The Should I Become a Mathematician? Thread

quasar987

mathwonk,

I see in your VITA that at the end of the 80s, you and R. Varley received 2 ~90k grants for research.

Did you actually spend all that money on research? If so, how?

-plane tickets to conferences
-subscriptions to journals (?)
-paying grad students for research

What else?

mathwonk

federal research grants are kind of a mechanism for the government to fund universities. i.e. the university takes about 30-50% off the top for "overhead", claiming reimbursement for the lights in our building, etc...

then we sometimes obtain a grant for a piece of equipment, such as a computer, but often the feds say that should be paid for by the university, although often it isn't.

There is usually money in there to fund graduate students in the summer to work on their research projects, and visitor money to fund airfare for people to come in and talk to us.

the basic grant moneys that fund research are twofold:

1) we ask for salary for two months in the summer so we do not have to teach or go without pay while doing research in the summer. In Canada this is unnecessary since they receive 12 month salaries but in the US we only receive 9 months pay per year, and must either obtain grants for summer work or teach or go without pay. most of the past 10 years i have done my research in the summer without pay, while my wife supported me.

2) travel money so we can visit other universities and learn and collaborate. this buys plane tickets and food and lodging.

so out of a grant of whatever, for one year, each recipient can expect to receive at most 2 months pay per year, plus the right to buy some plane tickets. sometimes we only got one month's pay, or none. one year i wrote a grant that paid a group of students a stipend so they could afford to study with me instead of working. It also paid their teacher while i donated my own time. One of those students, Jeff Brock, is now a full professor at Brown, so I consider that time well spent.

research is expensive simply because to do it one needs free time. So to buy a month's research one needs to buy a month's free time for a scientist. but it is much more expensive because most of it goes to the university.

the person doing the research and writing the grant receives relatively little of the money, sometimes none at all. for a while i know there were NSF programs, notably topology, that gave grants with no salary in them at all, just travel, visitor and student moneys. the researchers donated all their time. Still there is prestige from the university for bringing in money that benefits the Uni. I.e. you are expected by your university to bring in money for them, not yourself.

the point is to get your name on that money, i.e. to have it on your vita, although you do not get your hands on much of it.

and those sums you read were for multi year (2-3 year) grants.

once as a young person i obtained an NSF grant for about 15K to finance a large conference that has become a famous event in the subject of curves and abelian varieties, the athens conference headed by phillip griffiths, and leading to the book by arbarello cornalba griffiths harris on geometry of algebraic curves. when trying to augment the grant with local university sources i was told that money was tight and i offered to donate my own $700 salary for the conference, which provoked amusement from the research VP at that time, who said that was not needed. Later I learned he had found over $400,000 unspent dollars the day before and given it to other more favored programs immediately. I was asking for $5K, and being stonewalled.

some 30 years ago i read in our university research reporter that in the us, over 50% of all grant dollars go to biological and medical sciences, while less that 2% goes to all physical and mathematical sciences combined. so if you want to be well funded go into genetics, not algebraic geometry. of course nowadays the genome projects are being told to obtain mathematical input to be more competitive but it is not happening to my knowledge.

grant money is awarded by politicians hence for political reasons, not scientific ones. look on our departmental website and see where most of the grant money is coming from: we have a recent renewal for an educational VIGRE grant for millions of dollars, because we are doing a good job of helping train US citizens in math.

at the same time researchers are being denied money for their research, they may be granted money to try to bring US students up to snuff.

serkan

I've just recently discovered this forum and want to say it is amazing to find such a topic.

I've completed two semesters in financial mathematics program, and am quite confused about the direction of my further study. I find thinking about dynamics and the nature of the markets and formulating them quite interesting, That's why I got into this program, but I think a graduate education is also necessary in order to get into maths as much as I want to. My aim is to make a doctoral study on applied mathematics in an US university and I was wondering if my background would be enough for this, and if not what courses should I take in order to make it so. This is the link to our curriculum. I was eager to make a double major with mathematics but the director of the department said it is beyond human capacity as much as I disagree. Which courses do you think can I overtake to be a good PhD. applicant? Or should I abandon studying financial mathematics and get into mathematic program? I considered this too but although my university's math program is well regarded and one of the most rigorous ones in Turkey, it is a new one and might not be much known by US universities. As there are not much place to study applied mathematics in Turkey, the possibility makes me think. I need some guidance at the moment and any input would be really much appreciated.

By the way, I think at the end of the undergraduate study, my GPA would be close to 4.0 and I would have some good recommendation letters. But what makes me think is that it is hard to get admitted from a US university from Turkey. Especially from a new university.

mathwonk

with few or no courses in algebra, topology, real and complex analysis, geometry, you have littlw exsperience in the areas that are tested in PhD pure nmath programs. Still you could poick it up if you are very strong.

here are the qualifying requirements at UGA:
The PhD Qualifying Examination System consists of two parts. The first part consists of four Written Qualifying Exams and the second consists of an Oral Qualifying Exam.

