What Do Math PhD Students Actually Do?

[jmcgraw]

O.K. This question shows just how ignorant I am about things academic, but what do people working on a PhD do? And how long does it take to get your PhD?

I'm mainly interested in knowing about a PhD in mathematics. Here are my questions:


1)Do you take only classes that relate to math (or whatever your field is)? Do you ever take courses that are outside your field? And if not, can't this eventually lead to a sort of mental tunnel vision?

2)Do you spend most of your time in classes? I know you have to write a dissertation, and then present it to a panel or something... But is that what you spend most of your time on? If so, does that mean you spend most of your time flying solo?

3)How long does it take to get your PhD?

4)If you get a PhD in one field, is it usually easier and faster to get a 2nd PhD in another field?

Well, I guess that's enough questions for now. Thanks.

 

[ircdan]

I'm not in grad school but I've spent the last few weeks looking at them.


You can sometimes take only math classes yes. Typically your first 2 years you take 3-4 courses a semester, then you take the qualifying exams. The courses you take help you prepare for the qualifying exams. After passing the qualifying exams(preferably before), you find an advisor and pass an oral exam based on certain topics related to the area your interested in. This advisor usually ends up being your thesis advisor if he isn't already, and gives you guidance while work on your thesis problem. The thesis hopefully takes 2-3 years. You usually continue taking courses during this time, reading courses, topics courses, etc. So in total, 5-6 years is realistic. I guess you could do it in 4, but this would be tough. Every program is different, but that's how it works in general from what I've read.

 

[Norman]

I would have to agree with ircdan's assessment. I am beginning my 4th year in a physics Ph.D. program. I spent my first 2 years taking classes, studying for the qualifying exam, teaching classes and doing a little research when I had time. The classes have all been in physics. At the beginning of my 3rd year I won a fellowship so I no longer have to teach to support myself.

Typically, in math and hard science programs, you are supported under a Teaching Assistantship for the first 2 years or so. This position usually requires about 20 hours per week of teaching duties and pays you a (usually) very meager salary for your time. In addition, if you have a TA position, your tuition fees are typically waived. Because your tuition is paid by your department, you cannot usually take classes outside of your department without having to pay for them. You can look to spend about 40 hours per week on class work in graduate school. So as you can see, you will be very busy those first few years. You have balance the fact that teaching is what pays your bills (and if you do a bad job- they may not be paying the bills too much longer...) with the fact you must do well in your classes to remain in graduate school.

After passing the qualifying exam and finishing my classes, I spend all my time focusing on my research project for my dissertation. It is very nice to not have the background noise of classes and teaching duties to interfere with what the main purpose of receiveing Ph.D. is all about. YOUR RESEARCH! This is the meat of becoming a Ph.D.- working on NEW research in a field that you are excited about and that will translate well once you are looking for a real job- in whatever sector that may be.

Good luck and I hope that helps.

 

[jtbell]

When I was a grad student in physics at Michigan, we were required to take two courses outside the department ("cognate courses"). Most of us chose math courses. I took Intermediate Differential Equations and Complex Variables.

 

[jmcgraw]

Thanks guys.

Another thing: Are you expected to get lots of papers published in journals while working on your PhD?

After passing the qualifying exam and finishing my classes, I spend all my time focusing on my research project for my dissertation. It is very nice to not have the background noise of classes and teaching duties to interfere with what the main purpose of receiveing Ph.D. is all about. YOUR RESEARCH!

Is this phase of the program a solitary one? Is there some sort of arrangment where you discuss your research with supervisors on a regular basis? Or are you just let loose on your own?

Also, do you often discuss your dissertation work with other PhD candidates, or is it very competitive?

Finally, I saw this on the Wikipedia article for PhD:

William Henry Bragg, the noted physicist, was famously known to have said, "whatever you do, don't do a Ph.D.".

What's up with that??

 

[Norman]

Thanks guys.

Another thing: Are you expected to get lots of papers published in journals while working on your PhD?

I don't know what your notion of lots is. I don't know anything about math programs, but in physics you are expect to have published usually a few (~3 or so) papers in good journals. The better and more papers you have published- the better your odds are of getting a job afterwards!

Is this phase of the program a solitary one? Is there some sort of arrangment where you discuss your research with supervisors on a regular basis? Or are you just let loose on your own?

Also, do you often discuss your dissertation work with other PhD candidates, or is it very competitive?

Well you typically work very closely with your advisor. Most advisors are very involved- but I have seen a few who leave their student to their own devices too much. You usually come into grad school with some idea of the research you want to be doing and you find an advisor who will work with you on it. But you have to realize also that how you get paid (after your first few years you will want to be a Research Assistant- being paid by your research advisor through one of their grants or if you are really lucky like myself you can get a fellowship that allows you to work on what you want!) affects what you are going to be working on sometimes. If you cannot get funding for the research you want to do- it is going to be hard to get paid! So sometimes you have to comprimise with your advisor about what kinda work you will be doing. You need to get paid somehow to live- so you have to be realistic about your research topics.

