Should I Become a Mathematician?

  • Other
  • Thread starter mathwonk
  • Start date
  • #1,976
mrb
101
0


Sure, the material on the test is not extremely advanced. But it is also not a cakewalk for most math undergrads. In a perfect world every undergrad would have decent classes in abstract algebra, topology, and analysis before taking the test. But it doesn't always work out like that... What tends to be difficult for me is changing gears quickly. "Compute this line integral. Now find the error in this proof about compactness. Now determine when this sequence converges. Now answer this question about complex analysis, which you haven't taken. And do each in about 2 minutes."
 
  • #1,977
mathwonk
Science Advisor
Homework Helper
2020 Award
11,184
1,382


heres another one from the website above: if the domain of a continuous function is a finite open interval, then the range is which:
i) an interval, ii) an open interval, iii) a finite interval?


this is again something any layperson who has seen trig (graph of sin and tangent) could do.

but my point is I believe these are not taken seriously by good schools as having much bearing on readiness for grad school so don't stress out over it. when i applied to columbia, brandeis and maryland, none of them required this test so i didnt even take it. i presume it was because they considered it irrelevantly trivial.

well things have changed, columbia now requires the gre general and math subject. what used to be trivial is now required. or maybe i just got a pass somehow.
 
Last edited:
  • #1,978
142
1


my old school did not require GRE or even engineering GRE to get in engineering grad school. you could take the Miller Analogies Test. i'm not even sure that was required if your GPA was high enough, but my memory is fuzzy now.
 
  • #1,979
mathwonk
Science Advisor
Homework Helper
2020 Award
11,184
1,382


well of the three schools i applied to in 1965, two now require the gre and subject test, columbia and maryland, but not brandeis. maybe i got into brandeis with a nice fellowship and just skipped taking the gre.

but really, i was talking to an undergrad the other day who is planning to apply to some good schools, and he is taking our graduate analysis course and knows it well enough to explain things to me that i do not know well.

this is the kind of student who will get into a good program, certainly not someone for whom mickey mouse questions about first year calculus area calculations are a challenge, such as one sees on the gre.

you recall when i interviewed at columbia i was thought ignorant and denied because i did not know and could not recreate spontaneously the theory of singular homology, not based on some trivial first year undergraduate topic, or worse yet some high school topic like which of these rational numbers could be a root of this equation.

if you want to go to a good math grad program, you should be able to ace gre's, but they will not determine much about your readiness, nor your competitiveness with strong applicants.

one of our best young products a few years ago was a high school student who took our grad courses as a high school student, finished high in the putnam competition, and then went to an ivy league school for college and aced the most advanced courses.

those kids are the competition at top grad schools like princeton, not people who are puzzled by questions on "which of these multiplication tables gives a group of order 4?".

still there are a lot of programs which do need all the applicants they can get, and even at columbia there is a reason the tuition is free for phd candidates.

the fundamental tools of a mathematician remain linear algebra and advanced calculus, so try to learn those well. mastering hoffman and kunze , and spivak's calculus on manifolds is a good project.

gre's are there to weed out the totally unqualified i imagine, not to determine the top candidates.
 
  • #1,980
mrb
101
0


So the message I've gotten from you over the past few posts is that anyone who cannot currently dominate the Math GRE is a moron and should not even bother trying to become a mathematician. Could you possibly be any more elitist and condescending?

Here's the reality for me: math was extremely easy for me in elementary & middle school and after a lot of begging my mother convinced the school to let me advance a grade... which turned out to also be really easy. Nobody was around to show me more advanced math or point the way (and this was in the early/mid 90s, so looking online wasn't an option) so I just stopped going to school and barely graduated. ~10 years later I started undergrad as a math major, and just recently realized how weak the math program is at my school and how unprepared I was. So now I'm doing a lot of study on my own and have learned a lot in the last few months (3 months ago I didn't know what a vector space was... because vector spaces were only mentioned once in my linear algebra class). So no, I cannot ace the Math GRE at the moment but I am very confident in my talent and know I will be able to before too long.

You should be a little more careful throwing around terms like "mathematical imbecile" because you are insulting probably almost everyone who has posted in this thread (look at the table of data on Math GRE scores and realize that most prospective math grad students get only about half or fewer questions correct).
 
  • #1,981
mrb
101
0


Since you did undergrad at an Ivy League school, perhaps you are not aware that most undergrad programs are less than ideal and the fact that students come out of them with a weak background does not necessarily imply the students are stupid.
 
  • #1,982
429
2


I just got used to the elitism in math and physics. I don't accept it, but these are field where this kind of thing is prevalent.

If you like doing math, keep trying to be the best possible mathematician. That's all I try to stick to now.
 