Written Qualifying Exams are offered every year in August before the start of Fall semester classes and in January before the start of Spring semester classes. Study guides and copies of previous qualifying exams are available on the Graduate Program website for students to use in preparing for their Written Qualifying Exams.

The Written Qualifying Exams are divided into three groups:

Group 1: Complex Analysis, Real Analysis

Group 2: Algebra; Topology

Group 3: Probability; Numerical Analysis

Each PhD candidate is required to pass four Written Qualifying Exams, including both exams from Group 1 and at least one exam from Group 2. The exams in Group 1 are two hours long, and the other exams are three hours long. Each of the six introductory 8000-level courses (MATH 8000, 8100, 8150, 8200, 8500, and 8600, along with the associated 8xx5 problem session) is designed to help prepare students for the written qualifying exam in the corresponding subject area.

since you have to pass tests in these areas at the graduate level it is advised to have undergraduate courses in the areas you will choose, but very bright students can sometimes make up deficiencies in grad school. it is hard to do though- i know as i tried and did not succeed at first.

serkan

thanks for the input mathwonk. would you say that those are the same criteria of applied mathematics phds?

mathwonk

i think so, in our dept. it looks as if our analysts voted in a block to force everyone to take both analysis prelims, and then the otherr gpure groups voted to force everyone to take at least one of algebra or topology.

we let the applied people express this preference in their choice of exams from the third part of the syllabus, but apparently do not ;let them choose the two applied exams and no algebra or topology.

as usual, analysis is still strongly represented over algebra and geometry.

serkan

thanks a lot mathwork. it is great to ask a question and get the answer in hours. you have been very helpful.

altcmdesc

This is a question to any PhD holders out there: How was life directly following the PhD? The moving around from university to university, searching for and getting postdoc positions, the salary earned from those positions - what was your experience?

mathwonk

good question, and one I seem to have stopped short of answering in my general discussion. real world survival is very tough. with all the shortcomings the attractiveness of doing math research for a living is so appealing to many very bright people here and abroad that the job situation is often difficult. perhaps that will change as my generation of baby boomers retires beginning now and continuing for some time. but there are many emigres looking for these jobs too and they are very well trained.


i myself wrote a decent thesis and had a very fine advisor with some contacts, and I had several offers of temporary jobs, including one at columbia. However I myself generated another offer, the very tenure track offer i have tenure in now at UGA, and preferred it to the others because with a family, tenure track seemed very attractive.

however the shortcoming was there was no one else strictly in my field although at least one person was interested in it. having no one to learn from or work with, my future development was hindered. so i went to work and obtained an nsf grant for a regional conference headed by the famous phillip griffiths, and this brought a large number of outstanding people to my school for me to make contact with.

professor griffiths also said if i would come to harvard to visit i could have some fun doing algebraic geometry with his team, so my university gave me leave to do this. i also met david mumford and heisuke hironaka there, learned from all of them, and wound up staying 18 months.
thus i survived by doing things backwards, tenure track first, then postdoc.

others no doubt have different stories.

mathwonk

for more on my career path and related matters, go back and read posts 166 and 177-186.

altcmdesc

Hello again,

Now that I've started college, I've had some time to think about my Math career. Right now I'm absolutely loving my current math course (a theoretical treatment of multivariable calculus that uses linear algebra and differential forms) even though we haven't gotten very far. The rigor of the course is very stimulating.

I'm at the U of MN - Twin Cities campus right now. How is the U of MN PhD program in Pure math? Applied? Or does it really matter that much what university I obtain my PhD from?

mathwonk

minnesota seems an excellent place, but it is usual to go somewhere else from your undergraduate school for a phd. please go see my friend joel roberts for more advice. tell him roy smith sent you.

v.dinesh

i wanna become a good theorotical physicist how far pure maths is useful for that????

mathwonk

well witten, who seems to me a fine theoretical physicist is a fields medalist in math. so the two are certainly related. i have also mnyself been a guest lecturer in math at the ictp in trieste lecturing on riemann surfaces to physicists and mathematicians. as far as i know physicists are often interested in learning as much math as possible e.g. group representations, operator theory differentiable manifolds, and riemann surfaces, for application to quantum mechanics, string theory, relativity,.....

muppet

I want to do theoretical physics, so I decided to do half of my degree in maths-the best courses my universty offers on GR or quantum field theory are taught by the maths department. The reason Witten got a fields medal is because the maths he needed to use didn't exist... so he invented it

eastside00_99

Hey mathwonk. I am taking a year of complex analysis now. Its good stuff!

mathwonk

Great!! are you enjoying a particular book you think others might like too? and would you like to give your prof a plug?