As far as discussing your work with other students... this can be delicate. Some schools are very competitive and some people are really jerks. Some people will try to steal your ideas. I have not had any problems but I have known people who have. All in all, I am very open with my research since nobody I know does what I do except my advisor. The other students in my research group are not at the same level as me yet, so I don't have to worry. A good advisor will be able to provide you with some sort of a shield from other students stealing your ideas.

On another note- competition in classes can be VERY strong. I know people who were completely ostrisized from their classmates in grad school because they were the kid who always did well and everyone was trying to do better than. So their can be a lot of competition there. On the other hand, I only experienced the "us against them" feeling from my fellow grad students as we all struggled to deal with the amount of work thrown at us in those first 2 years.

Finally, I saw this on the Wikipedia article for PhD:
What's up with that??

Hmm... for some people the amount of effort that they put into a Ph.D. program does not correlate highly enough with the compensation you receive afterward. Just because you have a Ph.D. does NOT mean you will get a job when you graduate. You have to spend a good amount of time networking with other researchers in your field and producing important work so that these researchers want to work with you and help you get hired where they work, etc.

There are some jaded views and some very "head in the clouds" notions about whether a Ph.D. is a good idea or not. Your first two years in Grad School will usually let you know where you fall in the spectrum of whether or not Grad School was a good idea for you...

 

[Gokul43201]

Recently, the trend is to generally disallow academic courses outside the department, barring consent from your advisor or (lacking at advisor) a strong argument from you that the course you wish to take is directly relevant to the grooming in your field.

Eg: It is easy for a theoretical physicist to make a case to take an applied math course. It is similarly easy for a condensed matter experimentalist to make a case to take a EE course in semiconductor devices, say. A math student may find it hard to make a case to take a course in say, biochemistry.

The reason for this restriction is likely because of a history of students switching programs after taking a few courses in another dept (especially from math/physics -> EE/CS).

Now, if you have an RA and are working for someone, you will have to convince this person (your advisor) as well, that you "need" to take this outside course. That may be trickier than convincing the dept.

However, many depts will generally let you take recreational courses (dance classes, skating lessons, horseback riding!). And while this is easy to do if you have a TA, good luck with convincing your advisor to part with his precious grant money so you can learn to play golf!

 

[jmcgraw]

Recently, the trend is to generally disallow academic courses outside the department, barring consent from your advisor or (lacking at advisor) a strong argument from you that the course you wish to take is directly relevant to the grooming in your field.

How about courses on the history of mathematics if you are a math major? (do they even use the term "major" when talking about grad students?) That's something that has always interested me. Would it be easy to take those courses?

I obviously have very little knowledge about grad school, so let me use this undergraduate language: Could you major in math and then "minor" in the history of math?

I know people who were completely ostrisized from their classmates in grad school because they were the kid who always did well and everyone was trying to do better than. So their can be a lot of competition there. On the other hand, I only experienced the "us against them" feeling from my fellow grad students as we all struggled to deal with the amount of work thrown at us in those first 2 years.

Sounds like grad school can be a little nastier than I thought.

 

[Manchot]

I know people who were completely ostrisized from their classmates in grad school because they were the kid who always did well and everyone was trying to do better than.

Who would've thought that there's anti-intellectualism in grad school?

 

[ircdan]

I obviously have very little knowledge about grad school, so let me use this undergraduate language: Could you major in math and then "minor" in the history of math?

There are some universities which require all graduate students to obtain what they call a Ph.D. Minor; ie, take a required number of courses in another department. However, in the case of math Ph.D. candidates, they are usually exempt in the sense that they are allowed to do there minor within the math department by either taking a required number of math courses or passing a qualifying exam in an area not related to there research. It really depends on the school because all programs are different.

If the history of mathematics course is taught by the math department, then I don't think this would be a problem anywhere. Also just a fyi there are actually Ph.D. programs in the history of mathematics, however I don't know much about them because I didn't look into them. I think I saw at least 2 programs that had this while looking at graduate programs but I don't recall the schools.

 

[gazzo]

Learning something isn't equivalent to enrolling in a class, if you find something interesting why don't you read up about it?

There's nothing stopping you from auditing interesting classes although auditing students have a tendency to slack off, I find it sometimes hard to do assignments/turn up to class. This semester it was ancient egyptian history, and the lecturer always had interesting photographs to show us from her expeditions!

 

[J77]

Hmm... for some people the amount of effort that they put into a Ph.D. program does not correlate highly enough with the compensation you receive afterward. Just because you have a Ph.D. does NOT mean you will get a job when you graduate. You have to spend a good amount of time networking with other researchers in your field and producing important work so that these researchers want to work with you and help you get hired where they work, etc.

Yeah - if you want to earn money, get a job when you're 21, when you finish your first degree/major.

If you want to do research in an academic setting do the PhD, but don't expect the cash to flow in

The networking part's not a chore. It really helps, not only with securing posts later but also with the understanding of your subject, ie. from different points of view.

 

[jmcgraw]

I just thought of another question...

I remember a while back someone told me that you have to learn to read/write a mathematically relevant foreign language (German/Russian/French, any others?) in order to get a PhD in math. Is this true?

I'm sort of hoping that it is. I'd really like to be required to learn a third language. (I'm fluent in Spanish, but I'm guessing it's not very relevant for math.)