the work was wrong or, worse still, if I intentionally made up results, we would cross the boundary from human error to fraud.
Unfortunately, it can be very difficult to detect intentional fraud without some assistance from the perpetrators themselves. A major example of this was the Jan-Hendrik Schön scandal of the early 2000's. Schön's fraud was discovered because he was reusing the same figures to different ends in papers in various journals.

Isn't the question asking how you could tell the difference from the outside? You can't measure someone's intent.

@JessicaB How to tell the difference is not an exact science. But consistency is an indicator. Somebody steps on your foot. Probably accidentally - but how do you know it is intentional? A multitude of minor signals which are consistent with intention while for accidents they could be expected to be "statistically independent".

As @aeismail says, the difference between falsifying data and just being wrong is intent.
As for how one can judge this, often you simply can't, and your own question provides a rather nice example. Daniel Collins in a comment mentioned that he suspected your question was posted out of a desire to learn how to game the system so that you can apply what you learned to actually game the system. On the other hand, it seems totally possible that the question is legitimate and motivated by a genuine desire to understand how science works and how fraud in academia is detected and handled. So you see, we cannot judge and cannot accuse you of having bad intent with a high level of confidence, but can only raise suspicions.
Similarly, when wrong results in science can be plausibly attributed to error, that is usually the interpretation that will be assumed. People usually don't go around accusing others of fraudulent intent to falsify data unless they have some pretty convincing and damning evidence. Smoking guns are rare, which is why you don't hear about such cases very often. On the other hand, we do occasionally have such cases, since people who falsify data are usually not very smart or sophisticated to begin with, so often they will be sloppy and careless and go about their data falsification in some very obvious and easy-to-detect manner, and then they are discovered.

You mean, the people we know about who falsify data. We don't really know how many people are good enough at doing so not to be detected.

You should document what you have done while you are doing it, e.g. in a research log. You should make that documentation available at the same moment that you publish your results. If a wrong result happens, then it will usually be possible to track down in the documentation where the mistake happened. That will make it more plausible that it is an honest mistake.

Goldfinger's law:

Once is happenstance
Twice is bad luck
Thrice is enemy action

Intention is something that can be proven over a lingerer period; an isolated mistake in a development is usually not interpreted as intentional. Nevertheless, even isolated honest mistakes can cost you your reputation, especially in high-stakes research results. Fleischmann & Pons in "cold fusion" is an example; I do not know what happened to the reputation of the Gran Sasso "Faster than Light Neutrinos" group, but I am sure their mistake didn't help.
Sometimes, there are tricks to make intentional scientific fraudsters reveal themselves, but I won't mention them here to not render them ineffective. But a famous example you can read up about are the N rays. Also, some nice chapters in the (first) Freakonomics book about made up results and rigged fights.
For anyone contemplating faking results: what'd be the point of it? Why not going to politics, stock markets, poker competitions, army - that's where generating misleading information is desirable and part of the job description. But in science, we are in the business of truth-finding.

There are circumstances where incorrect results are published and it is clearly and unmistakably the result of academic falsification (although I would concede that perhaps only a small percentage of all academic falsification ever gets caught). Of the instances of academic falsification that gets caught, they fall into a few (but growing) catagories:

Image manipulation. There is no logical or scientific reason for copy/pasting a band in a gel other than to mislead. This is the closest thing we have to a smoking gun, because the data is obvious without any kind of statistical analysis needed. Here is an excerpt from a recent anonymous peer review via pubpeer:

Unusual statistical practices. This is particularly true in RNA-Seq experiments, when there are multiple ways to skin a cat. However, every now and again someone conducts their analysis in such a convoluted way that one can only assume it was an attempt to deliberately mislead. I'm not talking about applying the wrong statistical test, i'm talking about using different statistical tests in the same paper for the same type of data. I'm talking about arbitrary cut-offs to 3 decimal places which just-so-happen to produce a statistically significant result, but any other value for that cutoff would have produced a non-significant result (p-hacking). Essentially here we imply motive due to incredibly improbable actions taken by the authors in how they reasoned about their data.
Whistleblowers. Occasionally, and more frequently, we see collaborators or individuals who left academia for one reason or another coming out and proclaiming that they know such-and-such a publication was fraudulent because they actively participated in it. Unfortunately, this scenario is not very effective at getting a fraudulent publication retracted, as many publishers and academic integrity investigators can brush off such reports as hear-say or that the whistleblower has some ulterior motivation. This method, however, does have the ability to expose types of fraud that are impossible to detect in a publication - such as samples excluded from the analysis that would have otherwise contradicted the published result.

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Is it possible to get a teaching job in US/Canadian universities with an NZ/Aus PhD?
I am dithering between an NZ/Australia PhD, and the US/Canada one. Is it ever possible to teach in the US/Canadian universities with an NZ/Aus PhD?

The short answer to your question is "yes." Do you have reason to believe otherwise?

We treat Ph.D. holders from the southern hemisphere the same as everyone else, once we've turned you right side up.

I found that that (at least in my field, which is TESOL/Applied Linguistics) the US/Canadian Universities always prefer (actually it happens 99% of the time) people with an US/Canadian PhD or at least a UK PhD to fill in their tenure track faculty positions.

In most (actually all) of the faculty profiles of US/Canadian universities, I found that they have an MS/MA from the US/Canada followed by a PhD from a North American university. But of course exceptions are there for high profile professors/researchers who have extensive research publications,who have jobs all around the globe.

But I am not sure if a regular (not high profile) PhD holder from an NZ/Australian university, and that of an US/Canada of a similar caliber (teaching experience, research experience, publications and so on) are treated equally in terms of recruitment.

My own assumption is that the US/Canadian universities think that their PhDs are much more rigorous (with course work, and a comprehensive exam before a PhD candidate even starts his/her thesis, and it takes 5-6 years) than a NZ/Australan PhD (usually with no course work, and no comprehensive exam, and it takes 3 years), and that is why they prefer their PhDs to NZ/Australian ones. I may be wrong. Any thoughts on this?

@MohammadHaque Your arguments are the same for UK PhD as for ones from down under. They are NOT less rigorous than a US PhD (averaging on both sides). They are shorter because our schooling is (a bit) better and less broad, so students start with rather more specialist knowledge.

