Other Should I Become a Mathematician?

[J77]

How is anyone supposed to know what to suggest? No one is that wise.

* shakes magic 8-ball *

 

[mathwonk]

if total persistence has been proven to fail, you are probably dead.

 

[pivoxa15]

Can you explain why i haven't been able to grasp pure maths but is perfectly capable at applied maths subjects?

 

[JasonRox]

Persistence isn't the best method to solving anything in life.

Take a step back and re-think the strategy everytime.

 

[mathwonk]

good advice. persisting in the wrong direction is not going to work.

i don't know the answer to the most recent question, except to say the obvious, that everyone is better at some things than others.

i used to always be better at geometry and topology than algebra and analysis, but i spent so long studying algebra that at least i now know the basics fairly well, as witness my books and notes on my website.

analysis is still hard. but people who do something well have a certain way of thinking about it that one can gradually learn from them.

 

[Werg22]

Is it somehow rewarding for a mathematician to come up with an overly complicated but deep proof even when an alternate way to approach the problem in question would make things much easier?

 

[timur]

Not for that particular problem but it may mean there is another more difficult problem you can apply your method to.

 

[PowerIso]

Persistence isn't the best method to solving anything in life.

Take a step back and re-think the strategy everytime.

Isn't trying new strategies being persistent? Sounds like someone didn't think this through.

 

[mathwonk]

easier prooofs are considered better.

 

[Werg22]

Mathwonk, I memory serves me well, you are familiar with Bourbaki's books. Do you recommend reading the original work, that is reading the French version, or does it not matter at all?

 

[mathwonk]

there is no difference at all mathematically in the french and english versions, so unless you enjoy the beauty of the french language i would read in the language that is easiest for you. for me that's english.

 

[mathwonk]

easier proofs of a result are usually ones that ignore all the information except the minimum amount needed to get ot the weakest version of the result. the harder proof usually proves more than necessary, and will hence sometimes indeed be useful for some other purpose as well.

 

[jostpuur]

Oh, btw:

who wants to be a mathematician?

o/ (jostpuur raises a hand)

I'm a student who found himself a little bit disappointed with physics, and who then became a student of mathematics. I hope I would be interested in mathematical physics, but I'm not really sure, because I don't think I know what it is, actually... Does this forum have university folks who do research in some mathematical physics group?

 

[eastside00_99]

Help!...

Hey, I am need some help actually with becoming a mathematician. I very worried about my graduate prospects. I feel as if the competition is very fierce (which I kind of like), but its so much that I feel as if my application my get looked over for undeserving reasons.

I am interested in Geometry (Possibly Algebraic Geometry or Arithmetic Geometry (They are hard so I am not completely sure it is the best choice even-though they attract me the most)). I also like Algebra, Combinatorics, and Global Analysis. I have hit a brick wall trying to understand schemes and am missing a lot of commutative algebra, so Analysis is starting to appeal to me an more (especially as I study more advanced Analysis). Nevertheless, I don't give up that easily. So I am still pursuing it.

Here is my raw data:
Senior NCSU
overall gpa 3.3
math gpa 3.5
gre v 530
gre q 710
gre math sub ... results pending


As you can see my overall gpa is somewhat low (maybe terribly low for most who apply to grad school in math). But, it really isn't a good indicator for my ability to get my Ph.D. I will have three solid recs. (one prof taught at two of the schools I am apply to). The greatest strength I have (and I consciously planned this), is that I will have 36 hours of grad credit when I graduate. These are the grad courses I have or will take:

Advanced Analysis
Functional Analysis (two courses)
general topology
algebraic topology
linear algebra (grad)
lie algebra
Abstract algebra (two courses, grad)
smooth manifolds
computational algebraic geometry
graph theory

I should mention I did independent study in Algebraic Curves all summer long also. I had, am, and will work very hard to do this, but it is worth it because my aim as an undergrad is to be prepared to pass the quals at whatever uni that accepts me with the minimum or no fuss (which will pretty much ensure that I get the Ph.D.--meaning most who drop out are those who can't pass the quals).

