Other Should I Become a Mathematician?

[mobe]

Also, is there an age limit for postdocs?

 

[Jon_]

I would like to be a mathematician.But I don't think I have the skill set to be an accomplished mathematician. A while back, during the 1990's, I was studying applied math/minor physics.It was during my sophomore year,when I was talking with a friend at the time about engineering.He told me that the field had high monetary rewards and that if I chose to leave my current field, I would get a job right after graduation. Well, he was wrong.
I did change over and to put it nicely,I crashed and burned.I did not finnish school and my classmates did.I missed my boat.

I was 27 at the time.Now 20 years later,back in school trying to make it all work. I have one year left till I finish my BA in physics.It wasn't until the end of my junior year that I decided to take a minor!

What's the point in all this? Well, I chose physics because it is applied math,yet,I don't feel that my ability alone in physics is all that good.I fare much better doing math problems,modeling,etc.My rationale is "if I wanted to pursue applied math and get a physics degree at the same time" then this would be the route I'd go.

Unfortunatley,so much time has passed since the "prime of youth" that I cannot with all my abilities recall pertinant ideas I learned so long ago. Before college I always wanted to do math,but now,I think it's too late. I also lack the motivation I was had.

So back to my minor degree.The minor I chose is in geology/volcanology and it is my hope and I'm banking on it, that all I will need is a masters degree.I really don't know how much more complicated the geosciences are than mathematics but I'm hoping it's less rigourous.

For me,physics is just a vehicle to acquire the things I truly want to do.It's important to know and understand and it helps with abstract ideas as well. Had I stayed the course,I would have finished with my friends and been much happier and successful than I am today.

all that remains is to finish the BA,intership and take the GRE's and find a school that'll accept me. Hopefully,before it's too late.

 

[Werg22]

Mathwonk, say I want to get into a top notch grad school, what would you recommend me to do during my undergrad years? I am thinking something along the lines of spending the summers of my 2nd and 3rd year assisting professors in areas I'm interested in. Maybe also work part-time during my school terms. Do you think that's a good idea? Is there more stuff I could do? Also, I'm not sure professors will need the assistance of an undergrad, even if the latter offers his services for free. What is the best way to approach a professor for that sort of thing anyways?

 

[mathwonk]

I really don't know much about this. I myself teach at agood school, but not a top notch one, and we are always starved for talent. But I guess the criteria are the same everywhere, so I guess I know what to do to prepare, I just don't know how competitive the top schools are at the grad level, so I don't know how likely one is to get in by doing them.

It is not so much a matter of doing special activities or projects, or endearing yourself to professors, but just a matter of working hard to learn as much as possible, and trying to polish ones ability to do research. Although we talk otherwise in education, in recruiting we tend to behave as if math is an inherent talent rather than an acquired skill.

so we are always looking for that person who sees deeply into the subject they encounter, and who comes up with insightful comments and questions, and who finds creative approaches to problems, and who then pursues them successfully, with strong computational skills.

I guess the only part of this that you can acquire is the knowledge by sustained study with the best masters and books, and strengthened computational abilities through persistent practice at working out examples.

In my own career, I made a quantum leap by spending 2 postdoctoral years at harvard, trying to soak up as much as possible from people like david mumford and phillip griffiths, and heisuke hironaka.

i went to their lectures, asked them questions, and read the papers they referred me to (I did not read as many of those as I should have in some cases.) i volunteered to give talks and invited them to attend.

eventually i got better, and they seemed to notice it, and they helped me. but as to getting into a top grad school, i think the goal should rather be to get into the grad school that is at the right level for you, that offers courses in what you want to study and that has professors you can learn from.

for me harvard would have been a disastrous grad school, but it was an ideal postdoctoral experience. utah was perfect for me as a grad school, because it had herb clemens, the advisor who helped me find and improve my research abilities, and gave me an appropriate problem, and helped me learn to solve it.

before that my stay at brandeis helped too, by contact with brilliant and accessible professors like alan mayer, paul monsky, robert seeley, maurice auslander, david buchsbaum. i learned much more at brandeis than as an undergrad at harvard, because the professors at brandeis seemed to notice us and try to teach us. we were run over roughshod at harvard undergrad, by professors who ignored us or made us feel we were wasting their time, a really awful experience.