Australian Ph.D. programs tend to be shorter than American Ph.D. programs because their system is similar to that of the United Kingdom; I believe that New Zealand is much the same.  This isn't "worse", just different.  This sort of difference is familiar to many scholars, and there are no special barriers to Australia/New Zealand scientists getting faculty positions in the US or Canada.  These days, of course, they will likely need to do a postdoc first, just like any other scientist.
A nice example of an Australian scientist who has done well in America is Rod Brooks, famous roboticist at MIT for many years before he headed out for greener pastures.
So why do you see so few Australians and New Zealanders in the US and Canada?  Let's start with the simple fact that there aren't all that many around, period.  Right now, there's about 24 million Australians and 4.5 million New Zealanders.  By contrast, there are about 320 million Americans and 35 million Canadians.  Thus, even if there were perfect mixing between the two countries there would be a pretty small percentage of Australians and New Zealanders in American and Canadian faculties.  And of course, it's not perfect mixing: scientists are much more mobile than many other professions, but even scientists are most likely to stay in their home country, where their professional networks are strongest and where they are likely to have good personal reasons to stay as well.  Put those together, and I would be surprised to see more than about 1% Australians in US faculties, no matter how good their education.

Rod Brooks got his PhD in the USA so I'm not sure if he's a good example.

It definitely is possible, but it is somewhat unusual for someone from Australia or New Zealand to get an academic career in the US after doing the PhD. From a New Zealand perspective, most of our famous scientists did their PhDs overseas. For example, the most famous New Zealand mathematician, Vaughan Jones, did his PhD overseas and never came back. So did the most famous New Zealand physicist, Earnest Rutherford. (It might be different in your field; I have no idea.)
A couple of reasons why a New Zealand PhD might make it difficult to get a job in the US later:

New Zealand academics tend to be working in niche areas because the opportunities for overseas collaboration are necessarily more limited. In a PhD here, unless you are really well-funded, you might get one trip to the US or Europe during your PhD, and several to Australia.

(As for people coming in the other direction, sometimes one of our universities will puff itself up because a famous person is coming to NZ to do a lecture tour, but really they are often just taking a paid vacation.)

As jakebeal says, our PhD is shorter.
It is very expensive for a US institution to bring you over for an interview. Even if universities claim that they don't take this into consideration, I am sure that they do.

So, if you have the chance to do a PhD in Aus/NZ, I would think carefully about it unless you have the chance to work with a real international celebrity, or unless you are happy spending the rest of your life down here if you are determined to remain in academia. Because it can be hard to escape.
My current boss did a PhD in New Zealand and he said that he wouldn't have done it if he had been planning to stay in academia, even though he was at one of the best departments in his field. Furthermore, if you look at the profiles of academics in Aus and NZ, you will find that many of them have PhDs from Europe and the US too. So even here, a PhD from NZ is considered somewhat inferior. I remember when I was asking for PhD advice as an undergrad, everyone strongly encouraged me to go overseas. (It's not like you can't return later!)


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Nominating a professor for a fellowship
I know a professor who is really brilliant, but also very modest. This professor has helped me to progress in life. Now, I want to express my gratitude by nominating him as ACM Fellow. However, I have no experience in situations of this kind and I would like to ask you a couple of questions:

When you are nominating a professor for a fellow title, do you need to ask permission to him? or should I keep the process in secrecy?
In case the fellow title may not be granted to him, could this fact hurt his reputation?
Is it ethical to try convince other professors to support my nomination application?

Hi, and welcome to Academia.SE! This is a nice first question. Have you read the ACM guidelines for nominations? That should take care of your third question, since you already need five endorsers who are ACM members.

What a kind person you are. No matter how this turns out, I believe your professor will be grateful.

First make sure that you have read all the regulations for the award (in the case of ACM fellows: http://awards.acm.org/fellow_nom_guide.cfm). You see that the nomination in this case is quite some work. Especially question 3 is already answered there: You need five endorsers. Hence, it is expected that you "convince five people to support the nomination".
For question 2 it seems pretty clear that the ACM fellowship is really very competitive, so not getting the fellowship will not really hurt (not getting the Nobel price is also not a big deal for most people).
For question 1: In my opinion you do not need to ask for permission. The awardees do not have any obligations so they will not have any burden from this award. I also think (but I am not sure about this) that is usual to not inform people that you want to nominate them. However, you need to provide a lot of information to the award giving institution and it is also not unusual to ask the person that you want to nominate "I (better: We) plan to nominate you for this award and would appreciate if you could provide us this and that information to prepare the nomination."

That's all great information. I should also say that for an ACM fellowship, being "brilliant" and kind is by itself not enough. One also needs to be (very) accomplished in one's field of research, and the proposers / endorsers themselves also need to be rather high-profile. It's not really appropriate as a sort of "thank you note" to a good mentor, as the OP seems to envision.

It's great that you would like to help your mentor, but this is a tricky issue.
First, writing a good nomination is not easy, and it's far from obvious what the conventions are.  If you don't get advice and guidance from someone more experienced, you are unlikely to write a successful nomination.
Second, nominators are usually senior and accomplished academics, typically fellows themselves or scholars of equivalent stature.  (I don't know for sure about the ACM, but this is the case for analogous mathematical societies.)  This isn't strictly necessary, but the committee will generally not have any expertise in the specific subject matter of each nomination, so they need to be able to rely on the judgment and perspective of the nominator.  If you are young or inexperienced, then the committee will be much more skeptical of your nomination.  In extreme cases they might not take it seriously at all.

In case the fellow title may not be granted to him, could this fact hurt his reputation?

That won't be a problem in itself.  However, the situation might look bad to the committee.  Self-nominations are generally highly discouraged, if they are allowed at all, so people who wish to become fellows sometimes ask other people to nominate them.  The committee might wonder whether your mentor asked you to do this, in which case choosing someone inexperienced could make your mentor look unwise.

When you are nominating a professor for a fellow title, do you need to ask permission to him? or should I keep the process in secrecy?

You don't need to ask permission in general.  It's unclear to me whether you should do so here.  On the one hand, it's an unusual situation and your mentor might prefer not to be nominated under these circumstances.  On the other hand, he might feel put on the spot, having to either agree to be nominated or find a tactful way of declining.
My recommendation is that you should find another way to express your gratitude, since this nomination is unlikely to work and could be awkward.  (But I don't mean this as criticism: there's no way you could have known this without more experience.)
Instead of writing a nomination yourself, you could talk with other faculty about whether they would be willing to do it, but don't push them if they seem reluctant.


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How do I write a cover letter for a journal that has a double blind review process when I need to reference my previous conference paper?
My research area is in Computer Science.
I am going to submit a paper to a journal, that has a double blind review process. The paper builds upon our previously published work in a conference paper. It has over 40-50% new content, experiments and results, and less than 30% textual similarities. This is allowed by the journal (according to their website)
I need to reference the original conference paper in the journal paper and say the current submission has X,Y,Z content, which are new and not included in the conf. paper. I would also like to write a cover letter stating that this submission contains new material, over the original conf. publication, outlined in bullets. I would like to cite the conf. paper in the cover letter too.
The journal says, all indication of author names should be blanked out. Hence, their guidelines are a bit conflicting.
So how can I write the cover letter without giving the author names away ? How can I point to the original conference paper without giving away the author identity ?
Many thanks for your help.
EDIT:
I checked the journal website, it says :
"...Of course authors  have  rights  to publish in journals enhanced  versions of a their conference presentations. Such papers however should be submitter as regular papers. Obviously, the conference paper must be cited and it should be explained how the conference paper has been enhanced. The lack of this citation is considered a serious violation of ethics and as a
consequence the manuscript must be rejected..."
http://tii.ieee-ies.org/o/SubPostConf.pdf

The editor is not subject to the double-blindness and is usually the only one to see the cover letter. They have to know who the authors are so that they can reconnect with you once reviews are in, not try to use any of the authors as reviewers, etc. I'd submit a normal cover letter and make sure that the paper itself is properly blinded. You must cite the prior conference article you are extending, but you have to do it in the third person (e.g., "...in Rosh, et al. they show that..., in this article, we extend their work to show that ...", etc.).
If you are still confused about this issue, contact an editor at the journal and ask for clarification.