  • #1,983
329
1


Math GRE is over hyped. I tend to agree with mathwonk's assessment of the test . It is essentially a cutoff point.

mrb if you feel you will one day be able to dominate the GRE than you should relax a bit. I believe Mathwonk was simply saying that if you can't do well on the GRE then you probably are not ready for graduate school and you have to admit right now at your level you are not ready for graduate school. One day, sure, but not right now.
 
  • #1,984
326
0


I think that one can often overcome the weakness of his school's math program. My school does not have the strongest math program, it is really quite weak(actually not as weak as mrb's, we covered everything in chapter 1-6 or so in David Lay's book. You must not have even covered eigenspace, nul space,collumn space, rowspace ect. if you didn't cover vector spaces.). I took the matter into my own hands and started self study in tough books before I even started college before I was really ready for them so I had to put them down,but; if you really love the subject you will not give up on a difficult aspect, you go back again and again until you can muscle through every concept and problem.(I'm talking about books by authors like Rudin, Goursat, Lang, Artin). I also make it a point to get to know my professors and ask less trivial questions that I might have encountered in my self study. I also ask for a lot of advice as far as what I should be doing, what books will prepare me well for grad school, ect.

I don't see why a weak math program would hold back a strong student. I can see how time constraints might, if one does not have the time to supplement their courses. If, on the other hand, you find a weak program too difficult to juggle with outside study, you might not be cut out for grad school, I don't know. Working might be a mitigating factor ect. There are many things which can put a hold on extra study. Hanging out with friends too much is something that might have to be sacrificed.

It seems like it would really depend on how strong the grad school is. For instance, UC Berkeley's math grad program has a very high drop out rate. This is a very difficult program that only people who can ace the Math Subject GRE and were published as an undergrad or something along those lines can do well in.

My personal circumstance is kind of similar to mrb's. I studied algebra in elementary school and became very interested in it and picked up concepts quickly, but much to my dismay, every year of advanced middle school math and basic high school math was essentially the same and I quickly became disinterested. The same thing was true of science. My 7th grade science teacher was a soccer coach or something along those lines and he would have no answers to my questions pertaining to astronomy or physics.

I did poorly in high school(not terribly, but a 2.98 gpa) and had intended to do art or music, which are two other passions of mine, but my interest in science was rekindled by my Honors physics teacher senior year(a friend told me that I should take the class). I started to self study calculus, analytic geometry, and trig, because I had not gone beyond geometry and algebra. I got a 1400 on my SAT but went to a local state university because I was wary of my math skills at that point. I nearly tested out of calc I, and could have skipped the first segment(the split it into two segments Calc I a and b) but decided not to. Instead I took the extra time I had since I knew the material in class to work on less trivial problems and study some theory. I looked at some of Apostle's book and did some problems and that really gave me a bit of an edge. Now I am a sophomore studying Rudin and Goursat on my own and I will have exhausted my school's math curriculum as of next year and will have to try to do courses at a nearby university and independent study.

The point is, if you really love math, and you have any spare time, read math, do math and talk about math to anyone you can. You don't necessarily have to abandon your social life totally, but at the same time, don't spend every waking hour hanging with your homies.
 
  • #1,985


The syllabus was very intimidating. But I just found their sample questions and was quite surprised - at least half the questions could easily be done with high school stuff and the most of the rest were very guessable considering that they furnish us with an explanation before they ask the question. And it's all multiple choice!!! I haven't had multiple choice maths questions since... I can't remember. :D
 
  • #1,986
mrb
101
0


(actually not as weak as mrb's, we covered everything in chapter 1-6 or so in David Lay's book. You must not have even covered eigenspace, nul space,collumn space, rowspace ect. if you didn't cover vector spaces.).

Vector spaces were maybe not the perfect example. We also used Lay and covered through part of Chapter 5; the big problem was that this was a summer course lasting barely over a month so we got less than a week on Ch 4. A concept you work with for 3 or 4 days and then don't ever hear about again for a year tends not to be retained.

Here's another example, though: I was through Calculus 3 and Diff Eq before I ever heard of the Mean Value Theorem or the Intermediate Value Theorem (which I first read about on this forum, and then on my own from Spivak's Calculus, and finally just recently in my Analysis class).

There really is no avenue at this school for excelling. I realized last semester that my advisor was suggesting the classes she was for me based on the fact that they were easy, despite my clearly telling her I was interested in grad school and wanted to learn and my 4.0 Math GPA. We supposedly have a Math Honors program which involves undergrad research. I have been trying for 3 weeks to find a prof to be my advisor for the program. None of the profs I've asked knew there was a Math Honors program or had ever advised anyone for it. And none have been willing to advise me except possibly one, and he seems reluctant because he has admin duties and worries about his time. So I honestly don't think there really IS a Math Honors program; it's just something they put on their web site and other materials because it looks good.