 

[JWHooper]

I didn't know Pikachu was good at math. :)

Talking about PokeMath!

 

[mobe]

Hi Mathwonk,

I am a first year MA student in Math at a small university. I am interested in studying algebra/algebraic geometry. I have noticed that your research area is algebraic geometry. My question for you is: what are some good universities to study algebraic geometry? I have looked at several universities such as: Michigan, Chicago but these are top ten universities. Where else can I consider? Thanks in advance.
--Mobe

(@admin: please move my question if it is not posted under the right topic. Thanks)

 

[proton]

hey mathwonk

i just finished my REU in physics this summer and was a little disapointed by it, so I'm sure that at this point I want to focus on pure math. I'll be entering my 4th yr this fall, though I plan on staying for a 5th year. So I need advice on what classes to take this fall and in the future

The only pure math classes my school is offering this fall are Honors Abstract Algebra, which I signed up for already, and Differential Geometry A. But since my school doesn't offer Diff Geom B until the spring (which comes after winter quarter, since we're on the trimester system), I figure I'll wait until the winter to take Diff Geom A. So what else should I take? Would a class in German be useful since I heard that its required for math phDs to read another language than English? or possibly take a numerical analysis class, which could prove useful should I go into industry instead of academia? or instead do undergrad research with a professor?

 

[mathwonk]

mobe, we have some very strong young and more senior people here at georgia, in algebraic geometry, algebra, as well as algebraic number theory. i think we are a good candidate for you. there are a lot of other places as well.

most of my friends are at places like stanford, harvard, brown, chicago, and so on, but there are good people also at florida state, duke, unc chapel hill, chicago circle, vancouver. let me look around a little.

you can look too. there is a big conference coming up in spring 2009 at msri in berkeley, and many many people will be there. you might track the program on their website and look for names of speakers and participants.

 

[mathwonk]

proton, i think numerical analysis has more promise than german. but everything you mentioned is helpful.

 

[tgt]

How are Phd scholarships (the ones that cover living expenses) given in the US? Do all Phd students get one? If not then what percentage of Phd students are on one?

 

[mathwonk]

i think most students accepted at most schools receive such a stipend. occasionally we accept students without support but it is rare since few students have independent means.

 

[mathwonk]

i have recently written advanced undergraduate linear algebra notes, covering jordan forms and spectral theory, although they technically begin at the beginning of vector spaces. they should be available on my website soon. this is a 66 page version of the 14 page "primer" of linear algebra now on my site. they are my notes for math 4050.

 

[j0k3R_]

mathwonk,

can you recommend to me a book for studying advanced group theory, after studying hungerford ch. 1, 2, etc.

 

[mobe]

Thanks for all the notes mathmonk! They are quite useful.

 

[mathwonk]

thank you!. i will send my new linear algebra notes to anyone who asks, since it may be awhile before they get posted to my website. I feel i have finally understood jordan form, and I hope this comes through in the notes.

 

[quasar987]

I would really love to see those new notes of yours. Any updates other than the Jordan form?

my email in a pm

 

[altcmdesc]

Hey everybody, great thread.

I'm fairly certain I want to major in mathematics. I'm just having trouble deciding where to go in the field. Calculus was really the course that made me truly love mathematics. The idea of a limit and all that proceeds that (sequences, series, integration, differentiation, etc) are things I simply could not get enough of. What current research is being done in this branch of mathematics (Analysis, I assume)? I'm not too familiar with it because the mathematics involved are usually presented in such a way that an undergraduate cannot readily understand the concepts.

Also, the idea of applying mathematics to biological systems seems very interesting to me. What sort of mathematics are frequently used? I can imagine differential equations and stochastic processes are used to death, but what else?

The only problem I see with pursuing a career in Biomathematics is that I would seemingly have to study applied mathematics in lieu of pure mathematics. I guess that question comes down to: how probable is it that a pure mathematician is able to perform applied mathematical research (at a university-level)? Basically, I want to take pure math courses, some biology/physics/chemistry courses and leave behind some of the dryer applied mathematics courses. I like applying math, but for some reason I don't like wasting course time on it.