Hi Bill, yes I have contacted the editor, however his response was very vague and just said to 'cite the conf. paper in the journal submission'. My worry is that, reviewers would complain we did not explicitly say this is an extended version of our own conference paper (i.e. for them to judge the novelty of our new work)

That's a problem for the editor and you to sort out after the reviews come in. Everyone who is involved in double-blind review knows that some of these problems have to be worked around.

@Rosh When citing the conference paper, blind the citation.


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I've created a new formula in the field of math, as a bachelor student, what should I do now?
I'm a computer science student and recently developed a new formula in the field of math. It's something important and I'm confident that the formula does what is intended to do because of my tests.
But I don't have experience in research mathematics and I don't know how to proceed now, what should I do?

hmm, you are right, it's probably an meaningless assumption....so i will take "i'm confident" instead.

I'm not a mathematician, but from my limited understanding of mathematicians, they don't really operate in "new formulas", they work in proofs. Having a formula is not really important or useful; showing that something is always true when some other thing plus some assumptions, for example, is useful. The "rules" for what makes a proof in math are quite different from running some tests, because those tests present very narrow assumptions around what specifically is tested.

That question does looks like mine, thank you for sending...did not showed up in the possible duplicates while publicating the post...but i still have an worry...can a professor that i don't know little about take my idea if i try to talk to them? maybe i should start a new post on this topic...

Is the useful discovery here the formula itself, or is it the fact that your quantity of interest can even have a formula? Or did you just discover an approximation that happens to work really well, but which has no mathematical justification? It might help to tease apart some of this when discussing whatever you discovered.

@BryanKrause  It worked for Fermat :-) .  || I have a proof of Fermat's last theorum that "I haven't quite fully worked through yet " :-):-) :-) - I suspect that I never will.

Occasionally I see questions like "is this formula known?" on math.stackexchange.com and I think that's considered acceptable with the reference-request tag, so you might consider asking there.  If you use your real name, this would also establish priority, if that's a concern.  If there's a related integer sequence, I recommend contributing it to OEIS (or leaving a comment if the sequence already exists.)

@BryanKrause there are some useful formulas in mathematics, e.g. prime generating functions that generate all prime numbers between (a,b); or the infinite series that, when summed, generates e.

Essentially echoing @Buffy's answer:
First, it's a great thing that you have found something cool, and are happy about it. That really is the immediate personal reward for "research". Sure, maybe "benefiting others", or "advancing human understanding", but those are distant and not-immediately-gratifying mechanisms.
Still, there are "professional" mathematicians and computer scientists (etc.), and collectively they/we have been thinking about things for a long time. So, first, it is all-too-possible that you've rediscovered something that's been known for some decades. I've done that myself "uncountably-many" times. There's no dishonor there... quite the contrary, it shows that your sensibilities about what to look at are aimed in a good direction.
Apart from the actual scientific content, there are pretty stringent stylistic conventions in various fields' publications, even on preprint servers. I cannot pretend to communicate these to you in an answer here. You need a more senior person to help you navigate the conventions. And, sadly, to be clear, if you transgress those conventions, people won't take you seriously, and may not even be willing to read what you've written.
Good luck, and have fun! :)

You need feedback on your idea and how to present it. Talk to a professor in your department who you trust and who might be interested in what you have done. You might want to also talk to someone in the math department who will advise you about the significance of what you have. Perhaps the CS prof can put you in touch with a math prof if you can't do that directly.
Once you have established that it is something possibly publishable, write it up. Focus in the paper on what it is and why it is important. Mention possible applications. Provide a proof if necessary or what evidence you have. Get feedback on what you write (and read a few math papers to get a feel for the "flavor" of the writing.
Then, if the feedback is good, figure out an appropriate journal (or conference in CS) and submit it there. You will get additional, but independent feedback in most cases, unless it is judged trivial. Follow the journal's process.
The process will be long and a lot of work. The original inspiration is often the easy part.

I will take a bit of an unconventional stand on this but:
You probably have not "developed a new formula in the field of math".
When stating something like this you have to consider that there is a very large volume of published information in the very old field of math. In order to establish that your formula is actually new, you'd have to have read up on at least the adjacent fields of math that are relevant to your problem.
It is a very heartbreaking thing, but when you stand between the large number of bookshelves in your institution's math department's library: Are you sure that what you came up with is new? A considerable amount of time in research goes into establishing what has been published on the matter before.
I don't write this to be mean. It is a painful experience many of us have gone through many times to come up with an interesting thought, only to find out that it was well documented in anno. ~1700. Please talk to your department and professor about it and be prepared that they will hand you a reference. Then do not give up and continue! This is part of the process.

I might disagree. Coming up with a 'new' formula is not that difficult. One can count some  family of (combinatorial) objects, see if one gets a hit in the OEIS, and presto, a (conjectured) formula might be discovered.
The hard part is to prove it, but it might not be difficult. I am supervising a bachelor student at the moment, and from his data, we could guess a formula (well, these turned out to be Fibonacci numbers) and it was easy to also prove this fact.

I agree with @Per Alexandersson. I think the hardest part is not coming up with a new formula per se, but coming up with something new that others would be particularly interested in. After that the task is to communicate it to those people in an understandable way that acknowledges the literature and respects the conventions of the field.

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


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How should I present my German medical degree (Staatsexammen, Dr. med) degrees in the US?
I have recently graduated in Germany and will be moving to the US. I have completed my medical degree (Staatsexammen) and my doctoral thesis in medicine (Dr. med), so I will have two degrees. For the latter, I published about 10 papers in various high impact journals, which fulfills the ERC criteria of the work "being equivalent to the work needed for a PhD".
How should I present my degrees in the US? I've seen people use just MD, I've seen others use MD/PhD. More confusingly, I've seen some using both alternatively (e.g. on LinkedIn vs. on the University Website etc.).

which fulfills the ERC criteria of the work "being equivalent to the work needed for a PhD".
But you are moving to the US, so ERC may not be very relevant. Try to look into equivalent criteria from NSF or similar funding agencies in the US.