I don't know; I just feel very prepared to do grad work because I have been doing it. I have gotten use to the level of work that is required for the first or second year of grad school. But, I am worried that this will not really show up in the application because of silly factors like overall gpa. Anyway, here is the list of schools I am applying to (they are listed in order of preference based on overall rep, strength in algebraic geometry, and location):

1) brown
2) berkeley
3) Rice
4) Duke
5) U of Washington
6) Washington U
7) Cuny
8) U of Ill (urbana)
9) unc (chapel hill)
10) georgia

Now, I actually think that schools like georgia, ill, and unc are better than Rice and Duke and maybe Cuny, but the location or overall rep forces to put them in this order. I may turn out to decline an acceptance from say Duke over something lower on the list. I don't really know at this point. I do know that these are all really good schools and that I would be very happy at any of them (brown and berkeley are completely out of reach but I am applying just for fun). Now, what do you think my chances are for getting accepted to any of these schools? Do you think I am prepared and/or are desirable to any of these programs?

I do have the ultimate fall back; I can do a masters at NCSU in a year or a masters at wake forest in a year if I want to. I think I will apply to these things so that I have such a fall back (I can get support for doing this). The reason I am kind of afraid of my chances is the people I keep running into really have stellar marks (albeit I have not ran into a single person who has completed the level of course work I have) but they balance that out quite nicely with 4.0s or being from a very nice school. For instance, I was talking to an undergrad who is at one of the top schools (but not in math) and he said that I will probably not get into any of these schools. Although he said Georgia is feasible. He probably doesn't know what he is talking about because I kind of think if none of these schools accept me then georgia will not either. He said that my overall gpa and quant score is too low and that I should aim much lower (whatever that means). But, this does confirm my thinking that I am in a very stiff competition here and that others although not as well prepared as me will have much better looking applications. This infuriates me a little; but, it is how it goes.

Anyway, what advice do you guys have? What are my chances? Do you think some of these schools will see that I am prepared and ignore the annoying average overall gpa as well as gre scores? If they don't, I have to admit I will be little bit angry. I mean as much work as I have put into this and everything and then getting rejected I know would be a miserable experience as well as probably effect my confidence in my own future. Regardless, I am happy with doing the grad work when I could have just taken easier math courses and gotten all A's. I feel challenged and stimulated. Mathematics is great at any level; and I have gotten four years to spend as much time on math as I have wanted. Finally, the prof I worked with over the summer doesn't seem very concerned. He gives me the impression I will not have very much trouble getting into some of these schools. He knows my work and my grades, but maybe he doesn't see the competition I see. Anyway, please respond with your comments and suggestions on whether or not my choices are viable.

 

[cristo]

Now, what do you think my chances are for getting accepted to any of these schools? Do you think I am prepared and/or are desirable to any of these programs?

You appear to be prepared, and it seems somewhat apparent from your post that grad school is something you want to do. I don't know much about the US education system, but I can't imagine that universities will accept people on solely their GPA.

(Incidentally, mathwonk is a professor at uga, so may have something to say!)

The reason I am kind of afraid of my chances is the people I keep running into really have stellar marks (albeit I have not ran into a single person who has completed the level of course work I have) but they balance that out quite nicely with 4.0s or being from a very nice school.

I presume that your GPA is calculated from an average over your the grad classes as well as the undergrad classes you've taken? If so, it's pretty obvious that it's easier to get a higher score on less advanced classes! I imagine if you send in your transcript (list of marks in specific modules) then this will be looked at, and probably won't matter half as much as you are worrying about!

For instance, I was talking to an undergrad who is at one of the top schools (but not in math) and he said that I will probably not get into any of these schools.

Would you take your car to a doctor to get fixed? I wouldn't pay much attention to what someone who isn't studying maths has to say, especially as he appears to be just discouraging you!

Anyway, what advice do you guys have?

Just keep working hard, and stay enthusiastic. I imagine if you get an interview then it'll be easy to show your enthusiasm; the hard part os getting an interview (that's even if they interview in the US; I imagine they would, but not 100% sure!) Either way, make sure your application letter and CV (if needed) are good-- i.e. don't write them the day before your application is due!

Good luck!

 

[PowerIso]

For instance, I was talking to an undergrad who is at one of the top schools (but not in math) and he said that I will probably not get into any of these schools.