The point is, if you really love math, and you have any spare time, read math, do math and talk about math to anyone you can. You don't necessarily have to abandon your social life totally, but at the same time, don't spend every waking hour hanging with your homies.

I agree 100% but it took me a while to realize how much I should be studying on my own, partly because I previously had not decided with certainty to do math grad school. Social issues are, ahem, not a problem for me. I have no social life except for a gf who is generally tolerant about me spending hours and hours on math.
 
  • #1,987
326
0


Thats pretty bad. I had at least some knowledge of the IMVT and MVT in Calc 1 and definitely by calc 2. It seems necessary to give some basic results, I don't know if the teacher simply glossed over how most formulae involving it are derived? How did you guys go over the fundamental theorems of calculus and taylor series?

I guess it really isn't a big deal since you know it now and grad schools probably assume that most early calc courses are the same or generally don't care.

My school doesn't have a honors math program either.

A couple questions, directed more towards mathwonk,

Do you think that Bartle is a good Analysis text, and do you know much about Paul Dienes Text The Taylor Series (i.e. how would you rate it and why.)
 
  • #1,988
mrb
101
0


Thats pretty bad. I had at least some knowledge of the IMVT and MVT in Calc 1 and definitely by calc 2. It seems necessary to give some basic results, I don't know if the teacher simply glossed over how most formulae involving it are derived? How did you guys go over the fundamental theorems of calculus and taylor series?

Nothing was ever derived. FTC and Taylor Series stuff was presented but not proved or even informally demonstrated.
 
  • #1,989
mathwonk
Science Advisor
Homework Helper
2020 Award
11,184
1,382


I was responding to some posts in which people said essentially: here are my gre scores, where am i going to get in? princeton? washington? etc etc...

i am saying that gre is not a big factor in getting into the best places, that anyone struggling with the gre is simply not going to get in those places.

i hope that is useful time saving information to people thinking of applying to princeton. namely if you think the gre is hard, don't bother. princeton IS an elite school.

some students come into harvard having already read and worked through books like griffiths and harris algebraic geometry. my first advisor came to columbia having already proved the riemann singularity theorem in a rigorous way for the first time by anyone in over 100 years.

this does not mean someone who has to work to do well on gre cannot find a home where they will fit in well, but it won't be at harvard or princeton or mit or columbia.

I think I made it very clear that my post was aimed at people who want to know how to tell if they are going to get into the very best schools. i say that unless you find the gre easy, you are not going to.

when i was an undergraduate at harvard, the only people even applying to harvard grad school had already taken year long graduate courses in algebra (lang), algebraic topology (spanier), real and complex analysis (big rudin, cartan, ahlfors) as undergrads.

the rest of us looked elsewhere.



....sorry i am not familiar with bartle and dienes. bartle is a familiar name though, so probably has a good track record.
 
Last edited:
  • #1,990


Heh, same thing here. Nothing is derived and IMVT and MVT weren't taught in any of the calc units. They present stuff like Stokes's and Gauss' theorems but aren't very clear on what they actually mean much less derive it. They've neglected to mention Green's theorem or Fubini's - we just change the order of integration as we wish. But that's not really important. It'll be covered again in real analysis anyway, right?
 
  • #1,991


when i was an undergraduate at harvard, the only people even applying to harvard grad school had already taken year long graduate courses in algebra (lang), algebraic topology (spanier), real and complex analysis (big rudin, cartan, ahlfors) as undergrads.

Australian unis don't really offer that kind of courses. The most I can get is a year's worth of grad analysis and algebra with a mix of self-study, honours year units and maybe an exchange. Does that mean that the top universities won't be an option? o_O
 
  • #1,992
mathwonk
Science Advisor
Homework Helper
2020 Award
11,184
1,382


not necessarily. those were options at harvard so they expected the harvard undergrads to have taken them. talented people from less rich environments could be cut more slack.

but remember that was 45 years ago. things are different now. but harvard students are still very very sophisticated and advanced.

one thing is sure however as my friend told me about applying for an nsf postdoc:

'if you do not apply you definitely will not get in. (I got the postdoc)
 
  • #1,993
mrb
101
0


But that's not really important. It'll be covered again in real analysis anyway, right?

At my school the standard undergrad real analysis is a 2 semester sequence, with single variable topics covered first and multivariable covered next. Unfortunately the single variable portion is never completed in the first semester, so the second semester is mostly spent doing what should have been done the first semester.

I don't want to drag this thread away from its purpose, but as long as I'm complaining about my math education, I want to provide this contrast:

When I thought I wanted to go into Bioinformatics, I emailed the coordinator in that department who invited me to come to his office. I met him, he told me about Bioinformatics in general, and about each of the profs and what their research was on and so forth. I contacted 2 of the profs about doing research with them; met with both of them; both offered to let me work in their labs. I chose one of them and had a rewarding semester.