I would strongly suggest against using MD/PhD, based on what I have read in this paper. People already complain that the PhD portion of MD/PhD training in the US is too abbreviated.

On your CV and in author biographies, you should call yourself Dr. Med. as this is your title and since it is self-explaining. If you feel differently, then put the MD in parentheses as an explanation. You could also use MD and then put the German degree in parentheses afterwards or vice versa. In more informal settings, you can use MD as the nearest US equivalent. There are research Ph.D.s in medicine in the US, so I would not use the combination of M.D. / Ph.D. as it could be misunderstood to mean that you have two different titles.
You seem to have excellent credentials, so I would not expect anyone questioning you using an equivalent title.

I think this question is bordering the legal counselling, so please keep in mind I am not a lawyer and this is not legal advice.
There are various official sources that will help you in deciding what you can and what you cannot do.
https://www.fau.eu/graduate-centre/doctoral-degrees/promotion-und-ph-d/#collapse_7
https://www.fau.de/files/2017/03/doktortitel_en.pdf
Regarding MD, the first link tells you:

Professional degrees such as these are roughly equivalent to the
Staatsexamen (state examination) in medicine. The holder of a
professional degree in medicine may only use the title in the original
form in which it was granted.

Which I interpret as "you can sign as MD only if you a MD, i.e. you took your degree in the USA".

What business does the German institution have telling the US government what they can and cannot allow? I will say from my personal experience that my hospital's electronic health record routinely lists individuals with MBBS or MBCHB as "MD".

@Ian it is unclear to me what you mean. The link I posted are german institutions giving some official guidance on "Differences between 'Promotion' (Germany), PhD (English-speaking countries) and MD." (as per the title of the page)

The question author asked how how they should refer to their degree in the US. At least one US state grants "MD Licenses" to individuals with equivalent non-US degrees. A common electronic health record displays these individuals throughout the system (including the patient-facing side) as "MD". Therefore, I believe a German institution is not well suited to instruct individuals on US customs.

@Ian please make an answer out of your comments. It will be immensely helpful to OP, since they are even referring to ERC (European Research Council) rules!


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How important is the grade of your Maths PhD thesis if you want to stay in academia?
I would like to ask if there are people out there having made experiences regarding the following quesion:
Assume you would like to stay in academia. How important is the final grade of your Maths PhD thesis - assuming that the PhD holder will stay in Germany (say) ?
Rumors told that some professors don't care what your final grade is and they say instead that only publications matter.
On the other hand, I have also heard that other professors say that if you get a grade which is lower than "magna cum laude" then you can resign.
Hence, it would be most interesting if some people which know examples of that kind shared their examples / experiences.

Seems like it depends which of those professors is on the hiring committee.

Requiring Magna Cum Laude for hiring seems like a foolish standard. I don't know if it happens, but...foolish.

If you publish your thesis in Annals or Inventiones or JAMS (my list is incomplete), I do not think anybody will care about your grade.

My understanding is that German-speaking Europe is different than most other places in this regard. Might be worth stating more strongly (in the title, say) that you’re asking about Germany, if that’s indeed where you’re applying for jobs.

@MoisheKohan: Well, if ones publishes the results of one's thesis in Annals or Inventiones or JAMS, then it's extremely unlikely to get a grade that is not at least "magna cum laude".

It's probably worth to consider that with a good grade you have options from both categories whereas with a bad grade you have options from only one. Now, whether that makes it important depends on you but it certainly doesn't make it easier...

There are a number of laws that explicitly define the prerequists to become a professor in Germany:
On the one hand, there is the "Hochschulrahmengesetz" (which can be roughly translated as "regulatory framework about institutions of higher educations"). This is a federal law. In § 44(3) the following requirement for becoming a professor is listed:

besondere Befähigung zu wissenschaftlicher Arbeit, die in der Regel durch die Qualität einer Promotion nachgewiesen wird [...]

My translation:

Particular qualification for scientific work, evidence of which is usually given by the quality of the PhD.

In addition, each federal state has a law about institutions of higher educations - called "Hochschulgesetz" or a version thereof for most states - where one typically finds similar requirements (examples for Bavaria, see § 57 (3), and North-Rhine Westphalia, see § 36(3)).
To understand how those laws are applied in practice, one needs experience with the common meaning of PhD grades in Germany. If you get a PhD from a German university, you will get one of the grades "summa cum laude", "magna cum laude", "cum laude", and "rite". Those latin expressions are purely traditional. Their literal translations have very little to do with their actual meaning nowadays. Their actual meaning is roughly as follows:

summe cum laude: an exceptionally strong thesis

magna cum laude: this is the standard grade that you'll get when your thesis is of a reasonable quality.

cum laude: the thesis is subpar

rite: this should happen really rarely. If you get this grade, something went really wrong during your PhD

So if you have a PhD from a German university and your grade is not "magna cum laude" or "summa cum laude", this will typically be interpreted in the sense that you do not meet the requirement in law explained above.
Note that arguments of the type "if you did good work during your PhD, then nobody will care about your grade" are a bit strawmanish: if you did good work during your PhD, you will get "magna cum laude" or better, so the issue will not arise.
Summary: Yes, if your grade in a PhD from a German university is lower than "magna cum laude", this will cause severe problems for an academic career in Germany and those problems exist by law.

Honestly this answer surprises me, as a US academic. But it is good to see an answer that is both knowledgeable and definitive. Thanks for the education. And then there is "habilitation", of course. Mystifying.

If you wish to stay in Germany, please ignore my answer.
However, if you are prepared to consider relocation to the US/Canada, please be advised that here no one even knows that in some European countries people get grades for their PhD dissertations. (Sexagenarian, I only recently learned this curious fact -- and I learned it from someone's question at Stackexchange.)
On our side of the pond, you will be judged by your publication record and by your reference letters.  Your marketing skills (like your performance at conferences) will matter also.  Of a great importance will be your ability to strike collaborations.  But no one will ever ask you about your PhD thesis grade.

One's history of failure can be forgiven by future success in the US system. It gives the opportunity to work hard and improve.

@jdods "We know from what failings our virtues spring."  Gotthold E. Lessing


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Is it alright to share the abstract of my article while it is under review
I am in contact with another researcher and want to share the direction of my current research for a possible opportunity. Would it be okay to share just the abstract and author list of my article with them. The article is still under review and not accepted/published yet.

Yes, until you sign away your copyright after acceptance for publication, the article (in full) is yours and your co-authors.
And, even after you sign away the copyright, you normally get back a license that would permit such local sharing in any case - especially for collaboration purposes.
As user Snijderfrey notes in a comment it would be proper to get agreement from co-authors.

For unpublished work, I would like to be informed as a co-author. I would not object to the kind of sharing OP has in mind, of course.