There will always be people who will want to hold you back and make you afraid. Just shrug it off. I say you probably will have a good chance to get into these schools depending one how good your recommendations are, and what activities you have done. It's really hard to tell though, grad school admins are a crazy bunch.

 

[J77]

and i also recommend as the greatest geometry book of all time, the one by euclid.

I've just received this edition -- what a great book!

I've never read any Euclid before, but having read the first few propositions, it's brought back to me what I first enjoyed during elementary school.

The simplicity of the proofs is the real winner here.

I've seen mentioned a few times that the simplest proofs are the best, and these writings prove this. I think I mentioned that a couple of weeks ago I fell asleep in my office reading a proof. If only all current mathematicians wrote in the same style as Euclid (translation assumed) did, the world would be a much brighter place

 

[eastside00_99]

Thanks cirsto and poweriso. I had a long talk with one of my professors and he said that I should be able to get in, but he said that my score on the math subject is going to be very important because of my GPA. He said that the university is going to want to know that I took the graduate courses because I really understand the basics and the GRE subject will indicate that. He said a 700 should be good enough and that anything above 750 is very strong. He also said that if I get below 650 I should take it again. So, we will see what my score is. I will know this in a couple of weeks.

To mathwonk, any information about how I compare to other students applying to UGA would be very appreciated. I am sure you get all kinds of people: people with stellar grade, great GREs, and people with a lot of grad credit. Do you think a 700 hundred with my gpa and the grad credit will make very strong application to UGA?

 

[morphism]

I have a question. How well did you do on the graduate courses?

 

[eastside00_99]

Some As some Bs.

 

[morphism]

Then, personally, I don't see why your overall GPA will be a hindrance.

 

[Werg22]

Mathwonk, would you happen to have introductory lecture notes on commutative rings the arithmetic of their elements?

 

[mathwonk]

look at my web notes in algebra.

as to your grad application, these are the things in your post that appeal to me:

I feel as if the competition is very fierce (which I kind of like) ...[this is good]....Nevertheless, I don't give up that easily. [this is good.]

"Here is my raw data:
Senior NCSU
overall gpa 3.3
math gpa 3.5
gre v 530
gre q 710
gre math sub ... results pending "

this means nothing without knowing the school, the average grade, the other students, the profesors opinion of you etc... but the gre is kind of low."These are the grad courses I have or will take:

Advanced Analysis
Functional Analysis (two courses)
general topology
algebraic topology
linear algebra (grad)
lie algebra
Abstract algebra (two courses, grad)
smooth manifolds
computational algebraic geometry
graph theory"

[this means also nothing unless i know how you did in these courses, just taking courses means nothing.]

I should mention I did independent study in Algebraic Curves all summer long also.

[this is good since it shows interest.]

I had, am, and will work very hard to do this [this is good, as evidence of motivation.]

"my aim as an undergrad is to be prepared to pass the quals at whatever uni that accepts me with the minimum or no fuss (which will pretty much ensure that I get the Ph.D.--meaning most who drop out are those who can't pass the quals)."

[this is bad, as it indicates a desire to take the low road.]1) brown
2) berkeley
3) Rice
4) Duke
5) U of Washington
6) Washington U
7) Cuny
8) U of Ill (urbana)
9) unc (chapel hill)
10) georgia

[this is a good list of schools.]

Now, what do you think my chances are for getting accepted to any of these schools? Do you think I am prepared and/or are desirable to any of these programs?

[without your letters of evaluation from your profs it is impossible to guess at your chance of acceptance at these schools. even at georgia your gre is low. without more data i would myself not vote to admit someone with those scores. with all those grad courses it is hard to understand why you would not score 780 or more on gre. i hope this helps.]

 

[eastside00_99]

I guess I could take the general again. I don't know why I didn't get a perfect score on the quant section. I guess I made some mistakes. I have to admit that I always envisioned the gre general as something grad schools do not care terribly about (in regards to math). Maybe, this is a mistake. I had the impression that the GRE general was something for the overall graduate school that one has to get a minimum score in order to get support. I am sure if I take it again I will do better; I will wait for my GRE subject test scores to come in before I decide to do this.