Thanks

 

[mathwonk]

you sound like someone who is going to be very successful. biomath is a very hot well funded topic today, and as always in applied math, the problems are hard and demand the best you have.

i am not an analyst, and will try to find some more expert advice for you. nice to meet you.

 

[quasar987]

I'm not an expert of course, but from reading the titles of seminars and workshop in analysis, I have the impression that most of the work done in analysis is in connection with differential equations.

For instance, I'm currently doing a master's thesis in analysis and specifically critical point theory. The typical theorem in critical point theory reads "If a function f:V-->R, where V is a (complete) vector space, is such that [hypothesis], then it has a critical point", where a critical point of f is, as you maybe know, a point p such that f '(p)=0.

Now the interest in critical point theory stems from the fact that if we have a differential equation, it is sometimes possible to find a function f:V-->R where V is a space of functions, such that critical points of f correspond to solutions of the differential equation.

It suffices then, to show that f satisfies the hypothesis of a critical point theorem to conclude that the differential admits a solution. This is useful because it means we're not looking in vain for a solution!

 

[altcmdesc]

That actually seems pretty interesting. I guess I'll take the Honors (Real) Analysis course when it comes around as well as Complex and see how I like it.

What about my other question: How probable is it for a pure mathematician to do a bit of work in a more applied field as well? I just hate restricting myself like that.

 

[quasar987]

Have you read the wiki articles on pure and applied math? I just skimmed through them and I believe they might give you an idea of the "odds" involved.

I guess the odds would depend on what you decide to specialize into. If you go into number theory, which is like the flagship of pure math, then the odds of doing something applied in relation to that are quite low.

But if you go into analysis, and consider that everything differential equation-related is applied math, then the odds of doing something applied in relation to your research in pure math are much higher.

In my case above, proving a critial point theorem would be the pure part, and finding a differential equation whose associated functional satisfies the hypothesis of the theorem would be the applied part.

 

[mathwonk]

altcmdesc, here is a response from a colleague of mine in analysis:

"If this student is at UGA, the best advice is to steer him to Andrew
Sornborger and/or Caner Kazanci. You might also mention this term's
remaining VIGRE introductions:

Monday, August 18
3:30 PM – 4:10 PM Room 304
VIGRE Presentation: Neil Lyall, “Geometry, Combinatorics, and Fourier
Analysis”

Tuesday, August 19
2:00 PM – 2:35 PM Room 304
VIGRE Presentation: Caner Kazanci, “Modeling the Health of Ecosystems”
2:40 PM – 3:15 PM Room 304
VIGRE Presentation: Jason Cantarella, “Tabulating Composite Links”

In any event, applied interests need not preclude concentration on
rigorous math courses. In particular, a serious baby Rudin type course
would be valued in any applied program. Also some general info on Math
careers can be found at http://www.math.uga.edu/undergraduate/careers.html"

 

[altcmdesc]

Thanks a lot mathwonk! You have all been a great help.

In the "Intro to Analysis" course at the UMN, the text is, in fact, Rudin's "Principles". I'll definitely make sure to take this.

I've come to the conclusion that I'll stay in what the UMN calls the "Graduate Track" for Mathematics (which is basically a "pure" math track), taking some applied coursework on the way to test the water. Would taking this route harm my chances of doing applied work in graduate school (specifically in Biomathematics, which requires a bit of Biology) should I choose to do so? Would it be difficult to take the necessary Biology in graduate school (I hear most biomathematicians teach themselves)?

 

[mathwonk]

the new notes for my summer course 4050 in advanced linear algebra are up on my webpage. they cover jordan and generalized jordan form, duality, spectral theorems, determinants, finite abelian groups, and constant coefficient linear ode's. they are an expansion to 68 pages of my 14 page linear algebra primer. they are much more explanatory. still they cover in 68 pages more than most books do in several hundred pages. i hope they are readable. there is a table of contents. the introduction got omitted from the notes but appears on the webpage. enjoy!

 

[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, is now a full professor at Brown, and 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. http://www.bilgi.edu.tr/pages/faculties.asp?fid=3&did=20&curri=true&mfid=2&mdid=92&r=8" 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 little experience in the areas that are tested in PhD pure math programs. Still you could pick 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 myself 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 other pure 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.