On the other hand, now I want to do some math research. I have talked to four professors about it. One met with me and it went like this:

Prof: "Well, I'm a numerical guy, so you would have to be able to program to work with me, I'm sorry."
mrb: "I can program. I've been programming for years."
Prof: "Oh. Well, you would have to know C, so I guess..."
mrb: "I know C."
Prof: "Oh. Well have you had Calculus 4?"
mrb: "Yes."
Prof: "Have you taken Applied Math? [this is a course only offered every other year]"
mrb: "No."
Prof: "I'm sorry, but any work I would have for you would depend on that material, so I don't think we can do this."

He couldn't just say he couldn't do it, he had to search for some excuse. Another prof stopped responding to my emails after one reply. Another was enthusiastic and agreed to meet with me but then didn't show up and is now incommunicado. And finally there's the last one, who is still a possibility but as I mentioned above seems reluctant and since he hasn't replied to my email from a few days ago he may be going incommunicado as well.
 
  • #1,994
Vid
401
0


Hmm...

I took Calculus 1-3 in high school, and we derived everything. We had a pop quiz on the formal definition of a limit for a quadratic. These wasn't an honors class this was one of the many sections of calculus taught at this school. If you didn't cover these things in a college course, something is very wrong.
 
  • #1,995
mrb
101
0


Well, yes. I agree. There are some good people in our math department but something is broken at a very fundamental level.
 
  • #1,996
mathwonk
Science Advisor
Homework Helper
2020 Award
11,184
1,382


I assure you there are many "good" colleges where a standard calculus class may not even include the rigorous definition of a limit.

at most schools the population is so diverse that they offer two or three or even four different calculus classes, only the most "elite" being for math majors, and hence including any theory at all.

many entering students, even those who took calculous in high school, or maybe especially those, object strongly to being asked to state a theorem, or a definition, much less actually learn to prove a theorem, since this usually never occurred in their high school course.

where did you go to school that you had a rigorous course? i think this, although desirable and excellent, is very rare.
 
  • #1,997
mathwonk
Science Advisor
Homework Helper
2020 Award
11,184
1,382


mrb, it sounds to me as if the first step toward a math honors program for you would be to work through spivak's calculus book. maybe a prof at your school would supervise that, or at least sign on to give you credit for it. and try to organize a group of other like minded students and give lectures on it to them.

when i was out of grad school i taught all the way through this book in 8 weeks, to a group of returned teachers. it helped both of us. the next year i went back to grad school.
 
  • #1,998
mathwonk
Science Advisor
Homework Helper
2020 Award
11,184
1,382


I interviewed some students I consider quite strong, and they thought the general gre was quite easy, but the math subject test was significantly harder.

They likened the general gre to just an sat test, but when I asked if the subject test was like an AP test, I did not get a response.

I also recall from decades ago a friend who said he did not do too well on the gre, who is now a full professor of math at a top school.

so it seems as if indeed the gre may be kind of a filter, but may not have huge relevance for actually predicting success in grad school in math.

If I feel like wasting an hour or so, I may take the sample myself and give a more informed opinion later, but to em it is kind of a waste of time, except to know what it means when I see the scores in future if I happen to be on the admissions committee.

As of now, I still do not know anyone who thinks it is highly important as a factor in measuring likelihood of success in grad school, which is ironic since it is an obstacle to admission.

Maybe Ill ask the graduate coordinator.
 
  • #1,999
mathwonk
Science Advisor
Homework Helper
2020 Award
11,184
1,382


well i didn't find him but someone else who took the gre as a student said they seem designed to measure whether you know enough to be a TA in calculus. I had never thought about that aspect of readiness for grad school. he also said studying for them was useful as a way of shoring up knowledge that somehow had been omitted from his background.
 
  • #2,000
326
0


Mathwonk,
How much would you think that being published, more specifically, publishing a result in field theory showing that a closure property is not held by any finite fields, and showing that either this closure property which is superficially weaker and much easier to test for is equivalent to a commonly considered property of an infinite field or that it is a unique kind of closure that has not been considered much if at all, but I will have quite a bit of information about its properties in relation to the field, would weigh in grad admissions?

Sorry if the description is too vague.
 

Related Threads on Should I Become a Mathematician?

Replies
4
Views
199
Replies
19
Views
11K
  • Sticky
  • Last Post
44
Replies
1K
Views
773K
  • Last Post
Replies
1
Views
7K
  • Last Post
Replies
7
Views
3K
Replies
7
Views
3K
  • Last Post
Replies
5
Views
8K
Replies
20
Views
4K
  • Last Post
Replies
6
Views
2K
Top