Anyway, thanks for your comments mathwonk. Yeah, I didn't mean that I don't want to work hard my first or second year to pass quals. It is just that I had a friend at the time who was a grad student at U Penn who said that in order to prepare for grad school in math, it is best for me to try and get as much exposure as possible to the level of work expected for the quals. Maybe that was misguided in that I could have taken a lot more general math courses at the undergrad level. Truly, I have heard mixed things about this, and I am not sure what is the best path. But, at a certain point in undergrad math -- it was probably during my junior year taking my first real analysis course and a general topology course -- I noticed this huge difference in the instruction of these two classes. Real analysis was basically about how to write rigirous proofs; but topology (while that was of course a part of it) was about having a good idea or two. Truthfully, topology was a very hard class (and I had even studied general topology before I took it); the test were difficult and completing them in 50 minutes was quite a frantic time. But, man, when you had that geniune good idea, and you solved this "tough" problem under pressure; that was a good feeling. I never got that from any of my undergrad classes (although they served another purpose which was to learn about some of the basics of modern mathematics and to be able to write proofs). Maybe, it was a bad idea to skip a few undergrad classes, but I haven't been able to help myself.
This is enough raving. I guess you recommend I consider taking the GREs again (or else balance that out with something else). That is understandible. My Recs should be pretty good; and hopefully the GRE subject could sooth doubts about my ability to think quickly about basic material.

Anyway, back to the orginal discussion I guess.

Here is a good website for some writtings of Alexander Grothendieck:

http://www.grothendieckcircle.org/

Its really amazing to read his letters to Serre to see how casually he talks about really abstract mathematics, how he offers advice on possible future research, and just a good mixture of formal and informal mathematical writing.

I personally want to read the something by Galois. He is sort of the person the young adolecent future mathematician can relate to.

 

[mathwonk]

if you really care about doing math, you have nothing to worry about. you will find a school where you can progress.

 

[eastside00_99]

Yes. This is true. I have a place I can go and there is no need to worry a terrible amount.

I can't force a school to accept me. If these schools feel as if I am not qualified, then that is what happens. I pretty confident in my abilities but there may be something to such a thing happenning to me in that it may be a good idea to stay a year and study some more. I am a little concerned that if this happens, it would be somewhat of a waste of time in respect to getting the Ph.D. But, that doesn't mean some good will not come out of it. Maybe, I will be able to get into a very good school after such a time and also be more prepared for the competition at this school. I guess I feel as if I want to be "great" and very attractive to the schools I apply to, but right now I feel as if I am in a position of just squeeking into admissions which is kind of a downer. It definitely hurts that my GPA was a 3.7 just a year ago but that I got one very low grade in a statistics course (the abosolute minimimum that will count toward my degree) and a C in a basic computer programming course because of the lack of time I spent on the course. I envisioned graduating with a very high GPA and a lot of grad credit. I actually transferred to the university I am at and these are really the only "bad" grades I have gotten. I fumbled the ball a little and I am paying for it without a doubt.

 

[mathwonk]

i did not say you were not qualified, or did not appear qualified. i said much of the data you present is not that useful in deciding. the best data is the letters from the professors.

i had a 1.2 gpa my first three semesters in college, out of 4, and still got into a good grad school. then i flailed around for 5 years without finishing, doing essentially nothing the last 2 years. i still was recruited by one of the professors from that grad school as a student at the next school he went to, with a top fellowship. it all depends on what they see in you. that is hard to discern from a list of courses.

 

[eastside00_99]

ah, yes, I see. Ok. Thanks for your help.

 

[mathwonk]

a vote for possibly my favorite physicist: bill amend, the cartoonist who writes the foxtrot comic strip, recently retired from the dailies. i always thought physicists were more creative than mathematicians, who ever heard of a funny mathematician?

 

[mjmetro]

complex analysis

as an undergraduate junior, I'm considering taking a graduate complex analysis course next semester (apparently, this is the most commonly taken graduate course by undergrads in the math major at my school). I've taken 2 courses in algebra (abstract), real analysis, 2 courses in linear algebra and the basic undergrad complex variables course. how much does taking graduate courses as an undergrad factor into grad school admissions and in the most general sense, is it generally a good idea? i realize that this is a tough question since anyone answering it knows nothing about my mathematical ability. another question: what is the main difference between a graduate math course and the corresponding undergrad one?

thanks for any help.

edit: by the way, I'm at suny stony brook, if that helps at all.