@Snijderfrey, yes, thanks. Edited.

After it's published it's public. Anyone can read it. There might be an unlikely  small ethical problem sending a copy if the published version is behind a paywall,

@EthanBolker, I'm pretty sure the license covers such things.

What is copyrighted is the concrete work. Ideas as such aren't copyrightable. You are free to share your insights with others.
In any case, publication is precisely to disseminate ideas, I'd be very surprised if the journal objects to sharing e.g. preliminary versions or preprints (but look up their policies or ask if in any doubt).


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Should authors disclose that they are a writer of one of the methods in a benchmarking paper?
I read a paper written by two authors which benchmarked various methods to analyse genetic data. The authors concluded that method X was the best in terms of sensitivity and precision.
I later realised that both of the authors writing the benchmark paper were also on the original paper for method X, which had three authors in total. The authors did not explicitly state they were authors of method X, but the paper from method X was cited with the author names visible.
Is it generally expected that authors should make this clear to readers of the paper?

Yes, such things should be noted to avoid claims of a conflict of interest. It seems that, in the current case, sufficient notice was given even if not stated explicitly (the citation).
But if you create something (a method, say) and then claim that it is "best", people should know the details. The authors aren't exactly disinterested in the results and it may take additional scrutiny to be assured of the outcomes.


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What factors to consider when visiting universities that you have received offers from when making a decision?
I am an economics undergraduate, and I applied abroad for my master’s. Luckily, I was admitted to two top schools – one in Germany, other in France. I have spoken with students from both schools, their programme directors, my professors and, in general, weighted the pros and cons of living and studying in them.
The result from all this is that I am still very uncertain which programme to choose. There are plenty of differences, but the most important distinguishing factor is that one is a PhD-programme (MSc included) with funding while the other is a MSc and no funding (However, entrance to PhD-programme with funding after first year is guaranteed if grades are good enough. On the flip side of the coin, funding as well as the right to continue PhD studies ceases in the other programme if grades drop below a certain threshold.) For completeness, I should add that I am very interested in doing a PhD but I am not interested in an academic career.
I have decided to visit both schools in person in the near-future and make my decision after that. My question is that is this a good idea and second, are there specific factors or things that I should pay attention to in my visit? I am wondering if there are certain things that I can and should investigate better in-person.

So if you go with option B, you have to do one year without funding; option A covers this. What is the cost differential here, in Euros? I assume tuition is minimal, so "funding" refers to a stipend that covers your living expenses, probably 20K euros or so?

Exactly. For two years the cost differential of choosing B is approximately -30K (including the stipend + tuition fees).

First, if you want a doctorate (for any reason) then I'd weigh the actual doctoral program quite a bit higher. Language might weigh one way or the other also.
But for the question itself, I'd think the most important thing is that you find a way to speak with some faculty and get an idea about how it would be to work with them. Visit a class if possible to see them in action. Visit the coffee lounge if there is one and listen for interactions. Often grad students are welcome there. If language is a consideration, consider how comfortable you are, especially if you aren't proficient in one or both languages.
Then, talk to some graduate students to get a sense about how they feel about working there. Helpful professors? Any frustrations? Seminars available and useful? Have coffee with a few students. Adequate office space? Private? Shared? Or just a desk in a big room.
It is probably also worth the time to walk around the local community/city and get a sense about what it would be like to live there for a few years.

You wrote in the comments:

For two years the cost differential of choosing B is approximately -30K (including the stipend + tuition fees).

Unless you are already wealthy, this is a huge amount. Especially if you’d have to take out loans to compensate for the lack of funding. So, it is already clear (to me, at least) that you should attend option A unless there is something huge problem that makes success at option A very unlikely.
I see no reason not to go visit as you suggest. Especially if (as is usually the case in Europe) this would allow you to meet your prospective advisor. But I think there is only one real consideration: is A so much worse than B that you’re willing to give up $30k at such an early stage of your career.


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Will it be a disadvantage if my diploma thesis advisor does not give me PhD recommendation?
My diploma thesis supervisor was ignoring me for 99% of my diploma thesis writing and even bailed on me and did not come to the defense. I graduated with distinction and I want to apply for PhD. However, my supervisor ignores me again when I am asking him to give me a recommendation for PhD to TUM. It is a classic situation for him, apparently: many students reported the same problem.
What would be the best solution? Should I try to "catch" him at campus despite him ignoring my emails? Should I instead ask my bachelor project supervisor (far less famous researcher, however)? Should I instead ask for a recommendation someone from my actual job (also a PhD but different field)?
What would be the best decision in this situation? Maybe someone has an insight specific to TUM? Would it be weird that from two recommendation letters I'll send none will be from my diploma supervisor despite me graduating with distinction? Should I explicitly explain why I did not have recommendation from my supervisor in my application?

Are you applying for a structured PhD program at TUM or for a specific open position as a scientific employee for which you can do the PhD while having that position (I think that this is roughly called "individual PhD" in English)? This makes a huge difference because in a structured program, there will often be some committee doing decisions while in the latter case, it's all up to the person you are sending your application to, and there you only need to be convincing.

Academic references are usually best when written by someone who knows you a little bit better and knows how you work, how motivated you are etc. You have to be aware of the fact that recommendation are usually always formulated positive, so in order for the reference to stand out of all the recommandation which some professor receives, it is best if it is written a little bit more personal.
In your specific situation, I think you have to decide between two factors:

Is it more important that the guy who writes your recommandation is famous in his field or in the field you apply for your PhD or
is it more important that it is written by someone who knows a little bit better (as you diploma supervisor probably can't say much about your working behaviour, presentation skills, etc.).

I personally think there is no really universal answer which of these two factors are more important and I would recommand to decide what you personally think is more suitable. For PhD-applications one usually needs anyway at least two references (at least in Germany and hence also at TUM, I guess), so what you can do is trying to ask you diploma supervisor to write one (if you think he is really famous in his field and that it would benefit your application) + one reference by someone who knows you better. The benefit of the latter one is that you can also ask them to specifically point out some skills which you think are important to mention...
Regarding your last question, I don't think that it is weird that your diploma supervisor is not your academic reference, if you decide to not take him. In the end, it is your choice of who you think can say most about you. In the end, since you graduated with distinction, it should be anyway clear that you did a good work in your diploma. It is not your fault that your supervisor seems to not really care about his students.


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What level of audience should one aim for in the introduction of a STEM thesis?
I am writing my STEM thesis, 90% percent of which is about mathematical modeling. However, I am unsure at what level I should write for the introduction.
Should I write it so it is accessible for everyone? Or should I assume a high level of technical expertise?
Does anyone have experience in this matter?

It's a good question, but why don't you jus ask your advisor/supervisor?

Is there a reason you can't look over past theses in your department? Usually university libraries and/or departments keep copies for archival purposes. And there's your advisor, other students in your department, . . . It would help to provide more context to your question. For example, when you say "everyone", surely you don't really mean everyone, since many people in the world probably cannot read your language, or even read at all. So what do you mean by "everyone"? This is just one example of giving additional context.

What level is your degree?

@DaveLRenfro 1. how does it help? There are like thousands of them and each is written differently. Even for my own supervisor, the last three I read had totally different styles and one even had some kind of parable or a fiction as motivation. 2. You are nitpicking on the word "everyone". Do you act like this with your family members? This isn't advanced real analysis and I don't have to define this word.

If even for your own supervisor, the styles are totally different, then it seems to me you already have your answer, at least in the case of your advisor (who you surely have much more knowledge about than us). And yes, I was a bit overboard with "everyone". But while I took it to a ridiculous extreme, the point remains that things like "everyone" and "high level of technical expertise" very much depend on context that you have not given. That said, I think Dirk's answer is the most useful in the absence of anything more specific that your advisor might desire.

@Roland While it is a good point, I think that many students will vastly overestimate the level of knowledge of their examiners. A typical examiner might not be more knowledgeable in the topic of a thesis than an advanced undergraduate student.

What is expected of you and your thesis varies from country to country, so you should ask your advisor what are the (written and unwritten) standards. To illustrate this, I think it is completely pointless to try to make the thesis accessible to non-experts. However, my opinion is not in accord with requirements that exist in my country.

Target anyone with an undergraduate degree in your field. Any more advanced and it becomes difficult for others to follow unless they are already specialists in your field. It does cost more space, which could be undesirable for research papers, but yours is a thesis - space is less important, and you could easily have readers who aren't specialists (I believe in many institutions one of the PhD examiners is intentionally chosen to be from another field).

My answer to this question is always:
Write the thesis for your past self!
What I mean is that you should write the thesis (especially the intro) in a way that if you would have read it when you started to work on the topic you would able to understand everything without additional sources.
This advice is close to "write it for a generic undergraduate" but I have the feeling that it helps to have a specific person in mind.

To name an example of this: for a small part of my thesis I had to implement an algorithm from someone else's thesis. Because the thesis was well written and adjusted for the target audience (me), I had no trouble implementing it for myself. It's no guarantee that your thesis will be used by someone else but I would consider that a realistic option

The future self might also wind up reading the thesis. Memory at 40-50 is a lot more fallible than most young doctoral candidates imagine it will be.

Thank you. Although my past self was not a STEMer and was more into humanities. This might be my major source of doubt...I am not sure if my STEMer supervisor and committee will appreciate this.

@EnPoverty Perhaps provide references for the very basics, then, instead of explaining them in detail. But don't overestimate how much is "basic"; that's a far more common trap than doing too much explanation.

I think it is an opinion-based question.
In my school (community), we follow a top-down writing approach. We first, start with an outline which should be understandable by any reader and then, we break it into pieces. We follow the same approach with every piece and so on.
This writing approach makes readability easier for all readers. Some of them will understand up the deepest level in the structure and some of them a bit earlier.

I am currently (procrastinating about) writing my thesis. As I am almost finished, I speak only from the recent experience of a student on this question.

Should I write it so it is accessible for everyone?

Definitely do not try to do that. Humans have far too diverse of interests to try to get everyone into it. Even if you covered your subject from absolutely elementary principles, your thesis may also become far too long for even your committee members to read it. Try to remember to respect their time.
And I just hinted to you who the primary target audience is: your supervisor, the external examiner, and the other committee members. While you can aim to write with a little more breadth than this small group of people as your target audience, remember that they are the gatekeepers to completing your thesis. I recommend attempting to get early feedback from your committee members since they can, and in my experience do, share valuable information about what they are looking for.
Writing for your committee members does not mean taking the argument maximum of technical level at every part of the thesis. Among others, I have a mathematician and a biologist on my committee. They do not speak the same language, so where their interests meet (e.g. mathematical modelling of something in biology) I have made the language accessible to both of them. But someone who studies something very different, say 17th century poetry, might not follow the jargon or train of thought if they happened to pick up my thesis.
This advice should hold for most of the thesis, although it may be fine to make a particular point that perhaps only a single committee member will understand if it is going to be important to them. Beyond that, show your models and the story they have to tell.

Spot on.  The purpose of a thesis is to satisfy a requirement for a degree.  Everything about it should be done with that in mind.  After it is signed off, you need the institution to certify that you have the degree and marketing of your skills, which probably includes letters of recommendation.  Everything else is optional.

When I want to learn something new, I often turn to PhD theses. Not all theses are equal, but some are very good to start with.
Very often, the introduction is quite naïve, in comparison to what a professor would write. Yet, I don't skip it. Every good thesis has the canonical references in the field cited there.
But, the most important part are the tools (experimental, and theoretical) that the student used for their work. In some theses, I can find a lot of details on how the results were obtained, and those details are often unavailable from other sources. There are also worked out examples, and results I could reproduce, that are described in detail in a PhD thesis.
As others mentioned, the best thing about a good thesis is that is accessible to people from somewhat different background than the author. In other words, a postdoc in Experimental Condensed Matter should be able to kick start his research in a field of Condensed Matter Theory, using a good thesis as a guide. With some more serious additional work and sources, a persistent postdoc should be able to learn a lot from a thesis in Quantum Optics.
In other words, the thesis should be aimed, in my opinion, at active researchers who want a quick and painless introduction to the author's field. The other category a thesis should be aimed at would be researchers who want to learn the methods and techniques used to obtained the results presented in it.

I also find some Ph.D. theses excellent for having introductory surveys of a topic, especially topics that are sufficiently new (or older but non-trendy) to not have a book or survey paper treatment. Example 1 and Example 2 and Example 3 and Example 4.

It really depends on the culture.
The introduction to my PhD thesis was

roughly what it would be about,
and references to books in case the reader did not understand the part above.

It was 1/3 of a page long.
My advisor was not thrilled (but we had a fantastic relationship, he knew that I was a bit "special" and finally was actually curious how this whole circus would unwind), and the reviewers were 50% "great" and 50% not thrilled. But they all conceded that it is a matter of taste and should not influence my thesis which was not about the history of physics either.
Reference: https://www.youtube.com/watch?v=hPUjtzS_zwY

Ask your advisor/supervisor.
It's a good question, but it should be answered really by your advisor/supervisor.
Every other answer here in my humble opinion is in effect speculating as to what the advisor/supervisor would say. Ultimately, mathematics doesn't exist in a vacuum. See Is a proof still valid if only the writer understands it? Any particular mathematical text always has a specific audience in mind. For example textbooks usually say at the start eg 'This is to introduce geometry for maths majors who have 1 course in point set topology but at the same time be not so highfalutin to be accessible to physics majors. This is not meant to be comprehensive or encyclopedic. This textbook introduces mainly only the minimum necessary in order to understand [big theorem X] and [big concept Y].'


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Is it self plagiarism if I use the same source for two different projects?
I found previous tuition and fees for other school years through reports that my university has published onto it website.
I am using these reports for two of my projects that I am turning into my professors next week that counts as a final exam for two different courses taught by two different professor.
Is it self plagiarism to use the same source such as a report showing tuition and fees from prior school year for two different projects that serve a different purpose and also intended audience?

While the answer of Snijdefrey is correct, let me add a warning. What is plagiarism or self plagiarism in the real world is often immaterial in the context of coursework.
If two professors discover and decide that you are essentially using the same paper for two different courses without prior permission then you will probably be punished regardless of the wider meanings of things.
You are protected in the real world from charges of self plagiarism if you cite earlier work of your own, but professors might consider some things improper in an educational context even then.
I recommend that you seek permission from both professors and explain what you are doing. If they agree that the "two" papers are sufficiently different then you should be fine.
It isn't however, that you rely on the same source data for the papers, but rather the questions you ask and answer about them and what you say. Just be cautious and protect yourself.

Can you clarify what you mean when you say "It isn't however, that you rely on the same source data for the papers, but rather the questions you ask and answer about them and what you say. Just be cautious and protect yourself". Are you saying that it not self plagiarism if using the same source more than once for two different paper that have a different purpose.

No, it is not self plagiarism to use a source more than once. However, it depends on the extent of text and thoughts that come with the reference. If you recycle to much of that, it might become a problem. But there is one safe way to avoid charges of self plagiarism: Cross-referencing and thus making the aspects the two texts have in common transparent. Something along the lines of...

[...] as also discussed in Text B [citation] [...]


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How specific should one be when mentioning research interests and prospective advisors?
I'm currently in the midst of drafting up my statement of purpose for the upcoming application cycle in the USA, and am feeling very confused as to how to go about the part where I mention how my research interests align up with those of prospective advisors.  More specifically I'm wondering how narrow my research focus should be, and how specific I should be when mentioning advisors I may want to work with.
I am well aware that I should be mentioning how my research interests line up and fit with those of prospective advisors that I hope to work with; on that note I've heard that I should be aiming for one (if not two) advisor that I would really like to work with.  However, I have also heard that being too specific on these things could potentially backfire, especially if prospective advisors aren't taking students or if research interests are too narrow to match up.
On the other hand, is it bad to be have interest in working with multiple advisors/labs at a department (since you may be able to work with another lab if one doesn't necessarily work out)?  Do they necessarily need to have similar research interests, especially if they are within a similar field?
Edit: I would be applying to a PhD holding just a BS, having worked as a consultant for the past year and a half, and I am applying in the USA, if this information helps.

Are students in the program you are applying to expected to have an advisor chosen at the point of admission or to decide some time in the future? Is admission on merit only or is there a different bar if a professor is able to fund you? How specific are your research interests - do you have a specific project or area you want to work on, specific people you want to work with, or are your interests more general?

Just made a slight edit to the question, if this helps people answer the question.

With rare exceptions in the US, you don't need to say much of anything when applying with only a BS. It will be helpful to have a general idea, but there is a lot to do before starting doctoral research. The exceptions might be primarily in engineering or some lab sciences where you need to join a lab early.
But for most universities and most fields, admission is by committed and funding is from the department/university, not the advisor.
The first task of a student entering with a BS/BA is to take the advanced courses that let you pass the comprehensive exams (again, there are some exceptions). Only then is it essential to have an advisor for the dissertation stage as opposed to a general academic advisor.
The flip side is that most advisors won't be in a position to do much for you until you pass comps. Many will put you off until you are able to "prove" yourself a bit.
But you can, and should, take one or two of those advanced courses with people you think you'd like to work with. Then, you get to know one another a bit and can make a more informed decision. You might also have the opportunity to join a "research seminar" with faculty and other grad students in your field of interest. These are often available at places with large faculties. There may be three or four faculty generally interested in the same set of problems. Even if your participation is informal, you might learn a lot to help you make a decision.
It is good to have interests and goals, and they can help your application, but it is also good to be flexible early on. Don't overcommit. The problem you will eventually work on may be quite a lot harder than you imagine at your current stage.


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International Students transferring between graduate programs
I'm an international graduate student in my first year as a PhD candidate. I'm looking to transfer schools for two reasons-

I had a hard time here with my health in jeopardy, so I'm looking to move to a school which is close to my extended family.
My research interests seem to be more aligned with a different school, which I had not considered when initially applying abroad.

I have a good research background in my field, and a four year bachelor's degree from a highly accredited institution in my home country. While I've taken all the first year courses necessary at my current school, I'm just finishing up and I haven't chosen a permanent advisor yet because I'd like to consider transferring.
Is this possible? If yes, could you guide me on how this process works?
Thank you in advance.

It's unlikely that you're a PhD candidate in your first year. I suspect you are a PhD student. See here https://academia.stackexchange.com/questions/10972/phd-candidate-vs-phd-student

Transferring schools is best done as soon as possible. Your first year credits may transfer seamlessly with another university, but the farther along you get the less likely the transfer will be successful. I would find someone at the university who has experience working with international students (there might even be an entire department dedicated to such) and ask specific questions of them (eg how to apply to another program, how to transfer in good standing etc). Then be in contact with the university that you wish to transfer to and make sure that you meet all of their requirements and apply for transfer prior to dropping out or officially leaving the program that you are in. You do not want to mess with your student visa etc, so make sure everything has transitioned successfully prior to withdrawing from your current location. Moving near family is a good idea, but also make sure that if you are really moving for health reasons that your health will be taken care of there. Make sure that the student health insurance will cover everything that you need for it to cover and that you can access specialists etc in the area that you are wanting to move to. Good luck!


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Will lack of teaching experience be a major hindrance for a faculty position?
I'm currently a post doc (in theoretical computer science) and the only teaching experience I had so far was to teach some tutorial classes for undergraduate courses and giving some "guest lectures" in some graduate classes. It seems that most positions for assistant professor require you to show some teaching experience, i.e. at least co-teaching some courses. The problem is, my current department is quite inflexible giving such assignments to postdocs.
On the positive side, I got some pretty good student evaluations for the tutorials I've been teaching, whether that is considered helpful without teaching a "real" course, is of course a different matter.
Overall, my research record (several tier-1 publications) beats my teaching record (by far).
Will my lack of teaching experience be a showstopper when applying for follow up positions?

I edited the title to reflect the body - please check if that fits your query.

I'm surprised to hear you say that "most positions for assistant professor require you to show some teaching experience, i.e., at least co-teaching some courses."  If you are applying to positions in the U.S. where research will be your primary duty, your prior tutorial and guest lecture experience should be sufficient to get you past whatever minimum you need, especially if you have evaluations to back this up.  Of the five colleagues of mine who received tenure-track offers at Reasearch I universities, only one of them had co-taught a class, and the others had one semester of TA experience which was, primarily, grading.
That said, there are other ideas for getting teaching experience:

Creating your own course or seminar to teach in the summer or during a January term.  If you pitch it as a non-credit course, it might be easier to convince your department to let you teach it.
Look for adjunct work at a local community college.  You'll probably be limited to introductory courses, but this gets you experience.  You may need the buy-in from your faculty boss at your current school.
Talking to individual professors about helping with their course -- I find it hard to believe that everyone has all the help they might like already, and you may have more luck getting your foot into a classroom without trying to be officially assigned to it.

Chris and Suresh answer for research-intensive institutions. At a primarily undergraduate institution, teaching experience is more important, but search committees (being composed of people who went through the process before) know that most PhDs and post-docs have very little teaching experience, and most of it is the type that you have listed. What most committees are probably looking for is any evidence of teaching potential. Teaching experience does not always mean good teaching. If you do not have a lot of experience, then you should ask your references to address teaching potential in your letters (and you should have difference letters for primarily undergrad institutions than for research institutions).

Does more teaching experience help you get a phone interview?

Probably. It's one of the few things that can make you stand out on paper.

Does more teaching experience help you get an onsite interview?

No. Once you make it to the phone interview, it's all about you, your personality, and how you might fit with the department. In addition to teaching experience/potential, you need to show that you are interested and capable of starting a research program with undergraduates, and that you have a project reasonable to the resources of the institution. If your research requires use of one of only a half-dozen specialized instruments in the world, you will likely not get called back.

Does more teaching experience increase your chances of getting the job once you do the onsite interview?

No. The onsite interview likely will include a sample lecture. If you are interviewing at a primarily undergraduate institution, and you mess up the sample lecture, you're done. The sample lecture is how your teaching potential is measured. I've seen people with very little experience do a fantastic job (i.e. engage the class, work examples, answer questions, etc.), and I've seen people with 5+ years of experience stare at their PowerPoint slides, read them word for word, and never look at the class.

Does more teaching experience help you get a phone interview? — Just to be clear: Most research-oriented CS departments in the US don't do phone interviews.

I hear that this might be changing. But your statement is certainly true right now.

@JeffE - note that my answer is for teaching-intensive positions at primarily undergraduate institutions. While phone interviews may not be the norm, some departments do them. Mine does.

I would add that at my (all undergrad) department in a directional state U, we're looking for an interest in teaching as well as some kind of evidence that the candidate can do it well. Our research has to be done around the corners, but teaching goes on all the time. You'd better like it!

It seems that most positions for assistant professor require you to
  show some teaching experience, i.e. at least co-teaching some courses.

Really ? We all ask for teaching statements, but it's rare to see committees in research-oriented departments pay more than lip service to this at application review time. For sure, if a candidate can't deliver a good lecture, it's unlikely that their job talk will be excellent. But that's only an indirect signal.
Now if you're talking about departments with a heaving teaching focus, then I'm sure they expect more in the way of provable teaching skills, and may even ask you to give a class lecture as part of the interview process.

I'm not sure if it would exactly be a major hindrance, but at every school I interviewed at this past season, all of them asked me about what I've taught before and what kind of courses I would teach and develop at the school if they hired me. I believe that answers to these questions are things that you can work on even if you don't have teaching experience. It's not exactly difficult to say, "I want to teach topic 1 and topic 2" for courses if that's what your research was in.
That said, actually teaching a course is quite different from doing guest lectures and teaching assistantships. One professor advised me, "You might want to teach at least one course to make sure that you can, at least, tolerate teaching before you commit to academia."

+1 for "Actually teaching a course is quite different from doing guest lectures and teaching assistantships."  Going from the planning stage through teaching all the classes, to the grading, tutoring, coordinating any TAs, dealing with feedback, and dealing with students with individual problems (not a complete list!) is significantly different than any other experience.  But, many of us think it is also awesome and marvel that we actually get paid to do it!

I have no experience in theoretical computer science.  But in mathematics: it seems to me a postdoc position that has no real teaching responsibilities is a disservice to the candidate.  For reasons such as those mentioned.  They prepare that guy only for a research position with no teaching.

Postdocs in math are different from postdocs in (almost?) every other field.  In fact, they are often called something like "visiting assistant professor" which indicates the distinction.

You don't have "a lot" of teaching experience, but what little you have is of "good quality," as evidenced by your good reviews.
Teaching is a "secondary" function at most universities, and will be judged on a "pass-fail" basis. Here, you have clearly "passed." You don't need to worry about "acing" teaching.
The thing that will get you considered for most positions is your research. If you had "no" teaching experience, that might be a handicap, but "limited" teaching experience probably is not. For your purposes, "tutorials" are as good as "real courses."


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When a journal requires that the work has not been published before except as a "preprint", is an arXiv publication considered a preprint?
In the copyright transfer agreement of a journal there is the following sentence:

"The Author warrants that the Work has not been published before in
  any form except as a preprint."

Nowhere do they mention ArXiv specifically, but does "published to ArXiv" fall under "published as a preprint"?

Basically in math, if the journal does not allow the paper to be put on arXiv, you should avoid that journal (and you can easily find a journal which is just as good a fit and which does allow posting on arXiv).

Usually depositing a paper in arXiv prior to journal submission does count as a preprint. Wikipedia explicitly says so...here's the wiki link: https://en.wikipedia.org/wiki/ArXiv.
You can check out this list of journals with preprint policy: https://en.wikipedia.org/wiki/List_of_academic_journals_by_preprint_policy
If you posted your paper in arXiv before submitting to the journal, do inform the journal (include the link to your paper in arXiv). From your post, it seems that your journal does not have such a tight preprint policy.

"The Author warrants that the Work has not been published before in any form except as a preprint" basically means "it's OK if you published a preprint already". I'm not sure why you say this journal "might have tighter preprint policy".

I meant by tighter policy that there are journals (though small in number) which do not allow preprints. Such as American Association for Cancer Research, JCI etc.

But you wrote "From your post, it seems that your journal" (i.e. the journal that Forever Mozart is asking about) has a tighter policy. This is misleading. From the quoted statement, it seems the opposite is true: that journal does allow preprints.

Oops! I seemed to have missed the word except. My apologies...EDITED

"The Author warrants that the Work has not been published before in any form except as a preprint."

The distinguishing characteristic of a preprint here is that it has not been reviewed. See also the SHERPA/RoMEO definition of a pre-print.
Academic publishers want to be the first to publish a paper and give it the 'seal of approval' that it has passed review.
So what this publisher is essentially requiring is that the paper was not reviewed and accepted for publication elsewhere.
If all you did was posting your pre-print on Arxiv (or some other repository/site), you comply with the publisher's wish.